MFEM  v4.5.2
Finite element discretization library
tmop.hpp
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11 
12 #ifndef MFEM_TMOP_HPP
13 #define MFEM_TMOP_HPP
14 
15 #include "../linalg/invariants.hpp"
16 #include "nonlininteg.hpp"
17 
18 namespace mfem
19 {
20 
21 /** @brief Abstract class for local mesh quality metrics in the target-matrix
22  optimization paradigm (TMOP) by P. Knupp et al. */
23 class TMOP_QualityMetric : public HyperelasticModel
24 {
25 protected:
26  const DenseMatrix *Jtr; /**< Jacobian of the reference-element to
27  target-element transformation. */
28 
29  /** @brief The method HyperelasticModel::SetTransformation() is hidden
30  for TMOP_QualityMetric%s, because it is not used. */
31  void SetTransformation(ElementTransformation &) { }
32 
33 public:
34  TMOP_QualityMetric() : Jtr(NULL) { }
35  virtual ~TMOP_QualityMetric() { }
36 
37  /** @brief Specify the reference-element -> target-element Jacobian matrix
38  for the point of interest.
39 
40  The specified Jacobian matrix, #Jtr, can be used by metrics that cannot
41  be written just as a function of the target->physical Jacobian matrix,
42  Jpt. */
43  virtual void SetTargetJacobian(const DenseMatrix &Jtr_) { Jtr = &Jtr_; }
44 
45  /** @brief Evaluates the metric in matrix form (opposed to invariant form).
46  Used for validating the invariant evaluations. */
47  virtual double EvalWMatrixForm(const DenseMatrix &Jpt) const
48  { return -1.0; /* not implemented -> checks would fail. */ }
49 
50  /** @brief Evaluate the strain energy density function, W = W(Jpt), by using
51  the 2D or 3D matrix invariants, see linalg/invariants.hpp.
52  @param[in] Jpt Represents the target->physical transformation
53  Jacobian matrix. */
54  virtual double EvalW(const DenseMatrix &Jpt) const = 0;
55 
56  /** @brief Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
57  @param[in] Jpt Represents the target->physical transformation
58  Jacobian matrix.
59  @param[out] P The evaluated 1st Piola-Kirchhoff stress tensor. */
60  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const = 0;
61 
62  /** @brief Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor
63  and assemble its contribution to the local gradient matrix 'A'.
64  @param[in] Jpt Represents the target->physical transformation
65  Jacobian matrix.
66  @param[in] DS Gradient of the basis matrix (dof x dim).
67  @param[in] weight Quadrature weight coefficient for the point.
68  @param[in,out] A Local gradient matrix where the contribution from this
69  point will be added.
70 
71  Computes weight * d(dW_dxi)_d(xj) at the current point, for all i and j,
72  where x1 ... xn are the FE dofs. This function is usually defined using
73  the matrix invariants and their derivatives. */
74  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
75  const double weight, DenseMatrix &A) const = 0;
76 
77  /** @brief Return the metric ID. */
78  virtual int Id() const { return 0; }
79 };
80 
81 class TargetConstructor;
82 
83 /// Abstract class used to define explicit combination of metrics with constant
84 /// coefficients.
85 class TMOP_Combo_QualityMetric : public TMOP_QualityMetric
86 {
87 protected:
88  Array<TMOP_QualityMetric *> tmop_q_arr; //the metrics are not owned
89  Array<double> wt_arr;
90 
91 public:
92  virtual void AddQualityMetric(TMOP_QualityMetric *tq, double wt = 1.0)
93  {
94  tmop_q_arr.Append(tq);
95  wt_arr.Append(wt);
96  }
97 
98  virtual void SetTargetJacobian(const DenseMatrix &Jtr_)
99  {
100  for (int i = 0; i < tmop_q_arr.Size(); i++)
101  {
102  tmop_q_arr[i]->SetTargetJacobian(Jtr_);
103  }
104  }
105 
106  virtual double EvalWMatrixForm(const DenseMatrix &Jpt) const;
107 
108  virtual double EvalW(const DenseMatrix &Jpt) const;
109 
110  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const;
111 
112  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
113  const double weight, DenseMatrix &A) const;
114 
115  /// Computes the averages of all metrics (integral of metric / volume).
116  /// Works in parallel when called with a ParGridFunction.
117  void ComputeAvgMetrics(const GridFunction &nodes,
118  const TargetConstructor &tc,
119  Vector &averages) const;
120 
121  /// Computes weights so that the averages of all metrics are equal, and the
122  /// weights sum to one. Works in parallel when called with a ParGridFunction.
123  void ComputeBalancedWeights(const GridFunction &nodes,
124  const TargetConstructor &tc,
125  Vector &weights) const;
126 
127  /// Changes the weights of the metrics in the combination.
128  void SetWeights(const Vector &weights)
129  {
130  MFEM_VERIFY(tmop_q_arr.Size() == weights.Size(), "Incorrect #weights");
131  for (int i = 0; i < tmop_q_arr.Size(); i++) { wt_arr[i] = weights(i); }
132  }
133 };
134 
135 /// Simultaneous Untangler + Worst Case Improvement Metric
136 /// Uses a base metric mu and is defined as:
137 /// mu_tilde = mu_hat, when WorstCaseType = None,
138 /// = mu_hat/(beta - mu_hat), when WorstCaseType = Beta,
139 /// = mu_hat^p, when WorstCaseType = PMean,
140 /// where beta = max(mu_hat) + muT_ep,
141 /// and mu_hat = (mu/2phi(tau,ep)) where
142 /// 2phi(tau,ep) = 1, when when BarrierType = None,
143 /// = 2*(tau - min(alpha*min(tau)-detT_ep,0)), when BarrierType = Shifted
144 /// = tau^2 + sqrt(tau^2 + ep^2), when BarrierType = Pseudo
145 /// where tau = det(T), and max(mu_hat) and min(tau) are computed over the
146 /// entire mesh.
147 /// Ultimately, this metric can be used for mesh untangling with the BarrierType
148 /// option and for worst case quality improvement with the WorstCaseType option.
149 class TMOP_WorstCaseUntangleOptimizer_Metric : public TMOP_QualityMetric
150 {
151 public:
152  enum class BarrierType
153  {
154  None,
155  Shifted,
156  Pseudo
157  };
158  enum class WorstCaseType
159  {
160  None,
161  Beta,
162  PMean
163  };
164 
165 protected:
166  TMOP_QualityMetric &tmop_metric; // non-barrier metric to use
167  double min_detT; // minimum Jacobian in the mesh
168  double max_muT; // max mu_k/phi(tau,ep) in the mesh
169  int exponent; // used for p-mean metrics
170  double alpha; // scaling factor for min(det(T))
171  double detT_ep; // small constant subtracted from min(detT)
172  double muT_ep; // small constant added to muT term
173  BarrierType btype;
174  WorstCaseType wctype;
175 
176 public:
177  TMOP_WorstCaseUntangleOptimizer_Metric(TMOP_QualityMetric &tmop_metric_,
178  int exponent_ = 1,
179  double alpha_ = 1.5,
180  double detT_ep_ = 0.0001,
181  double muT_ep_ = 0.0001,
182  BarrierType btype_ = BarrierType::None,
183  WorstCaseType wctype_ = WorstCaseType::None) :
184  tmop_metric(tmop_metric_), exponent(exponent_), alpha(alpha_),
185  detT_ep(detT_ep_), muT_ep(muT_ep_), btype(btype_), wctype(wctype_)
186  {
187  MFEM_VERIFY(wctype == WorstCaseType::None,
188  "Worst-case optimization has not been fully developed!");
189  if (btype != BarrierType::None)
190  {
191  const int m_id = tmop_metric.Id();
192  MFEM_VERIFY(m_id == 4 || m_id == 14 || m_id == 66,
193  "Incorrect input barrier metric -- must be 4 / 14 / 66");
194  }
195  }
196 
197  virtual double EvalW(const DenseMatrix &Jpt) const;
198 
199  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
200  { MFEM_ABORT("Not implemented"); }
201 
202  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
203  const double weight, DenseMatrix &A) const
204  { MFEM_ABORT("Not implemented"); }
205 
206  // Compute mu_hat.
207  virtual double EvalWBarrier(const DenseMatrix &Jpt) const;
208 
209  virtual void SetMinDetT(double min_detT_) { min_detT = min_detT_; }
210 
211  virtual void SetMaxMuT(double max_muT_) { max_muT = max_muT_; }
212 
213  virtual BarrierType GetBarrierType() { return btype; }
214 
215  virtual WorstCaseType GetWorstCaseType() { return wctype; }
216 };
217 
218 /// 2D non-barrier metric without a type.
219 class TMOP_Metric_001 : public TMOP_QualityMetric
220 {
221 protected:
222  mutable InvariantsEvaluator2D<double> ie;
223 
224 public:
225  // W = |J|^2.
226  virtual double EvalW(const DenseMatrix &Jpt) const;
227 
228  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const;
229 
230  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
231  const double weight, DenseMatrix &A) const;
232 
233  virtual int Id() const { return 1; }
234 };
235 
236 /// 2D non-barrier Skew metric.
237 class TMOP_Metric_skew2D : public TMOP_QualityMetric
238 {
239 public:
240  // W = 0.5 (1 - cos(angle_Jpr - angle_Jtr)).
241  virtual double EvalW(const DenseMatrix &Jpt) const;
242 
243  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
244  { MFEM_ABORT("Not implemented"); }
245 
246  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
247  const double weight, DenseMatrix &A) const
248  { MFEM_ABORT("Not implemented"); }
249 };
250 
251 /// 3D non-barrier Skew metric.
252 class TMOP_Metric_skew3D : public TMOP_QualityMetric
253 {
254 public:
255  // W = 1/6 (3 - sum_i cos(angle_Jpr_i - angle_Jtr_i)), i = 1..3.
256  virtual double EvalW(const DenseMatrix &Jpt) const;
257 
258  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
259  { MFEM_ABORT("Not implemented"); }
260 
261  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
262  const double weight, DenseMatrix &A) const
263  { MFEM_ABORT("Not implemented"); }
264 };
265 
266 /// 2D non-barrier Aspect ratio metric.
267 class TMOP_Metric_aspratio2D : public TMOP_QualityMetric
268 {
269 public:
270  // W = 0.5 (ar_Jpr/ar_Jtr + ar_Jtr/ar_Jpr) - 1.
271  virtual double EvalW(const DenseMatrix &Jpt) const;
272 
273  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
274  { MFEM_ABORT("Not implemented"); }
275 
276  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
277  const double weight, DenseMatrix &A) const
278  { MFEM_ABORT("Not implemented"); }
279 };
280 
281 /// 3D non-barrier Aspect ratio metric.
282 class TMOP_Metric_aspratio3D : public TMOP_QualityMetric
283 {
284 public:
285  // W = 1/3 sum [0.5 (ar_Jpr_i/ar_Jtr_i + ar_Jtr_i/ar_Jpr_i) - 1], i = 1..3.
286  virtual double EvalW(const DenseMatrix &Jpt) const;
287 
288  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
289  { MFEM_ABORT("Not implemented"); }
290 
291  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
292  const double weight, DenseMatrix &A) const
293  { MFEM_ABORT("Not implemented"); }
294 };
295 
296 /// 2D barrier shape (S) metric (polyconvex).
297 /// Grade - A.
298 class TMOP_Metric_002 : public TMOP_QualityMetric
299 {
300 protected:
301  mutable InvariantsEvaluator2D<double> ie;
302 
303 public:
304  // W = 0.5 |J|^2 / det(J) - 1.
305  virtual double EvalWMatrixForm(const DenseMatrix &Jpt) const;
306 
307  // W = 0.5 I1b - 1.
308  virtual double EvalW(const DenseMatrix &Jpt) const;
309 
310  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const;
311 
312  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
313  const double weight, DenseMatrix &A) const;
314 
315  virtual int Id() const { return 2; }
316 };
317 
318 /// 2D non-barrier shape (S) metric.
319 /// Grade - F.
320 class TMOP_Metric_004 : public TMOP_QualityMetric
321 {
322 protected:
323  mutable InvariantsEvaluator2D<double> ie;
324 
325 public:
326  // W = |J|^2 - 2*det(J)
327  virtual double EvalW(const DenseMatrix &Jpt) const;
328 
329  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const;
330 
331  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
332  const double weight, DenseMatrix &A) const;
333 
334  virtual int Id() const { return 4; }
335 };
336 
337 /// 2D barrier Shape+Size (VS) metric (not polyconvex).
338 class TMOP_Metric_007 : public TMOP_QualityMetric
339 {
340 protected:
341  mutable InvariantsEvaluator2D<double> ie;
342 
343 public:
344  // W = |J - J^-t|^2.
345  virtual double EvalW(const DenseMatrix &Jpt) const;
346 
347  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const;
348 
349  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
350  const double weight, DenseMatrix &A) const;
351 
352  virtual int Id() const { return 7; }
353 };
354 
355 /// 2D barrier Shape+Size (VS) metric (not polyconvex).
356 class TMOP_Metric_009 : public TMOP_QualityMetric
357 {
358 protected:
359  mutable InvariantsEvaluator2D<double> ie;
360 
361 public:
362  // W = det(J) * |J - J^-t|^2.
363  virtual double EvalW(const DenseMatrix &Jpt) const;
364 
365  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const;
366 
367  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
368  const double weight, DenseMatrix &A) const;
369 };
370 
371 /// 2D non-barrier Shape+Size+Orientation (VOS) metric (polyconvex).
372 class TMOP_Metric_014 : public TMOP_QualityMetric
373 {
374 public:
375  // W = |T-I|^2.
376  virtual double EvalW(const DenseMatrix &Jpt) const;
377 
378  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
379  { MFEM_ABORT("Not implemented"); }
380 
381  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
382  const double weight, DenseMatrix &A) const
383  { MFEM_ABORT("Not implemented"); }
384 };
385 
386 /// 2D Shifted barrier form of shape metric (mu_2).
387 class TMOP_Metric_022 : public TMOP_QualityMetric
388 {
389 protected:
390  double &min_detT;
391  mutable InvariantsEvaluator2D<double> ie;
392 
393 public:
394  TMOP_Metric_022(double &t0): min_detT(t0) {}
395 
396  // W = 0.5(|J|^2 - 2det(J)) / (det(J) - tau0).
397  virtual double EvalW(const DenseMatrix &Jpt) const;
398 
399  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const;
400 
401  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
402  const double weight, DenseMatrix &A) const;
403 };
404 
405 /// 2D barrier shape metric (polyconvex).
406 /// Grade - A.
407 class TMOP_Metric_050 : public TMOP_QualityMetric
408 {
409 protected:
410  mutable InvariantsEvaluator2D<double> ie;
411 
412 public:
413  // W = 0.5|J^t J|^2 / det(J)^2 - 1.
414  virtual double EvalW(const DenseMatrix &Jpt) const;
415 
416  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const;
417 
418  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
419  const double weight, DenseMatrix &A) const;
420 };
421 
422 /// 2D non-barrier size (V) metric (not polyconvex).
423 /// Grade - F.
424 class TMOP_Metric_055 : public TMOP_QualityMetric
425 {
426 protected:
427  mutable InvariantsEvaluator2D<double> ie;
428 
429 public:
430  // W = (det(J) - 1)^2.
431  virtual double EvalW(const DenseMatrix &Jpt) const;
432 
433  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const;
434 
435  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
436  const double weight, DenseMatrix &A) const;
437 
438 };
439 
440 /// 2D barrier size (V) metric (polyconvex).
441 /// Grade - C.
442 class TMOP_Metric_056 : public TMOP_QualityMetric
443 {
444 protected:
445  mutable InvariantsEvaluator2D<double> ie;
446 
447 public:
448  // W = 0.5( sqrt(det(J)) - 1 / sqrt(det(J)) )^2
449  // = 0.5( det(J) - 1 )^2 / det(J)
450  // = 0.5( det(J) + 1/det(J) ) - 1.
451  virtual double EvalW(const DenseMatrix &Jpt) const;
452 
453  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const;
454 
455  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
456  const double weight, DenseMatrix &A) const;
457 };
458 
459 /// 2D barrier shape (S) metric (not polyconvex).
460 class TMOP_Metric_058 : public TMOP_QualityMetric
461 {
462 protected:
463  mutable InvariantsEvaluator2D<double> ie;
464 
465 public:
466  // W = |J^t J|^2 / det(J)^2 - 2|J|^2 / det(J) + 2
467  virtual double EvalWMatrixForm(const DenseMatrix &Jpt) const;
468 
469  // W = I1b (I1b - 2).
470  virtual double EvalW(const DenseMatrix &Jpt) const;
471 
472  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const;
473 
474  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
475  const double weight, DenseMatrix &A) const;
476 };
477 
478 /// 2D non-barrier Shape+Size (VS) metric.
479 /// Grade - F.
480 class TMOP_Metric_066 : public TMOP_Combo_QualityMetric
481 {
482 protected:
483  mutable InvariantsEvaluator2D<double> ie;
484  TMOP_QualityMetric *sh_metric, *sz_metric;
485 
486 public:
487  TMOP_Metric_066(double gamma)
488  : sh_metric(new TMOP_Metric_004), sz_metric(new TMOP_Metric_055)
489  {
490  // (1-gamma) mu_4 + gamma mu_55
491  AddQualityMetric(sh_metric, 1.-gamma);
492  AddQualityMetric(sz_metric, gamma);
493  }
494  virtual int Id() const { return 66; }
495  double GetGamma() const { return wt_arr[1]; }
496 
497  virtual ~TMOP_Metric_066() { delete sh_metric; delete sz_metric; }
498 };
499 
500 /// 2D barrier size (V) metric (polyconvex).
501 /// Grade - C.
502 class TMOP_Metric_077 : public TMOP_QualityMetric
503 {
504 protected:
505  mutable InvariantsEvaluator2D<double> ie;
506 
507 public:
508  // W = 0.5(det(J) - 1 / det(J))^2.
509  virtual double EvalW(const DenseMatrix &Jpt) const;
510 
511  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const;
512 
513  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
514  const double weight, DenseMatrix &A) const;
515 
516  virtual int Id() const { return 77; }
517 };
518 
519 /// 2D barrier Shape+Size (VS) metric (polyconvex).
520 /// Grade - A.
521 class TMOP_Metric_080 : public TMOP_Combo_QualityMetric
522 {
523 protected:
524  mutable InvariantsEvaluator2D<double> ie;
525  TMOP_QualityMetric *sh_metric, *sz_metric;
526 
527 public:
528  TMOP_Metric_080(double gamma)
529  : sh_metric(new TMOP_Metric_002), sz_metric(new TMOP_Metric_077)
530  {
531  // (1-gamma) mu_2 + gamma mu_77
532  AddQualityMetric(sh_metric, 1.0 - gamma);
533  AddQualityMetric(sz_metric, gamma);
534  }
535 
536  virtual int Id() const { return 80; }
537  double GetGamma() const { return wt_arr[1]; }
538 
539  virtual ~TMOP_Metric_080() { delete sh_metric; delete sz_metric; }
540 };
541 
542 /// 2D barrier Shape+Orientation (OS) metric (polyconvex).
543 class TMOP_Metric_085 : public TMOP_QualityMetric
544 {
545 public:
546  // W = |T-T'|^2, where T'= |T|*I/sqrt(2).
547  virtual double EvalW(const DenseMatrix &Jpt) const;
548 
549  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
550  { MFEM_ABORT("Not implemented"); }
551 
552  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
553  const double weight, DenseMatrix &A) const
554  { MFEM_ABORT("Not implemented"); }
555 };
556 
557 /// 2D barrier Shape+Size+Orientation (VOS) metric (polyconvex).
558 class TMOP_Metric_098 : public TMOP_QualityMetric
559 {
560 public:
561  // W = 1/tau |T-I|^2.
562  virtual double EvalW(const DenseMatrix &Jpt) const;
563 
564  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
565  { MFEM_ABORT("Not implemented"); }
566 
567  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
568  const double weight, DenseMatrix &A) const
569  { MFEM_ABORT("Not implemented"); }
570 };
571 
572 /// 2D untangling metric.
573 class TMOP_Metric_211 : public TMOP_QualityMetric
574 {
575 protected:
576  const double eps;
577  mutable InvariantsEvaluator2D<double> ie;
578 
579 public:
580  TMOP_Metric_211(double epsilon = 1e-4) : eps(epsilon) { }
581 
582  // W = (det(J) - 1)^2 - det(J) + sqrt(det(J)^2 + eps).
583  virtual double EvalW(const DenseMatrix &Jpt) const;
584 
585  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const;
586 
587  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
588  const double weight, DenseMatrix &A) const;
589 };
590 
591 /// Shifted barrier form of metric 56 (area, ideal barrier metric), 2D
592 class TMOP_Metric_252 : public TMOP_QualityMetric
593 {
594 protected:
595  double &tau0;
596  mutable InvariantsEvaluator2D<double> ie;
597 
598 public:
599  /// Note that @a t0 is stored by reference
600  TMOP_Metric_252(double &t0): tau0(t0) {}
601 
602  // W = 0.5(det(J) - 1)^2 / (det(J) - tau0).
603  virtual double EvalW(const DenseMatrix &Jpt) const;
604 
605  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const;
606 
607  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
608  const double weight, DenseMatrix &A) const;
609 };
610 
611 /// 3D barrier Shape (S) metric, well-posed (polyconvex & invex).
612 class TMOP_Metric_301 : public TMOP_QualityMetric
613 {
614 protected:
615  mutable InvariantsEvaluator3D<double> ie;
616 
617 public:
618  // W = 1/3 |J| |J^-1| - 1.
619  virtual double EvalWMatrixForm(const DenseMatrix &Jpt) const;
620 
621  // W = 1/3 sqrt(I1b * I2b) - 1
622  virtual double EvalW(const DenseMatrix &Jpt) const;
623 
624  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const;
625 
626  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
627  const double weight, DenseMatrix &A) const;
628 };
629 
630 /// 3D barrier Shape (S) metric, well-posed (polyconvex & invex).
631 class TMOP_Metric_302 : public TMOP_QualityMetric
632 {
633 protected:
634  mutable InvariantsEvaluator3D<double> ie;
635 
636 public:
637  // W = |J|^2 |J^{-1}|^2 / 9 - 1.
638  virtual double EvalWMatrixForm(const DenseMatrix &Jpt) const;
639 
640  // W = I1b * I2b / 9 - 1.
641  virtual double EvalW(const DenseMatrix &Jpt) const;
642 
643  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const;
644 
645  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
646  const double weight, DenseMatrix &A) const;
647 
648  virtual int Id() const { return 302; }
649 };
650 
651 /// 3D barrier Shape (S) metric, well-posed (polyconvex & invex).
652 class TMOP_Metric_303 : public TMOP_QualityMetric
653 {
654 protected:
655  mutable InvariantsEvaluator3D<double> ie;
656 
657 public:
658  // W = |J|^2 / 3 / det(J)^(2/3) - 1.
659  virtual double EvalWMatrixForm(const DenseMatrix &Jpt) const;
660 
661  // W = I1b / 3 - 1.
662  virtual double EvalW(const DenseMatrix &Jpt) const;
663 
664  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const;
665 
666  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
667  const double weight, DenseMatrix &A) const;
668 
669  virtual int Id() const { return 303; }
670 };
671 
672 /// 3D barrier Shape (S) metric, well-posed (polyconvex & invex).
673 class TMOP_Metric_304 : public TMOP_QualityMetric
674 {
675 protected:
676  mutable InvariantsEvaluator3D<double> ie;
677 
678 public:
679  // W = |J|^3 / 3^(3/2) / det(J) - 1.
680  virtual double EvalWMatrixForm(const DenseMatrix &Jpt) const;
681 
682  // W = (I1b/3)^3/2 - 1.
683  virtual double EvalW(const DenseMatrix &Jpt) const;
684 
685  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const;
686 
687  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
688  const double weight, DenseMatrix &A) const;
689 
690  virtual int Id() const { return 304; }
691 };
692 
693 /// 3D Size (V) untangling metric.
694 class TMOP_Metric_311 : public TMOP_QualityMetric
695 {
696 protected:
697  const double eps;
698  mutable InvariantsEvaluator3D<double> ie;
699 
700 public:
701  TMOP_Metric_311(double epsilon = 1e-4) : eps(epsilon) { }
702 
703  // W = (det(J) - 1)^2 - det(J) + (det(J)^2 + eps)^(1/2).
704  virtual double EvalW(const DenseMatrix &Jpt) const;
705 
706  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const;
707 
708  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
709  const double weight, DenseMatrix &A) const;
710 };
711 
712 /// 3D Shape (S) metric, untangling version of 303.
713 class TMOP_Metric_313 : public TMOP_QualityMetric
714 {
715 protected:
716  double &min_detT;
717  mutable InvariantsEvaluator3D<double> ie;
718 
719 public:
720  TMOP_Metric_313(double &mindet) : min_detT(mindet) { }
721 
722  // W = 1/3 |J|^2 / [det(J)-tau0]^(-2/3).
723  virtual double EvalW(const DenseMatrix &Jpt) const;
724 
725  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const;
726 
727  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
728  const double weight, DenseMatrix &A) const;
729 
730  virtual int Id() const { return 313; }
731 };
732 
733 /// 3D non-barrier metric without a type.
734 class TMOP_Metric_315 : public TMOP_QualityMetric
735 {
736 protected:
737  mutable InvariantsEvaluator3D<double> ie;
738 
739 public:
740  // W = (det(J) - 1)^2.
741  virtual double EvalW(const DenseMatrix &Jpt) const;
742 
743  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const;
744 
745  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
746  const double weight, DenseMatrix &A) const;
747 
748  virtual int Id() const { return 315; }
749 };
750 
751 /// 3D barrier metric without a type.
752 class TMOP_Metric_316 : public TMOP_QualityMetric
753 {
754 protected:
755  mutable InvariantsEvaluator3D<double> ie;
756 
757 public:
758  // W = 0.5 (det(J) + 1/det(J)) - 1.
759  virtual double EvalWMatrixForm(const DenseMatrix &Jpt) const;
760 
761  // W = 0.5 (I3b + 1/I3b) - 1.
762  virtual double EvalW(const DenseMatrix &Jpt) const;
763 
764  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const;
765 
766  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
767  const double weight, DenseMatrix &A) const;
768 };
769 
770 /// 3D barrier Shape+Size (VS) metric, well-posed (invex).
771 class TMOP_Metric_321 : public TMOP_QualityMetric
772 {
773 protected:
774  mutable InvariantsEvaluator3D<double> ie;
775 
776 public:
777  // W = |J - J^-t|^2.
778  virtual double EvalWMatrixForm(const DenseMatrix &Jpt) const;
779 
780  // W = I1 + I2/I3 - 6.
781  virtual double EvalW(const DenseMatrix &Jpt) const;
782 
783  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const;
784 
785  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
786  const double weight, DenseMatrix &A) const;
787 
788  virtual int Id() const { return 321; }
789 };
790 
791 /// 3D barrier Shape+Size (VS) metric, well-posed (invex).
792 class TMOP_Metric_322 : public TMOP_QualityMetric
793 {
794 protected:
795  mutable InvariantsEvaluator3D<double> ie;
796 
797 public:
798  // W = |J - adjJ^-t|^2.
799  virtual double EvalWMatrixForm(const DenseMatrix &Jpt) const;
800 
801  // W = I1b / (I3b^-1/3) / 6 + I2b (I3b^1/3) / 6 - 1
802  virtual double EvalW(const DenseMatrix &Jpt) const;
803 
804  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const;
805 
806  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
807  const double weight, DenseMatrix &A) const;
808 
809  virtual int Id() const { return 322; }
810 };
811 
812 /// 3D barrier Shape+Size (VS) metric, well-posed (invex).
813 class TMOP_Metric_323 : public TMOP_QualityMetric
814 {
815 protected:
816  mutable InvariantsEvaluator3D<double> ie;
817 
818 public:
819  // W = |J|^3 - 3 sqrt(3) ln(det(J)) - 3 sqrt(3).
820  virtual double EvalWMatrixForm(const DenseMatrix &Jpt) const;
821 
822  // W = I1^3/2 - 3 sqrt(3) ln(I3b) - 3 sqrt(3).
823  virtual double EvalW(const DenseMatrix &Jpt) const;
824 
825  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const;
826 
827  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
828  const double weight, DenseMatrix &A) const;
829 
830  virtual int Id() const { return 323; }
831 };
832 
833 /// 3D barrier Shape+Size (VS) metric (polyconvex).
834 class TMOP_Metric_328 : public TMOP_Combo_QualityMetric
835 {
836 protected:
837  mutable InvariantsEvaluator2D<double> ie;
838  TMOP_QualityMetric *sh_metric, *sz_metric;
839 
840 public:
841  TMOP_Metric_328(double gamma)
842  : sh_metric(new TMOP_Metric_301), sz_metric(new TMOP_Metric_316)
843  {
844  // (1-gamma) mu_301 + gamma mu_316
845  AddQualityMetric(sh_metric, 1.-gamma);
846  AddQualityMetric(sz_metric, gamma);
847  }
848 
849  virtual ~TMOP_Metric_328() { delete sh_metric; delete sz_metric; }
850 };
851 
852 /// 3D barrier Shape+Size (VS) metric (polyconvex).
853 class TMOP_Metric_332 : public TMOP_Combo_QualityMetric
854 {
855 protected:
856  TMOP_QualityMetric *sh_metric, *sz_metric;
857 
858 public:
859  TMOP_Metric_332(double gamma)
860  : sh_metric(new TMOP_Metric_302), sz_metric(new TMOP_Metric_315)
861  {
862  // (1-gamma) mu_302 + gamma mu_315
863  AddQualityMetric(sh_metric, 1.-gamma);
864  AddQualityMetric(sz_metric, gamma);
865  }
866 
867  virtual int Id() const { return 332; }
868  double GetGamma() const { return wt_arr[1]; }
869 
870  virtual ~TMOP_Metric_332() { delete sh_metric; delete sz_metric; }
871 };
872 
873 /// 3D barrier Shape+Size (VS) metric, well-posed (polyconvex).
874 class TMOP_Metric_333 : public TMOP_Combo_QualityMetric
875 {
876 protected:
877  mutable InvariantsEvaluator2D<double> ie;
878  TMOP_QualityMetric *sh_metric, *sz_metric;
879 
880 public:
881  TMOP_Metric_333(double gamma)
882  : sh_metric(new TMOP_Metric_302), sz_metric(new TMOP_Metric_316)
883  {
884  // (1-gamma) mu_302 + gamma mu_316
885  AddQualityMetric(sh_metric, 1.-gamma);
886  AddQualityMetric(sz_metric, gamma);
887  }
888 
889  virtual ~TMOP_Metric_333() { delete sh_metric; delete sz_metric; }
890 };
891 
892 /// 3D barrier Shape+Size (VS) metric, well-posed (polyconvex).
893 class TMOP_Metric_334 : public TMOP_Combo_QualityMetric
894 {
895 protected:
896  mutable InvariantsEvaluator2D<double> ie;
897  TMOP_QualityMetric *sh_metric, *sz_metric;
898 
899 public:
900  TMOP_Metric_334(double gamma)
901  : sh_metric(new TMOP_Metric_303), sz_metric(new TMOP_Metric_316)
902  {
903  // (1-gamma) mu_303 + gamma mu_316
904  AddQualityMetric(sh_metric, 1.-gamma);
905  AddQualityMetric(sz_metric, gamma);
906  }
907 
908  virtual int Id() const { return 334; }
909  double GetGamma() const { return wt_arr[1]; }
910 
911  virtual ~TMOP_Metric_334() { delete sh_metric; delete sz_metric; }
912 };
913 
914 /// 3D barrier Shape+Size (VS) metric, well-posed (polyconvex).
915 class TMOP_Metric_347 : public TMOP_Combo_QualityMetric
916 {
917 protected:
918  mutable InvariantsEvaluator2D<double> ie;
919  TMOP_QualityMetric *sh_metric, *sz_metric;
920 
921 public:
922  TMOP_Metric_347(double gamma)
923  : sh_metric(new TMOP_Metric_304), sz_metric(new TMOP_Metric_316)
924  {
925  // (1-gamma) mu_304 + gamma mu_316
926  AddQualityMetric(sh_metric, 1.-gamma);
927  AddQualityMetric(sz_metric, gamma);
928  }
929 
930  virtual int Id() const { return 347; }
931  double GetGamma() const { return wt_arr[1]; }
932 
933  virtual ~TMOP_Metric_347() { delete sh_metric; delete sz_metric; }
934 };
935 
936 /// 3D shifted barrier form of metric 316 (not typed).
937 class TMOP_Metric_352 : public TMOP_QualityMetric
938 {
939 protected:
940  double &tau0;
941  mutable InvariantsEvaluator3D<double> ie;
942 
943 public:
944  TMOP_Metric_352(double &t0): tau0(t0) {}
945 
946  // W = 0.5(det(J) - 1)^2 / (det(J) - tau0).
947  virtual double EvalW(const DenseMatrix &Jpt) const;
948 
949  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const;
950 
951  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
952  const double weight, DenseMatrix &A) const;
953 };
954 
955 /// 3D non-barrier Shape (S) metric.
956 class TMOP_Metric_360 : public TMOP_QualityMetric
957 {
958 protected:
959  mutable InvariantsEvaluator3D<double> ie;
960 
961 public:
962  // W = |J|^3 / 3^(3/2) - det(J).
963  virtual double EvalWMatrixForm(const DenseMatrix &Jpt) const;
964 
965  // W = (I1b/3)^3/2 - 1.
966  virtual double EvalW(const DenseMatrix &Jpt) const;
967 
968  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const;
969 
970  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
971  const double weight, DenseMatrix &A) const;
972 
973  virtual int Id() const { return 360; }
974 };
975 
976 /// A-metrics
977 /// 2D barrier Shape (S) metric (polyconvex).
978 class TMOP_AMetric_011 : public TMOP_QualityMetric
979 {
980 protected:
981  mutable InvariantsEvaluator3D<double> ie;
982 
983 public:
984  // (1/4 alpha) | A - (adj A)^t W^t W / omega |^2
985  virtual double EvalW(const DenseMatrix &Jpt) const;
986 
987  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
988  { MFEM_ABORT("Not implemented"); }
989 
990  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
991  const double weight, DenseMatrix &A) const
992  { MFEM_ABORT("Not implemented"); }
993 };
994 
995 /// 2D barrier Size (V) metric (polyconvex).
996 class TMOP_AMetric_014a : public TMOP_QualityMetric
997 {
998 protected:
999  mutable InvariantsEvaluator3D<double> ie;
1000 
1001 public:
1002  // 0.5 * ( sqrt(alpha/omega) - sqrt(omega/alpha) )^2
1003  virtual double EvalW(const DenseMatrix &Jpt) const;
1004 
1005  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
1006  { MFEM_ABORT("Not implemented"); }
1007 
1008  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
1009  const double weight, DenseMatrix &A) const
1010  { MFEM_ABORT("Not implemented"); }
1011 };
1012 
1013 /// 2D barrier Shape+Size+Orientation (VOS) metric (polyconvex).
1014 class TMOP_AMetric_036 : public TMOP_QualityMetric
1015 {
1016 protected:
1017  mutable InvariantsEvaluator3D<double> ie;
1018 
1019 public:
1020  // (1/alpha) | A - W |^2
1021  virtual double EvalW(const DenseMatrix &Jpt) const;
1022 
1023  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
1024  { MFEM_ABORT("Not implemented"); }
1025 
1026  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
1027  const double weight, DenseMatrix &A) const
1028  { MFEM_ABORT("Not implemented"); }
1029 };
1030 
1031 /// 2D barrier Shape+Orientation (OS) metric (polyconvex).
1032 class TMOP_AMetric_107a : public TMOP_QualityMetric
1033 {
1034 protected:
1035  mutable InvariantsEvaluator3D<double> ie;
1036 
1037 public:
1038  // (1/2 alpha) | A - (|A|/|W|) W |^2
1039  virtual double EvalW(const DenseMatrix &Jpt) const;
1040 
1041  virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
1042  { MFEM_ABORT("Not implemented"); }
1043 
1044  virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
1045  const double weight, DenseMatrix &A) const
1046  { MFEM_ABORT("Not implemented"); }
1047 };
1048 
1049 /// 2D barrier Shape+Size (VS) metric (polyconvex).
1050 class TMOP_AMetric_126 : public TMOP_Combo_QualityMetric
1051 {
1052 protected:
1053  mutable InvariantsEvaluator2D<double> ie;
1054  TMOP_QualityMetric *sh_metric, *sz_metric;
1055 
1056 public:
1057  TMOP_AMetric_126(double gamma)
1058  : sh_metric(new TMOP_AMetric_011), sz_metric(new TMOP_AMetric_014a)
1059  {
1060  // (1-gamma) nu_11 + gamma nu_14
1061  AddQualityMetric(sh_metric, 1.-gamma);
1062  AddQualityMetric(sz_metric, gamma);
1063  }
1064 
1065  virtual ~TMOP_AMetric_126() { delete sh_metric; delete sz_metric; }
1066 };
1067 
1068 /// Base class for limiting functions to be used in class TMOP_Integrator.
1069 /** This class represents a scalar function f(x, x0, d), where x and x0 are
1070  positions in physical space, and d is a reference physical distance
1071  associated with the point x0. */
1072 class TMOP_LimiterFunction
1073 {
1074 public:
1075  /// Returns the limiting function, f(x, x0, d).
1076  virtual double Eval(const Vector &x, const Vector &x0, double d) const = 0;
1077 
1078  /** @brief Returns the gradient of the limiting function f(x, x0, d) with
1079  respect to x. */
1080  virtual void Eval_d1(const Vector &x, const Vector &x0, double dist,
1081  Vector &d1) const = 0;
1082 
1083  /** @brief Returns the Hessian of the limiting function f(x, x0, d) with
1084  respect to x. */
1085  virtual void Eval_d2(const Vector &x, const Vector &x0, double dist,
1086  DenseMatrix &d2) const = 0;
1087 
1088  /// Virtual destructor.
1089  virtual ~TMOP_LimiterFunction() { }
1090 };
1091 
1092 /// Default limiter function in TMOP_Integrator.
1093 class TMOP_QuadraticLimiter : public TMOP_LimiterFunction
1094 {
1095 public:
1096  virtual double Eval(const Vector &x, const Vector &x0, double dist) const
1097  {
1098  MFEM_ASSERT(x.Size() == x0.Size(), "Bad input.");
1099 
1100  return 0.5 * x.DistanceSquaredTo(x0) / (dist * dist);
1101  }
1102 
1103  virtual void Eval_d1(const Vector &x, const Vector &x0, double dist,
1104  Vector &d1) const
1105  {
1106  MFEM_ASSERT(x.Size() == x0.Size(), "Bad input.");
1107 
1108  d1.SetSize(x.Size());
1109  subtract(1.0 / (dist * dist), x, x0, d1);
1110  }
1111 
1112  virtual void Eval_d2(const Vector &x, const Vector &x0, double dist,
1113  DenseMatrix &d2) const
1114  {
1115  MFEM_ASSERT(x.Size() == x0.Size(), "Bad input.");
1116 
1117  d2.Diag(1.0 / (dist * dist), x.Size());
1118  }
1119 
1120  virtual ~TMOP_QuadraticLimiter() { }
1121 };
1122 
1123 /// Exponential limiter function in TMOP_Integrator.
1124 class TMOP_ExponentialLimiter : public TMOP_LimiterFunction
1125 {
1126 public:
1127  virtual double Eval(const Vector &x, const Vector &x0, double dist) const
1128  {
1129  MFEM_ASSERT(x.Size() == x0.Size(), "Bad input.");
1130 
1131  return exp(10.0*((x.DistanceSquaredTo(x0) / (dist * dist))-1.0));
1132  }
1133 
1134  virtual void Eval_d1(const Vector &x, const Vector &x0, double dist,
1135  Vector &d1) const
1136  {
1137  MFEM_ASSERT(x.Size() == x0.Size(), "Bad input.");
1138 
1139  d1.SetSize(x.Size());
1140  double dist_squared = dist*dist;
1141  subtract(20.0*exp(10.0*((x.DistanceSquaredTo(x0) / dist_squared) - 1.0)) /
1142  dist_squared, x, x0, d1);
1143  }
1144 
1145  virtual void Eval_d2(const Vector &x, const Vector &x0, double dist,
1146  DenseMatrix &d2) const
1147  {
1148  MFEM_ASSERT(x.Size() == x0.Size(), "Bad input.");
1149  Vector tmp;
1150  tmp.SetSize(x.Size());
1151  double dist_squared = dist*dist;
1152  double dist_squared_squared = dist_squared*dist_squared;
1153  double f = exp(10.0*((x.DistanceSquaredTo(x0) / dist_squared)-1.0));
1154 
1155  subtract(x,x0,tmp);
1156  d2.SetSize(x.Size());
1157  d2(0,0) = ((400.0*tmp(0)*tmp(0)*f)/dist_squared_squared)+(20.0*f/dist_squared);
1158  d2(1,1) = ((400.0*tmp(1)*tmp(1)*f)/dist_squared_squared)+(20.0*f/dist_squared);
1159  d2(0,1) = (400.0*tmp(0)*tmp(1)*f)/dist_squared_squared;
1160  d2(1,0) = d2(0,1);
1161 
1162  if (x.Size() == 3)
1163  {
1164  d2(0,2) = (400.0*tmp(0)*tmp(2)*f)/dist_squared_squared;
1165  d2(1,2) = (400.0*tmp(1)*tmp(2)*f)/dist_squared_squared;
1166  d2(2,0) = d2(0,2);
1167  d2(2,1) = d2(1,2);
1168  d2(2,2) = ((400.0*tmp(2)*tmp(2)*f)/dist_squared_squared)+(20.0*f/dist_squared);
1169  }
1170 
1171  }
1172 
1173  virtual ~TMOP_ExponentialLimiter() { }
1174 };
1175 
1176 class FiniteElementCollection;
1177 class FiniteElementSpace;
1178 class ParFiniteElementSpace;
1179 
1180 class AdaptivityEvaluator
1181 {
1182 protected:
1183  // Owned.
1184  Mesh *mesh;
1185  FiniteElementSpace *fes;
1186 
1187 #ifdef MFEM_USE_MPI
1188  // Owned.
1189  ParMesh *pmesh;
1190  ParFiniteElementSpace *pfes;
1191 #endif
1192 
1193 public:
1194  AdaptivityEvaluator() : mesh(NULL), fes(NULL)
1195  {
1196 #ifdef MFEM_USE_MPI
1197  pmesh = NULL;
1198  pfes = NULL;
1199 #endif
1200  }
1201  virtual ~AdaptivityEvaluator();
1202 
1203  /** Specifies the Mesh and FiniteElementSpace of the solution that will
1204  be evaluated. The given mesh will be copied into the internal object. */
1205  void SetSerialMetaInfo(const Mesh &m,
1206  const FiniteElementSpace &f);
1207 
1208 #ifdef MFEM_USE_MPI
1209  /// Parallel version of SetSerialMetaInfo.
1210  void SetParMetaInfo(const ParMesh &m,
1211  const ParFiniteElementSpace &f);
1212 #endif
1213 
1214  // TODO use GridFunctions to make clear it's on the ldofs?
1215  virtual void SetInitialField(const Vector &init_nodes,
1216  const Vector &init_field) = 0;
1217 
1218  virtual void ComputeAtNewPosition(const Vector &new_nodes,
1219  Vector &new_field,
1220  int new_nodes_ordering = Ordering::byNODES) = 0;
1221 
1222  void ClearGeometricFactors();
1223 };
1224 
1225 /** @brief Base class representing target-matrix construction algorithms for
1226  mesh optimization via the target-matrix optimization paradigm (TMOP). */
1227 /** This class is used by class TMOP_Integrator to construct the target Jacobian
1228  matrices (reference-element to target-element) at quadrature points. It
1229  supports a set of algorithms chosen by the #TargetType enumeration.
1230 
1231  New target-matrix construction algorithms can be defined by deriving new
1232  classes and overriding the methods ComputeElementTargets() and
1233  ContainsVolumeInfo(). */
1234 class TargetConstructor
1235 {
1236 public:
1237  /// Target-matrix construction algorithms supported by this class.
1238  enum TargetType
1239  {
1240  IDEAL_SHAPE_UNIT_SIZE, /**<
1241  Ideal shape, unit size; the nodes are not used. */
1242  IDEAL_SHAPE_EQUAL_SIZE, /**<
1243  Ideal shape, equal size/volume; the given nodes define the total target
1244  volume; for each mesh element, the target volume is the average volume
1245  multiplied by the volume scale, set with SetVolumeScale(). */
1246  IDEAL_SHAPE_GIVEN_SIZE, /**<
1247  Ideal shape, given size/volume; the given nodes define the target
1248  volume at all quadrature points. */
1249  GIVEN_SHAPE_AND_SIZE, /**<
1250  Given shape, given size/volume; the given nodes define the exact target
1251  Jacobian matrix at all quadrature points. */
1252  GIVEN_FULL /**<
1253  Full target tensor is specified at every quadrature point. */
1254  };
1255 
1256 protected:
1257  // Nodes that are used in ComputeElementTargets(), depending on target_type.
1258  const GridFunction *nodes; // not owned
1259  mutable double avg_volume;
1260  double volume_scale;
1261  const TargetType target_type;
1262  bool uses_phys_coords; // see UsesPhysicalCoordinates()
1263 
1264 #ifdef MFEM_USE_MPI
1265  MPI_Comm comm;
1266 #endif
1267 
1268  // should be called only if avg_volume == 0.0, i.e. avg_volume is not
1269  // computed yet
1270  void ComputeAvgVolume() const;
1271 
1272  template<int DIM>
1273  bool ComputeAllElementTargets(const FiniteElementSpace &fes,
1274  const IntegrationRule &ir,
1275  const Vector &xe,
1276  DenseTensor &Jtr) const;
1277 
1278  // CPU fallback that uses ComputeElementTargets()
1279  void ComputeAllElementTargets_Fallback(const FiniteElementSpace &fes,
1280  const IntegrationRule &ir,
1281  const Vector &xe,
1282  DenseTensor &Jtr) const;
1283 
1284 public:
1285  /// Constructor for use in serial
1286  TargetConstructor(TargetType ttype)
1287  : nodes(NULL), avg_volume(), volume_scale(1.0), target_type(ttype),
1288  uses_phys_coords(false)
1289  {
1290 #ifdef MFEM_USE_MPI
1291  comm = MPI_COMM_NULL;
1292 #endif
1293  }
1294 #ifdef MFEM_USE_MPI
1295  /// Constructor for use in parallel
1296  TargetConstructor(TargetType ttype, MPI_Comm mpicomm)
1297  : nodes(NULL), avg_volume(), volume_scale(1.0), target_type(ttype),
1298  uses_phys_coords(false), comm(mpicomm) { }
1299 #endif
1300  virtual ~TargetConstructor() { }
1301 
1302 #ifdef MFEM_USE_MPI
1303  bool Parallel() const { return (comm != MPI_COMM_NULL); }
1304  MPI_Comm GetComm() const { return comm; }
1305 #else
1306  bool Parallel() const { return false; }
1307 #endif
1308 
1309  /** @brief Set the nodes to be used in the target-matrix construction.
1310 
1311  This method should be called every time the target nodes are updated
1312  externally and recomputation of the target average volume is needed. The
1313  nodes are used by all target types except IDEAL_SHAPE_UNIT_SIZE. */
1314  void SetNodes(const GridFunction &n) { nodes = &n; avg_volume = 0.0; }
1315 
1316  /** @brief Get the nodes to be used in the target-matrix construction. */
1317  const GridFunction *GetNodes() const { return nodes; }
1318 
1319  /// Used by target type IDEAL_SHAPE_EQUAL_SIZE. The default volume scale is 1.
1320  void SetVolumeScale(double vol_scale) { volume_scale = vol_scale; }
1321 
1322  TargetType GetTargetType() const { return target_type; }
1323 
1324  /** @brief Return true if the methods ComputeElementTargets(),
1325  ComputeAllElementTargets(), and ComputeElementTargetsGradient() use the
1326  physical node coordinates provided by the parameters 'elfun', or 'xe'. */
1327  bool UsesPhysicalCoordinates() const { return uses_phys_coords; }
1328 
1329  /// Checks if the target matrices contain non-trivial size specification.
1330  virtual bool ContainsVolumeInfo() const;
1331 
1332  /** @brief Given an element and quadrature rule, computes ref->target
1333  transformation Jacobians for each quadrature point in the element.
1334  The physical positions of the element's nodes are given by @a elfun. */
1335  virtual void ComputeElementTargets(int e_id, const FiniteElement &fe,
1336  const IntegrationRule &ir,
1337  const Vector &elfun,
1338  DenseTensor &Jtr) const;
1339 
1340  /** @brief Computes reference-to-target transformation Jacobians for all
1341  quadrature points in all elements.
1342 
1343  @param[in] fes The nodal FE space
1344  @param[in] ir The quadrature rule to use for all elements
1345  @param[in] xe E-vector with the current physical coordinates/positions;
1346  this parameter is used only when needed by the target
1347  constructor, see UsesPhysicalCoordinates()
1348  @param[out] Jtr The computed ref->target Jacobian matrices. */
1349  virtual void ComputeAllElementTargets(const FiniteElementSpace &fes,
1350  const IntegrationRule &ir,
1351  const Vector &xe,
1352  DenseTensor &Jtr) const;
1353 
1354  virtual void ComputeElementTargetsGradient(const IntegrationRule &ir,
1355  const Vector &elfun,
1356  IsoparametricTransformation &Tpr,
1357  DenseTensor &dJtr) const;
1358 };
1359 
1360 class TMOPMatrixCoefficient : public MatrixCoefficient
1361 {
1362 public:
1363  explicit TMOPMatrixCoefficient(int dim) : MatrixCoefficient(dim, dim) { }
1364 
1365  /** @brief Evaluate the derivative of the matrix coefficient with respect to
1366  @a comp in the element described by @a T at the point @a ip, storing the
1367  result in @a K. */
1368  virtual void EvalGrad(DenseMatrix &K, ElementTransformation &T,
1369  const IntegrationPoint &ip, int comp) = 0;
1370 
1371  virtual ~TMOPMatrixCoefficient() { }
1372 };
1373 
1374 class AnalyticAdaptTC : public TargetConstructor
1375 {
1376 protected:
1377  // Analytic target specification.
1378  Coefficient *scalar_tspec;
1379  VectorCoefficient *vector_tspec;
1380  TMOPMatrixCoefficient *matrix_tspec;
1381 
1382 public:
1383  AnalyticAdaptTC(TargetType ttype)
1384  : TargetConstructor(ttype),
1385  scalar_tspec(NULL), vector_tspec(NULL), matrix_tspec(NULL)
1386  { uses_phys_coords = true; }
1387 
1388  virtual void SetAnalyticTargetSpec(Coefficient *sspec,
1389  VectorCoefficient *vspec,
1390  TMOPMatrixCoefficient *mspec);
1391 
1392  /** @brief Given an element and quadrature rule, computes ref->target
1393  transformation Jacobians for each quadrature point in the element.
1394  The physical positions of the element's nodes are given by @a elfun. */
1395  virtual void ComputeElementTargets(int e_id, const FiniteElement &fe,
1396  const IntegrationRule &ir,
1397  const Vector &elfun,
1398  DenseTensor &Jtr) const;
1399 
1400  virtual void ComputeAllElementTargets(const FiniteElementSpace &fes,
1401  const IntegrationRule &ir,
1402  const Vector &xe,
1403  DenseTensor &Jtr) const;
1404 
1405  virtual void ComputeElementTargetsGradient(const IntegrationRule &ir,
1406  const Vector &elfun,
1407  IsoparametricTransformation &Tpr,
1408  DenseTensor &dJtr) const;
1409 };
1410 
1411 #ifdef MFEM_USE_MPI
1412 class ParGridFunction;
1413 #endif
1414 
1415 class DiscreteAdaptTC : public TargetConstructor
1416 {
1417 protected:
1418  // Discrete target specification.
1419  // Data is owned, updated by UpdateTargetSpecification.
1420  int ncomp, sizeidx, skewidx, aspectratioidx, orientationidx;
1421  Vector tspec; //eta(x) - we enforce Ordering::byNODES
1422  Vector tspec_sav;
1423  Vector tspec_pert1h; //eta(x+h)
1424  Vector tspec_pert2h; //eta(x+2*h)
1425  Vector tspec_pertmix; //eta(x+h,y+h)
1426  // The order inside these perturbation vectors (e.g. in 2D) is
1427  // eta1(x+h,y), eta2(x+h,y) ... etan(x+h,y), eta1(x,y+h), eta2(x,y+h) ...
1428  // same for tspec_pert2h and tspec_pertmix.
1429 
1430  // DenseMatrix to hold target_spec values for the (children of the)
1431  // element being refined to consider for h-refinement.
1432  DenseMatrix tspec_refine;
1433  // Vector to hold the target_spec values for the coarse version of the
1434  // current mesh. Used for derefinement decision with hr-adaptivity.
1435  Vector tspec_derefine;
1436 
1437  // Components of Target Jacobian at each quadrature point of an element. This
1438  // is required for computation of the derivative using chain rule.
1439  mutable DenseTensor Jtrcomp;
1440 
1441  // Note: do not use the Nodes of this space as they may not be on the
1442  // positions corresponding to the values of tspec.
1443  FiniteElementSpace *tspec_fesv; //owned
1444  FiniteElementSpace *coarse_tspec_fesv; //not owned, derefinement FESpace
1445  GridFunction *tspec_gf; //owned, uses tspec and tspec_fes
1446  // discrete adaptivity
1447 #ifdef MFEM_USE_MPI
1448  ParFiniteElementSpace *ptspec_fesv; //owned, needed for derefinement to
1449  // get update operator.
1450  ParGridFunction *tspec_pgf; // similar to tspec_gf
1451 #endif
1452 
1453  int amr_el;
1454  double lim_min_size;
1455 
1456  // These flags can be used by outside functions to avoid recomputing the
1457  // tspec and tspec_perth fields again on the same mesh.
1458  bool good_tspec, good_tspec_grad, good_tspec_hess;
1459 
1460  // Evaluation of the discrete target specification on different meshes.
1461  // Owned.
1462  AdaptivityEvaluator *adapt_eval;
1463 
1464  void SetDiscreteTargetBase(const GridFunction &tspec_);
1465  void SetTspecAtIndex(int idx, const GridFunction &tspec_);
1466  void FinalizeSerialDiscreteTargetSpec(const GridFunction &tspec_);
1467 #ifdef MFEM_USE_MPI
1468  void SetTspecAtIndex(int idx, const ParGridFunction &tspec_);
1469  void FinalizeParDiscreteTargetSpec(const ParGridFunction &tspec_);
1470 #endif
1471 
1472 public:
1473  DiscreteAdaptTC(TargetType ttype)
1474  : TargetConstructor(ttype),
1475  ncomp(0),
1476  sizeidx(-1), skewidx(-1), aspectratioidx(-1), orientationidx(-1),
1477  tspec(), tspec_sav(), tspec_pert1h(), tspec_pert2h(), tspec_pertmix(),
1478  tspec_refine(), tspec_derefine(),
1479  tspec_fesv(NULL), coarse_tspec_fesv(NULL), tspec_gf(NULL),
1480 #ifdef MFEM_USE_MPI
1481  ptspec_fesv(NULL), tspec_pgf(NULL),
1482 #endif
1483  amr_el(-1), lim_min_size(-0.1),
1484  good_tspec(false), good_tspec_grad(false), good_tspec_hess(false),
1485  adapt_eval(NULL) { }
1486 
1487  virtual ~DiscreteAdaptTC();
1488 
1489  /** @name Target specification methods.
1490  The following methods are used to specify geometric parameters of the
1491  targets when these parameters are given by discrete FE functions.
1492  Note that every GridFunction given to the Set methods must use a
1493  H1_FECollection of the same order. The number of components must
1494  correspond to the type of geometric parameter and dimension.
1495 
1496  @param[in] tspec_ Input values of a geometric parameter. Note that
1497  the methods in this class support only functions that
1498  use H1_FECollection collection of the same order. */
1499  ///@{
1500  virtual void SetSerialDiscreteTargetSpec(const GridFunction &tspec_);
1501  virtual void SetSerialDiscreteTargetSize(const GridFunction &tspec_);
1502  virtual void SetSerialDiscreteTargetSkew(const GridFunction &tspec_);
1503  virtual void SetSerialDiscreteTargetAspectRatio(const GridFunction &tspec_);
1504  virtual void SetSerialDiscreteTargetOrientation(const GridFunction &tspec_);
1505 #ifdef MFEM_USE_MPI
1506  virtual void SetParDiscreteTargetSpec(const ParGridFunction &tspec_);
1507  virtual void SetParDiscreteTargetSize(const ParGridFunction &tspec_);
1508  virtual void SetParDiscreteTargetSkew(const ParGridFunction &tspec_);
1509  virtual void SetParDiscreteTargetAspectRatio(const ParGridFunction &tspec_);
1510  virtual void SetParDiscreteTargetOrientation(const ParGridFunction &tspec_);
1511 #endif
1512  ///@}
1513 
1514  /// Used in combination with the Update methods to avoid extra computations.
1515  void ResetUpdateFlags()
1516  { good_tspec = good_tspec_grad = good_tspec_hess = false; }
1517 
1518  /// Get one of the discrete fields from tspec.
1519  void GetDiscreteTargetSpec(GridFunction &tspec_, int idx);
1520  /// Get the FESpace associated with tspec.
1521  FiniteElementSpace *GetTSpecFESpace() { return tspec_fesv; }
1522  /// Get the entire tspec.
1523  GridFunction *GetTSpecData() { return tspec_gf; }
1524  /// Update all discrete fields based on tspec and update for AMR
1525  void UpdateAfterMeshTopologyChange();
1526 
1527 #ifdef MFEM_USE_MPI
1528  ParFiniteElementSpace *GetTSpecParFESpace() { return ptspec_fesv; }
1529  void ParUpdateAfterMeshTopologyChange();
1530 #endif
1531 
1532  /** Used to update the target specification after the mesh has changed. The
1533  new mesh positions are given by new_x. If @a use_flags is true, repeated
1534  calls won't do anything until ResetUpdateFlags() is called. */
1535  void UpdateTargetSpecification(const Vector &new_x, bool use_flag = false,
1536  int new_x_ordering=Ordering::byNODES);
1537 
1538  void UpdateTargetSpecification(Vector &new_x, Vector &IntData,
1539  int new_x_ordering=Ordering::byNODES);
1540 
1541  void UpdateTargetSpecificationAtNode(const FiniteElement &el,
1542  ElementTransformation &T,
1543  int nodenum, int idir,
1544  const Vector &IntData);
1545 
1546  void RestoreTargetSpecificationAtNode(ElementTransformation &T, int nodenum);
1547 
1548  /** Used for finite-difference based computations. Computes the target
1549  specifications after a mesh perturbation in x or y direction.
1550  If @a use_flags is true, repeated calls won't do anything until
1551  ResetUpdateFlags() is called. */
1552  void UpdateGradientTargetSpecification(const Vector &x, double dx,
1553  bool use_flag = false,
1554  int x_ordering = Ordering::byNODES);
1555  /** Used for finite-difference based computations. Computes the target
1556  specifications after two mesh perturbations in x and/or y direction.
1557  If @a use_flags is true, repeated calls won't do anything until
1558  ResetUpdateFlags() is called. */
1559  void UpdateHessianTargetSpecification(const Vector &x, double dx,
1560  bool use_flag = false,
1561  int x_ordering = Ordering::byNODES);
1562 
1563  void SetAdaptivityEvaluator(AdaptivityEvaluator *ae)
1564  {
1565  if (adapt_eval) { delete adapt_eval; }
1566  adapt_eval = ae;
1567  }
1568 
1569  const AdaptivityEvaluator *GetAdaptivityEvaluator() const
1570  {
1571  return adapt_eval;
1572  }
1573 
1574  const Vector &GetTspecPert1H() { return tspec_pert1h; }
1575  const Vector &GetTspecPert2H() { return tspec_pert2h; }
1576  const Vector &GetTspecPertMixH() { return tspec_pertmix; }
1577 
1578  /** @brief Given an element and quadrature rule, computes ref->target
1579  transformation Jacobians for each quadrature point in the element.
1580  The physical positions of the element's nodes are given by @a elfun.
1581  Note that this function assumes that UpdateTargetSpecification() has
1582  been called with the position vector corresponding to @a elfun. */
1583  virtual void ComputeElementTargets(int e_id, const FiniteElement &fe,
1584  const IntegrationRule &ir,
1585  const Vector &elfun,
1586  DenseTensor &Jtr) const;
1587 
1588  virtual void ComputeAllElementTargets(const FiniteElementSpace &fes,
1589  const IntegrationRule &ir,
1590  const Vector &xe,
1591  DenseTensor &Jtr) const;
1592 
1593  virtual void ComputeElementTargetsGradient(const IntegrationRule &ir,
1594  const Vector &elfun,
1595  IsoparametricTransformation &Tpr,
1596  DenseTensor &dJtr) const;
1597 
1598  // Generates tspec_vals for target construction using intrule
1599  // Used for the refinement component in hr-adaptivity.
1600  void SetTspecFromIntRule(int e_id, const IntegrationRule &intrule);
1601 
1602  // Targets based on discrete functions can result in invalid (negative)
1603  // size at the quadrature points. This method can be used to set a
1604  // minimum target size.
1605  void SetMinSizeForTargets(double min_size_) { lim_min_size = min_size_; }
1606 
1607  /// Computes target specification data with respect to the coarse FE space.
1608  void SetTspecDataForDerefinement(FiniteElementSpace *fes);
1609 
1610  // Reset refinement data associated with h-adaptivity component.
1611  void ResetRefinementTspecData()
1612  {
1613  tspec_refine.Clear();
1614  amr_el = -1;
1615  }
1616 
1617  // Reset derefinement data associated with h-adaptivity component.
1618  void ResetDerefinementTspecData()
1619  {
1620  tspec_derefine.Destroy();
1621  coarse_tspec_fesv = NULL;
1622  }
1623 
1624  // Used to specify the fine element for determining energy of children of a
1625  // parent element.
1626  void SetRefinementSubElement(int amr_el_) { amr_el = amr_el_; }
1627 };
1628 
1629 class TMOPNewtonSolver;
1630 
1631 /** @brief A TMOP integrator class based on any given TMOP_QualityMetric and
1632  TargetConstructor.
1633 
1634  Represents @f$ \int W(Jpt) dx @f$ over a target zone, where W is the
1635  metric's strain energy density function, and Jpt is the Jacobian of the
1636  target->physical coordinates transformation. The virtual target zone is
1637  defined by the TargetConstructor. */
1638 class TMOP_Integrator : public NonlinearFormIntegrator
1639 {
1640 protected:
1641  friend class TMOPNewtonSolver;
1642  friend class TMOPComboIntegrator;
1643 
1644  TMOP_QualityMetric *h_metric;
1645  TMOP_QualityMetric *metric; // not owned
1646  const TargetConstructor *targetC; // not owned
1647 
1648  // Custom integration rules.
1649  IntegrationRules *IntegRules;
1650  int integ_order;
1651 
1652  // Weight Coefficient multiplying the quality metric term.
1653  Coefficient *metric_coeff; // not owned, if NULL -> metric_coeff is 1.
1654  // Normalization factor for the metric term.
1655  double metric_normal;
1656 
1657  // Nodes and weight Coefficient used for "limiting" the TMOP_Integrator.
1658  // These are both NULL when there is no limiting.
1659  // The class doesn't own lim_nodes0 and lim_coeff.
1660  const GridFunction *lim_nodes0;
1661  Coefficient *lim_coeff;
1662  // Limiting reference distance. Not owned.
1663  const GridFunction *lim_dist;
1664  // Limiting function. Owned.
1665  TMOP_LimiterFunction *lim_func;
1666  // Normalization factor for the limiting term.
1667  double lim_normal;
1668 
1669  // Adaptive limiting.
1670  const GridFunction *adapt_lim_gf0; // Not owned.
1671 #ifdef MFEM_USE_MPI
1672  const ParGridFunction *adapt_lim_pgf0;
1673 #endif
1674  GridFunction *adapt_lim_gf; // Owned. Updated by adapt_lim_eval.
1675  Coefficient *adapt_lim_coeff; // Not owned.
1676  AdaptivityEvaluator *adapt_lim_eval; // Not owned.
1677 
1678  // Surface fitting.
1679  GridFunction *surf_fit_gf; // Owned, Updated by surf_fit_eval.
1680  const Array<bool> *surf_fit_marker; // Not owned.
1681  Coefficient *surf_fit_coeff; // Not owned.
1682  AdaptivityEvaluator *surf_fit_eval; // Not owned.
1683  double surf_fit_normal;
1684 
1685  DiscreteAdaptTC *discr_tc;
1686 
1687  // Parameters for FD-based Gradient & Hessian calculation.
1688  bool fdflag;
1689  double dx;
1690  double dxscale;
1691  // Specifies that ComputeElementTargets is being called by a FD function.
1692  // It's used to skip terms that have exact derivative calculations.
1693  bool fd_call_flag;
1694  // Compute the exact action of the Integrator (includes derivative of the
1695  // target with respect to spatial position)
1696  bool exact_action;
1697 
1698  Array <Vector *> ElemDer; //f'(x)
1699  Array <Vector *> ElemPertEnergy; //f(x+h)
1700 
1701  // Jrt: the inverse of the ref->target Jacobian, Jrt = Jtr^{-1}.
1702  // Jpr: the ref->physical transformation Jacobian, Jpr = PMatI^t DS.
1703  // Jpt: the target->physical transformation Jacobian, Jpt = Jpr Jrt.
1704  // P: represents dW_d(Jtp) (dim x dim).
1705  // DSh: gradients of reference shape functions (dof x dim).
1706  // DS: gradients of the shape functions in the target configuration,
1707  // DS = DSh Jrt (dof x dim).
1708  // PMatI: current coordinates of the nodes (dof x dim).
1709  // PMat0: reshaped view into the local element contribution to the operator
1710  // output - the result of AssembleElementVector() (dof x dim).
1711  DenseMatrix DSh, DS, Jrt, Jpr, Jpt, P, PMatI, PMatO;
1712 
1713  // PA extension
1714  // ------------
1715  // E: Q-vector for TMOP-energy
1716  // O: Q-Vector of 1.0, used to compute sums using the dot product kernel.
1717  // X0: E-vector for initial nodal coordinates used for limiting.
1718  // H: Q-Vector for Hessian associated with the metric term.
1719  // C0: Q-Vector for spatial weight used for the limiting term.
1720  // LD: E-Vector constructed using limiting distance grid function (delta).
1721  // H0: Q-Vector for Hessian associated with the limiting term.
1722  //
1723  // maps: Dof2Quad map for fespace associate with nodal coordinates.
1724  // maps_lim: Dof2Quad map for fespace associated with the limiting distance
1725  // grid function.
1726  //
1727  // Jtr_debug_grad
1728  // We keep track if Jtr was set by AssembleGradPA() in Jtr_debug_grad: it
1729  // is set to true by AssembleGradPA(); any other call to
1730  // ComputeAllElementTargets() will set the flag to false. This flag will
1731  // be used to check that Jtr is the one set by AssembleGradPA() when
1732  // performing operations with the gradient like AddMultGradPA() and
1733  // AssembleGradDiagonalPA().
1734  //
1735  // TODO:
1736  // * Merge LD, C0, H0 into one scalar Q-vector
1737  struct
1738  {
1739  bool enabled;
1740  int dim, ne, nq;
1741  mutable DenseTensor Jtr;
1742  mutable bool Jtr_needs_update;
1743  mutable bool Jtr_debug_grad;
1744  mutable Vector E, O, X0, H, C0, LD, H0;
1745  const DofToQuad *maps;
1746  const DofToQuad *maps_lim = nullptr;
1747  const GeometricFactors *geom;
1748  const FiniteElementSpace *fes;
1749  const IntegrationRule *ir;
1750  } PA;
1751 
1752  void ComputeNormalizationEnergies(const GridFunction &x,
1753  double &metric_energy, double &lim_energy,
1754  double &surf_fit_gf_energy);
1755 
1756  void AssembleElementVectorExact(const FiniteElement &el,
1757  ElementTransformation &T,
1758  const Vector &elfun, Vector &elvect);
1759 
1760  void AssembleElementGradExact(const FiniteElement &el,
1761  ElementTransformation &T,
1762  const Vector &elfun, DenseMatrix &elmat);
1763 
1764  void AssembleElementVectorFD(const FiniteElement &el,
1765  ElementTransformation &T,
1766  const Vector &elfun, Vector &elvect);
1767 
1768  // Assumes that AssembleElementVectorFD has been called.
1769  void AssembleElementGradFD(const FiniteElement &el,
1770  ElementTransformation &T,
1771  const Vector &elfun, DenseMatrix &elmat);
1772 
1773  void AssembleElemVecAdaptLim(const FiniteElement &el,
1774  IsoparametricTransformation &Tpr,
1775  const IntegrationRule &ir,
1776  const Vector &weights, DenseMatrix &mat);
1777  void AssembleElemGradAdaptLim(const FiniteElement &el,
1778  IsoparametricTransformation &Tpr,
1779  const IntegrationRule &ir,
1780  const Vector &weights, DenseMatrix &m);
1781 
1782  // First derivative of the surface fitting term.
1783  void AssembleElemVecSurfFit(const FiniteElement &el_x,
1784  IsoparametricTransformation &Tpr,
1785  DenseMatrix &mat);
1786 
1787  // Second derivative of the surface fitting term.
1788  void AssembleElemGradSurfFit(const FiniteElement &el_x,
1789  IsoparametricTransformation &Tpr,
1790  DenseMatrix &mat);
1791 
1792  double GetFDDerivative(const FiniteElement &el,
1793  ElementTransformation &T,
1794  Vector &elfun, const int nodenum,const int idir,
1795  const double baseenergy, bool update_stored);
1796 
1797  /** @brief Determines the perturbation, h, for FD-based approximation. */
1798  void ComputeFDh(const Vector &x, const FiniteElementSpace &fes);
1799  void ComputeMinJac(const Vector &x, const FiniteElementSpace &fes);
1800 
1801  void UpdateAfterMeshPositionChange(const Vector &new_x,
1802  int new_x_ordering = Ordering::byNODES);
1803 
1804  void DisableLimiting()
1805  {
1806  lim_nodes0 = NULL; lim_coeff = NULL; lim_dist = NULL;
1807  delete lim_func; lim_func = NULL;
1808  }
1809 
1810  const IntegrationRule &EnergyIntegrationRule(const FiniteElement &el) const
1811  {
1812  if (IntegRules)
1813  {
1814  return IntegRules->Get(el.GetGeomType(), integ_order);
1815  }
1816  return (IntRule) ? *IntRule
1817  /* */ : IntRules.Get(el.GetGeomType(), 2*el.GetOrder() + 3);
1818  }
1819  const IntegrationRule &ActionIntegrationRule(const FiniteElement &el) const
1820  {
1821  // TODO the energy most likely needs less integration points.
1822  return EnergyIntegrationRule(el);
1823  }
1824  const IntegrationRule &GradientIntegrationRule(const FiniteElement &el) const
1825  {
1826  // TODO the action and energy most likely need less integration points.
1827  return EnergyIntegrationRule(el);
1828  }
1829 
1830  // Auxiliary PA methods
1831  void AssembleGradPA_2D(const Vector&) const;
1832  void AssembleGradPA_3D(const Vector&) const;
1833  void AssembleGradPA_C0_2D(const Vector&) const;
1834  void AssembleGradPA_C0_3D(const Vector&) const;
1835 
1836  double GetLocalStateEnergyPA_2D(const Vector&) const;
1837  double GetLocalStateEnergyPA_C0_2D(const Vector&) const;
1838  double GetLocalStateEnergyPA_3D(const Vector&) const;
1839  double GetLocalStateEnergyPA_C0_3D(const Vector&) const;
1840 
1841  void AddMultPA_2D(const Vector&, Vector&) const;
1842  void AddMultPA_3D(const Vector&, Vector&) const;
1843  void AddMultPA_C0_2D(const Vector&, Vector&) const;
1844  void AddMultPA_C0_3D(const Vector&, Vector&) const;
1845 
1846  void AddMultGradPA_2D(const Vector&, Vector&) const;
1847  void AddMultGradPA_3D(const Vector&, Vector&) const;
1848  void AddMultGradPA_C0_2D(const Vector&, Vector&) const;
1849  void AddMultGradPA_C0_3D(const Vector&, Vector&) const;
1850 
1851  void AssembleDiagonalPA_2D(Vector&) const;
1852  void AssembleDiagonalPA_3D(Vector&) const;
1853  void AssembleDiagonalPA_C0_2D(Vector&) const;
1854  void AssembleDiagonalPA_C0_3D(Vector&) const;
1855 
1856  void AssemblePA_Limiting();
1857  void ComputeAllElementTargets(const Vector &xe = Vector()) const;
1858 
1859  // Compute Min(Det(Jpt)) in the mesh, does not reduce over MPI.
1860  double ComputeMinDetT(const Vector &x, const FiniteElementSpace &fes);
1861  // Compute Max(mu_hat) for the TMOP_WorstCaseUntangleOptimizer_Metric,
1862  // does not reduce over MPI.
1863  double ComputeUntanglerMaxMuBarrier(const Vector &x,
1864  const FiniteElementSpace &fes);
1865 
1866 public:
1867  /** @param[in] m TMOP_QualityMetric for r-adaptivity (not owned).
1868  @param[in] tc Target-matrix construction algorithm to use (not owned).
1869  @param[in] hm TMOP_QualityMetric for h-adaptivity (not owned). */
1870  TMOP_Integrator(TMOP_QualityMetric *m, TargetConstructor *tc,
1871  TMOP_QualityMetric *hm)
1872  : h_metric(hm), metric(m), targetC(tc), IntegRules(NULL),
1873  integ_order(-1), metric_coeff(NULL), metric_normal(1.0),
1874  lim_nodes0(NULL), lim_coeff(NULL),
1875  lim_dist(NULL), lim_func(NULL), lim_normal(1.0),
1876  adapt_lim_gf0(NULL), adapt_lim_gf(NULL), adapt_lim_coeff(NULL),
1877  adapt_lim_eval(NULL),
1878  surf_fit_gf(NULL), surf_fit_marker(NULL),
1879  surf_fit_coeff(NULL),
1880  surf_fit_eval(NULL), surf_fit_normal(1.0),
1881  discr_tc(dynamic_cast<DiscreteAdaptTC *>(tc)),
1882  fdflag(false), dxscale(1.0e3), fd_call_flag(false), exact_action(false)
1883  { PA.enabled = false; }
1884 
1885  TMOP_Integrator(TMOP_QualityMetric *m, TargetConstructor *tc)
1886  : TMOP_Integrator(m, tc, m) { }
1887 
1888  ~TMOP_Integrator();
1889 
1890  /// Release the device memory of large PA allocations. This will copy device
1891  /// memory back to the host before releasing.
1892  void ReleasePADeviceMemory(bool copy_to_host = true);
1893 
1894  /// Prescribe a set of integration rules; relevant for mixed meshes.
1895  /** This function has priority over SetIntRule(), if both are called. */
1896  void SetIntegrationRules(IntegrationRules &irules, int order)
1897  {
1898  IntegRules = &irules;
1899  integ_order = order;
1900  }
1901 
1902  /// Sets a scaling Coefficient for the quality metric term of the integrator.
1903  /** With this addition, the integrator becomes
1904  @f$ \int w1 W(Jpt) dx @f$.
1905 
1906  Note that the Coefficient is evaluated in the physical configuration and
1907  not in the target configuration which may be undefined. */
1908  void SetCoefficient(Coefficient &w1) { metric_coeff = &w1; }
1909 
1910  /** @brief Limiting of the mesh displacements (general version).
1911 
1912  Adds the term @f$ \int w_0 f(x, x_0, d) dx @f$, where f is a measure of
1913  the displacement between x and x_0, given the max allowed displacement d.
1914 
1915  @param[in] n0 Original mesh node coordinates (x0 above).
1916  @param[in] dist Allowed displacement in physical space (d above).
1917  @param[in] w0 Coefficient scaling the limiting integral.
1918  @param[in] lfunc TMOP_LimiterFunction defining the function f. If
1919  NULL, a TMOP_QuadraticLimiter will be used. The
1920  TMOP_Integrator assumes ownership of this pointer. */
1921  void EnableLimiting(const GridFunction &n0, const GridFunction &dist,
1922  Coefficient &w0, TMOP_LimiterFunction *lfunc = NULL);
1923 
1924  /** @brief Adds a limiting term to the integrator with limiting distance
1925  function (@a dist in the general version of the method) equal to 1. */
1926  void EnableLimiting(const GridFunction &n0, Coefficient &w0,
1927  TMOP_LimiterFunction *lfunc = NULL);
1928 
1929  /** @brief Restriction of the node positions to certain regions.
1930 
1931  Adds the term @f$ \int c (z(x) - z_0(x_0))^2 @f$, where z0(x0) is a given
1932  function on the starting mesh, and z(x) is its image on the new mesh.
1933  Minimizing this term means that a node at x0 is allowed to move to a
1934  position x(x0) only if z(x) ~ z0(x0).
1935  Such term can be used for tangential mesh relaxation.
1936 
1937  @param[in] z0 Function z0 that controls the adaptive limiting.
1938  @param[in] coeff Coefficient c for the above integral.
1939  @param[in] ae AdaptivityEvaluator to compute z(x) from z0(x0). */
1940  void EnableAdaptiveLimiting(const GridFunction &z0, Coefficient &coeff,
1941  AdaptivityEvaluator &ae);
1942 #ifdef MFEM_USE_MPI
1943  /// Parallel support for adaptive limiting.
1944  void EnableAdaptiveLimiting(const ParGridFunction &z0, Coefficient &coeff,
1945  AdaptivityEvaluator &ae);
1946 #endif
1947 
1948  /** @brief Fitting of certain DOFs to the zero level set of a function.
1949 
1950  Having a level set function s0(x0) on the starting mesh, and a set of
1951  marked nodes (or DOFs), we move these nodes to the zero level set of s0.
1952  If s(x) is the image of s0(x0) on the current mesh, this function adds to
1953  the TMOP functional the term @f$ \int c \bar{s}(x))^2 @f$, where
1954  @f$\bar{s}(x)@f$ is the restriction of s(x) on the aligned DOFs.
1955  Minimizing this term means that a marked node at x0 is allowed to move to
1956  a position x(x0) only if s(x) ~ 0.
1957  Such term can be used for surface fitting and tangential relaxation.
1958 
1959  @param[in] s0 The level set function on the initial mesh.
1960  @param[in] smarker Indicates which DOFs will be aligned.
1961  @param[in] coeff Coefficient c for the above integral.
1962  @param[in] ae AdaptivityEvaluator to compute s(x) from s0(x0). */
1963  void EnableSurfaceFitting(const GridFunction &s0,
1964  const Array<bool> &smarker, Coefficient &coeff,
1965  AdaptivityEvaluator &ae);
1966 #ifdef MFEM_USE_MPI
1967  /// Parallel support for surface fitting.
1968  void EnableSurfaceFitting(const ParGridFunction &s0,
1969  const Array<bool> &smarker, Coefficient &coeff,
1970  AdaptivityEvaluator &ae);
1971 #endif
1972  void GetSurfaceFittingErrors(double &err_avg, double &err_max);
1973  bool IsSurfaceFittingEnabled() { return (surf_fit_gf != NULL); }
1974 
1975  /// Update the original/reference nodes used for limiting.
1976  void SetLimitingNodes(const GridFunction &n0) { lim_nodes0 = &n0; }
1977 
1978  /** @brief Computes the integral of W(Jacobian(Trt)) over a target zone.
1979  @param[in] el Type of FiniteElement.
1980  @param[in] T Mesh element transformation.
1981  @param[in] elfun Physical coordinates of the zone. */
1982  virtual double GetElementEnergy(const FiniteElement &el,
1983  ElementTransformation &T,
1984  const Vector &elfun);
1985 
1986  /** @brief Computes the mean of the energies of the given element's children.
1987 
1988  In addition to the inputs for GetElementEnergy, this function requires an
1989  IntegrationRule to be specified that will give the decomposition of the
1990  given element based on the refinement type being considered. */
1991  virtual double GetRefinementElementEnergy(const FiniteElement &el,
1992  ElementTransformation &T,
1993  const Vector &elfun,
1994  const IntegrationRule &irule);
1995 
1996  /// This function is similar to GetElementEnergy, but ignores components
1997  /// such as limiting etc. to compute the element energy.
1998  virtual double GetDerefinementElementEnergy(const FiniteElement &el,
1999  ElementTransformation &T,
2000  const Vector &elfun);
2001 
2002  virtual void AssembleElementVector(const FiniteElement &el,
2003  ElementTransformation &T,
2004  const Vector &elfun, Vector &elvect);
2005 
2006  virtual void AssembleElementGrad(const FiniteElement &el,
2007  ElementTransformation &T,
2008  const Vector &elfun, DenseMatrix &elmat);
2009 
2010  TMOP_QualityMetric &GetAMRQualityMetric() { return *h_metric; }
2011 
2012  void UpdateAfterMeshTopologyChange();
2013 #ifdef MFEM_USE_MPI
2014  void ParUpdateAfterMeshTopologyChange();
2015 #endif
2016 
2017  // PA extension
2018  using NonlinearFormIntegrator::AssemblePA;
2019  virtual void AssemblePA(const FiniteElementSpace&);
2020 
2021  virtual void AssembleGradPA(const Vector&, const FiniteElementSpace&);
2022 
2023  virtual double GetLocalStateEnergyPA(const Vector&) const;
2024 
2025  virtual void AddMultPA(const Vector&, Vector&) const;
2026 
2027  virtual void AddMultGradPA(const Vector&, Vector&) const;
2028 
2029  virtual void AssembleGradDiagonalPA(Vector&) const;
2030 
2031  DiscreteAdaptTC *GetDiscreteAdaptTC() const { return discr_tc; }
2032 
2033  /** @brief Computes the normalization factors of the metric and limiting
2034  integrals using the mesh position given by @a x. */
2035  void EnableNormalization(const GridFunction &x);
2036 #ifdef MFEM_USE_MPI
2037  void ParEnableNormalization(const ParGridFunction &x);
2038 #endif
2039 
2040  /** @brief Enables FD-based approximation and computes dx. */
2041  void EnableFiniteDifferences(const GridFunction &x);
2042 #ifdef MFEM_USE_MPI
2043  void EnableFiniteDifferences(const ParGridFunction &x);
2044 #endif
2045 
2046  void SetFDhScale(double dxscale_) { dxscale = dxscale_; }
2047  bool GetFDFlag() const { return fdflag; }
2048  double GetFDh() const { return dx; }
2049 
2050  /** @brief Flag to control if exact action of Integration is effected. */
2051  void SetExactActionFlag(bool flag_) { exact_action = flag_; }
2052 
2053  /// Update the surface fitting weight as surf_fit_coeff *= factor;
2054  void UpdateSurfaceFittingWeight(double factor);
2055 
2056  /// Get the surface fitting weight.
2057  double GetSurfaceFittingWeight();
2058 
2059  /// Computes quantiles needed for UntangleMetrics. Note that in parallel,
2060  /// the ParFiniteElementSpace must be passed as argument for consistency
2061  /// across MPI ranks.
2062  void ComputeUntangleMetricQuantiles(const Vector &x,
2063  const FiniteElementSpace &fes);
2064 };
2065 
2066 class TMOPComboIntegrator : public NonlinearFormIntegrator
2067 {
2068 protected:
2069  // Integrators in the combination. Owned.
2070  Array<TMOP_Integrator *> tmopi;
2071 
2072 public:
2073  TMOPComboIntegrator() : tmopi(0) { }
2074 
2075  ~TMOPComboIntegrator()
2076  {
2077  for (int i = 0; i < tmopi.Size(); i++) { delete tmopi[i]; }
2078  }
2079 
2080  /// Adds a new TMOP_Integrator to the combination.
2081  void AddTMOPIntegrator(TMOP_Integrator *ti) { tmopi.Append(ti); }
2082 
2083  const Array<TMOP_Integrator *> &GetTMOPIntegrators() const { return tmopi; }
2084 
2085  /// Adds the limiting term to the first integrator. Disables it for the rest.
2086  void EnableLimiting(const GridFunction &n0, const GridFunction &dist,
2087  Coefficient &w0, TMOP_LimiterFunction *lfunc = NULL);
2088 
2089  /** @brief Adds the limiting term to the first integrator. Disables it for
2090  the rest (@a dist in the general version of the method) equal to 1. */
2091  void EnableLimiting(const GridFunction &n0, Coefficient &w0,
2092  TMOP_LimiterFunction *lfunc = NULL);
2093 
2094  /// Update the original/reference nodes used for limiting.
2095  void SetLimitingNodes(const GridFunction &n0);
2096 
2097  virtual double GetElementEnergy(const FiniteElement &el,
2098  ElementTransformation &T,
2099  const Vector &elfun);
2100  virtual void AssembleElementVector(const FiniteElement &el,
2101  ElementTransformation &T,
2102  const Vector &elfun, Vector &elvect);
2103  virtual void AssembleElementGrad(const FiniteElement &el,
2104  ElementTransformation &T,
2105  const Vector &elfun, DenseMatrix &elmat);
2106 
2107  virtual double GetRefinementElementEnergy(const FiniteElement &el,
2108  ElementTransformation &T,
2109  const Vector &elfun,
2110  const IntegrationRule &irule);
2111 
2112  virtual double GetDerefinementElementEnergy(const FiniteElement &el,
2113  ElementTransformation &T,
2114  const Vector &elfun);
2115 
2116  /// Normalization factor that considers all integrators in the combination.
2117  void EnableNormalization(const GridFunction &x);
2118 #ifdef MFEM_USE_MPI
2119  void ParEnableNormalization(const ParGridFunction &x);
2120 #endif
2121 
2122  // PA extension
2123  using NonlinearFormIntegrator::AssemblePA;
2124  virtual void AssemblePA(const FiniteElementSpace&);
2125  virtual void AssembleGradPA(const Vector&, const FiniteElementSpace&);
2126  virtual double GetLocalStateEnergyPA(const Vector&) const;
2127  virtual void AddMultPA(const Vector&, Vector&) const;
2128  virtual void AddMultGradPA(const Vector&, Vector&) const;
2129  virtual void AssembleGradDiagonalPA(Vector&) const;
2130 };
2131 
2132 /// Interpolates the @a metric's values at the nodes of @a metric_gf.
2133 /** Assumes that @a metric_gf's FiniteElementSpace is initialized. */
2134 void InterpolateTMOP_QualityMetric(TMOP_QualityMetric &metric,
2135  const TargetConstructor &tc,
2136  const Mesh &mesh, GridFunction &metric_gf);
2137 }
2138 
2139 #endif
mfem::TMOP_Metric_066::GetGamma
double GetGamma() const
Definition: tmop.hpp:495
mfem::FiniteElement
Abstract class for all finite elements.
Definition: fe_base.hpp:232
mfem::TMOP_Integrator::LD
Vector LD
Definition: tmop.hpp:1744
mfem::TMOP_Metric_303::Id
virtual int Id() const
Return the metric ID.
Definition: tmop.hpp:669
mfem::TMOP_Integrator::ComputeUntangleMetricQuantiles
void ComputeUntangleMetricQuantiles(const Vector &x, const FiniteElementSpace &fes)
Definition: tmop.cpp:4238
mfem::TMOP_Metric_077::ie
InvariantsEvaluator2D< double > ie
Definition: tmop.hpp:505
mfem::AnalyticAdaptTC::ComputeElementTargets
virtual void ComputeElementTargets(int e_id, const FiniteElement &fe, const IntegrationRule &ir, const Vector &elfun, DenseTensor &Jtr) const
Given an element and quadrature rule, computes ref->target transformation Jacobians for each quadratu...
Definition: tmop.cpp:1648
mfem::TMOP_Integrator::GetDerefinementElementEnergy
virtual double GetDerefinementElementEnergy(const FiniteElement &el, ElementTransformation &T, const Vector &elfun)
Definition: tmop.cpp:3161
mfem::TMOP_Metric_014::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:466
mfem::TMOP_Metric_304::EvalWMatrixForm
virtual double EvalWMatrixForm(const DenseMatrix &Jpt) const
Evaluates the metric in matrix form (opposed to invariant form). Used for validating the invariant ev...
Definition: tmop.cpp:930
mfem::DiscreteAdaptTC::SetParDiscreteTargetSize
virtual void SetParDiscreteTargetSize(const ParGridFunction &tspec_)
Definition: tmop.cpp:1785
mfem::DiscreteAdaptTC::ComputeElementTargets
virtual void ComputeElementTargets(int e_id, const FiniteElement &fe, const IntegrationRule &ir, const Vector &elfun, DenseTensor &Jtr) const
Given an element and quadrature rule, computes ref->target transformation Jacobians for each quadratu...
Definition: tmop.cpp:2045
mfem::TMOP_Metric_077::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:670
mfem::TMOP_Metric_211::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.cpp:747
mfem::TMOP_Metric_252
Shifted barrier form of metric 56 (area, ideal barrier metric), 2D.
Definition: tmop.hpp:592
mfem::TMOP_Metric_311::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:964
mfem::TMOP_Metric_352
3D shifted barrier form of metric 316 (not typed).
Definition: tmop.hpp:937
mfem::DiscreteAdaptTC::ComputeAllElementTargets
virtual void ComputeAllElementTargets(const FiniteElementSpace &fes, const IntegrationRule &ir, const Vector &xe, DenseTensor &Jtr) const
Computes reference-to-target transformation Jacobians for all quadrature points in all elements...
Definition: tmop_pa_da3.cpp:126
mfem::TMOP_Metric_311::ie
InvariantsEvaluator3D< double > ie
Definition: tmop.hpp:698
mfem::AdaptivityEvaluator::SetInitialField
virtual void SetInitialField(const Vector &init_nodes, const Vector &init_field)=0
mfem::TMOP_Integrator::enabled
bool enabled
Definition: tmop.hpp:1739
mfem::TMOP_Metric_007::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.cpp:407
mfem::TMOP_QualityMetric::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const =0
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
mfem::TMOP_Metric_322::ie
InvariantsEvaluator3D< double > ie
Definition: tmop.hpp:795
mfem::TMOP_Integrator::AssembleElemVecSurfFit
void AssembleElemVecSurfFit(const FiniteElement &el_x, IsoparametricTransformation &Tpr, DenseMatrix &mat)
Definition: tmop.cpp:3588
mfem::TMOP_Metric_skew2D::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:222
mfem::IntegrationRule
Class for an integration rule - an Array of IntegrationPoint.
Definition: intrules.hpp:90
mfem::TMOP_Metric_303::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.cpp:910
mfem::AnalyticAdaptTC::vector_tspec
VectorCoefficient * vector_tspec
Definition: tmop.hpp:1379
mfem::TMOP_Metric_360
3D non-barrier Shape (S) metric.
Definition: tmop.hpp:956
mfem::TMOP_Metric_347::GetGamma
double GetGamma() const
Definition: tmop.hpp:931
mfem::TMOP_Integrator::EnableFiniteDifferences
void EnableFiniteDifferences(const GridFunction &x)
Enables FD-based approximation and computes dx.
Definition: tmop.cpp:4090
mfem::TMOP_Metric_302::Id
virtual int Id() const
Return the metric ID.
Definition: tmop.hpp:648
mfem::TargetConstructor::target_type
const TargetType target_type
Definition: tmop.hpp:1261
mfem::TMOP_Metric_322::Id
virtual int Id() const
Return the metric ID.
Definition: tmop.hpp:809
mfem::GridFunction
Class for grid function - Vector with associated FE space.
Definition: gridfunc.hpp:30
mfem::TMOP_Integrator::PMatO
DenseMatrix PMatO
Definition: tmop.hpp:1711
mfem::TMOP_WorstCaseUntangleOptimizer_Metric::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.hpp:202
mfem::TMOP_Metric_014::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.hpp:381
mfem::TMOP_Metric_316::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.cpp:1080
mfem::TMOP_Integrator::Jtr
DenseTensor Jtr
Definition: tmop.hpp:1741
mfem::TMOP_Combo_QualityMetric::ComputeAvgMetrics
void ComputeAvgMetrics(const GridFunction &nodes, const TargetConstructor &tc, Vector &averages) const
Definition: tmop.cpp:99
mfem::TMOP_AMetric_107a::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.hpp:1044
mfem::TMOP_Metric_022::min_detT
double & min_detT
Definition: tmop.hpp:390
mfem::TMOP_Metric_321
3D barrier Shape+Size (VS) metric, well-posed (invex).
Definition: tmop.hpp:771
mfem::TMOP_Metric_313::ie
InvariantsEvaluator3D< double > ie
Definition: tmop.hpp:717
mfem::TMOP_QualityMetric::Jtr
const DenseMatrix * Jtr
Definition: tmop.hpp:26
mfem::TMOP_Metric_321::ie
InvariantsEvaluator3D< double > ie
Definition: tmop.hpp:774
mfem::TMOP_Metric_352::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.cpp:1273
mfem::TMOP_WorstCaseUntangleOptimizer_Metric::BarrierType
BarrierType
Definition: tmop.hpp:152
mfem::TMOP_Metric_066
Definition: tmop.hpp:480
mfem::TMOP_Metric_334::ie
InvariantsEvaluator2D< double > ie
Definition: tmop.hpp:896
mfem::IntegrationRules::Get
const IntegrationRule & Get(int GeomType, int Order)
Returns an integration rule for given GeomType and Order.
Definition: intrules.cpp:923
mfem::TMOP_Integrator::GetSurfaceFittingWeight
double GetSurfaceFittingWeight()
Get the surface fitting weight.
Definition: tmop.cpp:3915
mfem::TMOP_Metric_050::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:539
mfem::TMOP_WorstCaseUntangleOptimizer_Metric::detT_ep
double detT_ep
Definition: tmop.hpp:171
mfem::TMOP_Metric_055::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.cpp:579
mfem::TMOP_Metric_334
3D barrier Shape+Size (VS) metric, well-posed (polyconvex).
Definition: tmop.hpp:893
mfem::VectorCoefficient
Base class for vector Coefficients that optionally depend on time and space.
Definition: coefficient.hpp:448
mfem::TMOP_Metric_002::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:346
mfem::TMOP_Metric_311::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.cpp:981
mfem::TMOP_Metric_334::~TMOP_Metric_334
virtual ~TMOP_Metric_334()
Definition: tmop.hpp:911
mfem::TMOP_ExponentialLimiter::Eval
virtual double Eval(const Vector &x, const Vector &x0, double dist) const
Returns the limiting function, f(x, x0, d).
Definition: tmop.hpp:1127
mfem::TMOP_Combo_QualityMetric::ComputeBalancedWeights
void ComputeBalancedWeights(const GridFunction &nodes, const TargetConstructor &tc, Vector &weights) const
Definition: tmop.cpp:70
mfem::TMOP_Integrator::Jrt
DenseMatrix Jrt
Definition: tmop.hpp:1711
mfem::TMOP_Integrator::lim_dist
const GridFunction * lim_dist
Definition: tmop.hpp:1663
mfem::DiscreteAdaptTC::SetSerialDiscreteTargetOrientation
virtual void SetSerialDiscreteTargetOrientation(const GridFunction &tspec_)
Definition: tmop.cpp:1898
mfem::TMOPComboIntegrator::GetElementEnergy
virtual double GetElementEnergy(const FiniteElement &el, ElementTransformation &T, const Vector &elfun)
Compute the local energy.
Definition: tmop.cpp:4307
mfem::TMOP_Integrator::AddMultGradPA_2D
void AddMultGradPA_2D(const Vector &, Vector &) const
Definition: tmop_pa_h2m.cpp:114
epsilon
double epsilon
Definition: ex25.cpp:140
mfem::TargetConstructor::UsesPhysicalCoordinates
bool UsesPhysicalCoordinates() const
Return true if the methods ComputeElementTargets(), ComputeAllElementTargets(), and ComputeElementTar...
Definition: tmop.hpp:1327
mfem::TMOP_Integrator::PA
struct mfem::TMOP_Integrator::@23 PA
mfem::TMOP_AMetric_036::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:1389
mfem::AdaptivityEvaluator::ComputeAtNewPosition
virtual void ComputeAtNewPosition(const Vector &new_nodes, Vector &new_field, int new_nodes_ordering=Ordering::byNODES)=0
mfem::TMOP_Metric_333::~TMOP_Metric_333
virtual ~TMOP_Metric_333()
Definition: tmop.hpp:889
mfem::TMOPMatrixCoefficient::EvalGrad
virtual void EvalGrad(DenseMatrix &K, ElementTransformation &T, const IntegrationPoint &ip, int comp)=0
Evaluate the derivative of the matrix coefficient with respect to comp in the element described by T ...
mfem::TMOP_Metric_007::Id
virtual int Id() const
Return the metric ID.
Definition: tmop.hpp:352
mfem::TMOP_Metric_055::ie
InvariantsEvaluator2D< double > ie
Definition: tmop.hpp:427
mfem::TMOP_Metric_311::eps
const double eps
Definition: tmop.hpp:697
mfem::TMOP_Integrator::EnableNormalization
void EnableNormalization(const GridFunction &x)
Computes the normalization factors of the metric and limiting integrals using the mesh position given...
Definition: tmop.cpp:3926
mfem::TMOP_Integrator::GetAMRQualityMetric
TMOP_QualityMetric & GetAMRQualityMetric()
Definition: tmop.hpp:2010
mfem::TMOP_Integrator::AssembleGradPA_2D
void AssembleGradPA_2D(const Vector &) const
Definition: tmop_pa_h2s.cpp:271
mfem::TMOP_Integrator::ComputeAllElementTargets
void ComputeAllElementTargets(const Vector &xe=Vector()) const
Definition: tmop_pa.cpp:167
mfem::TMOP_Integrator::H
Vector H
Definition: tmop.hpp:1744
mfem::TMOP_Integrator::GradientIntegrationRule
const IntegrationRule & GradientIntegrationRule(const FiniteElement &el) const
Definition: tmop.hpp:1824
mfem::Vector::SetSize
void SetSize(int s)
Resize the vector to size s.
Definition: vector.hpp:512
mfem::InterpolateTMOP_QualityMetric
void InterpolateTMOP_QualityMetric(TMOP_QualityMetric &metric, const TargetConstructor &tc, const Mesh &mesh, GridFunction &metric_gf)
Interpolates the metric&#39;s values at the nodes of metric_gf.
Definition: tmop.cpp:4460
mfem::TMOP_Metric_303
3D barrier Shape (S) metric, well-posed (polyconvex & invex).
Definition: tmop.hpp:652
mfem::TMOP_Integrator::metric
TMOP_QualityMetric * metric
Definition: tmop.hpp:1645
mfem::DiscreteAdaptTC::SetAdaptivityEvaluator
void SetAdaptivityEvaluator(AdaptivityEvaluator *ae)
Definition: tmop.hpp:1563
mfem::TMOP_AMetric_036::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.hpp:1023
mfem::TMOP_Metric_332::~TMOP_Metric_332
virtual ~TMOP_Metric_332()
Definition: tmop.hpp:870
mfem::TMOP_Metric_056::ie
InvariantsEvaluator2D< double > ie
Definition: tmop.hpp:445
mfem::TMOP_LimiterFunction::~TMOP_LimiterFunction
virtual ~TMOP_LimiterFunction()
Virtual destructor.
Definition: tmop.hpp:1089
mfem::TMOP_LimiterFunction
Base class for limiting functions to be used in class TMOP_Integrator.
Definition: tmop.hpp:1072
mfem::DiscreteAdaptTC::ComputeElementTargetsGradient
virtual void ComputeElementTargetsGradient(const IntegrationRule &ir, const Vector &elfun, IsoparametricTransformation &Tpr, DenseTensor &dJtr) const
Definition: tmop.cpp:2260
mfem::TMOP_Metric_022::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.cpp:512
mfem::TMOP_Metric_004::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.cpp:374
mfem::TMOP_QualityMetric::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const =0
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
mfem::TMOP_LimiterFunction::Eval_d2
virtual void Eval_d2(const Vector &x, const Vector &x0, double dist, DenseMatrix &d2) const =0
Returns the Hessian of the limiting function f(x, x0, d) with respect to x.
mfem::TMOP_AMetric_014a::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:1373
mfem::TMOP_Metric_skew3D
3D non-barrier Skew metric.
Definition: tmop.hpp:252
mfem::TMOP_Metric_080
Definition: tmop.hpp:521
mfem::TMOPComboIntegrator::GetTMOPIntegrators
const Array< TMOP_Integrator * > & GetTMOPIntegrators() const
Definition: tmop.hpp:2083
mfem::TMOP_Integrator::lim_normal
double lim_normal
Definition: tmop.hpp:1667
mfem::DiscreteAdaptTC::ParUpdateAfterMeshTopologyChange
void ParUpdateAfterMeshTopologyChange()
Definition: tmop.cpp:1754
mfem::TMOP_Integrator::Jpr
DenseMatrix Jpr
Definition: tmop.hpp:1711
mfem::TMOP_Integrator::IntegRules
IntegrationRules * IntegRules
Definition: tmop.hpp:1649
mfem::TMOP_Metric_080::sz_metric
TMOP_QualityMetric * sz_metric
Definition: tmop.hpp:525
mfem::TMOP_AMetric_126::sh_metric
TMOP_QualityMetric * sh_metric
Definition: tmop.hpp:1054
mfem::TMOP_Integrator::GetDiscreteAdaptTC
DiscreteAdaptTC * GetDiscreteAdaptTC() const
Definition: tmop.hpp:2031
mfem::TMOP_Integrator::SetFDhScale
void SetFDhScale(double dxscale_)
Definition: tmop.hpp:2046
mfem::TMOP_ExponentialLimiter::Eval_d2
virtual void Eval_d2(const Vector &x, const Vector &x0, double dist, DenseMatrix &d2) const
Returns the Hessian of the limiting function f(x, x0, d) with respect to x.
Definition: tmop.hpp:1145
mfem::TMOP_QualityMetric::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const =0
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
mfem::TMOP_Metric_001::ie
InvariantsEvaluator2D< double > ie
Definition: tmop.hpp:222
mfem::Vector::Size
int Size() const
Returns the size of the vector.
Definition: vector.hpp:199
mfem::TMOP_Combo_QualityMetric::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.cpp:55
mfem::DiscreteAdaptTC::SetMinSizeForTargets
void SetMinSizeForTargets(double min_size_)
Definition: tmop.hpp:1605
mfem::TMOP_Integrator::AddMultPA_3D
void AddMultPA_3D(const Vector &, Vector &) const
Definition: tmop_pa_p3.cpp:192
mfem::TMOP_Metric_332::Id
virtual int Id() const
Return the metric ID.
Definition: tmop.hpp:867
mfem::TMOP_Metric_323::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:1233
mfem::IntegrationRules
Container class for integration rules.
Definition: intrules.hpp:311
mfem::AdaptivityEvaluator::pfes
ParFiniteElementSpace * pfes
Definition: tmop.hpp:1190
mfem::DenseMatrix
Data type dense matrix using column-major storage.
Definition: densemat.hpp:23
mfem::TMOP_Metric_302
3D barrier Shape (S) metric, well-posed (polyconvex & invex).
Definition: tmop.hpp:631
mfem::TMOP_Metric_360::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:1318
mfem::TMOP_Integrator::GetSurfaceFittingErrors
void GetSurfaceFittingErrors(double &err_avg, double &err_max)
Definition: tmop.cpp:2882
mfem::TMOP_Metric_304::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.cpp:944
mfem::TargetConstructor::SetVolumeScale
void SetVolumeScale(double vol_scale)
Used by target type IDEAL_SHAPE_EQUAL_SIZE. The default volume scale is 1.
Definition: tmop.hpp:1320
mfem::TMOP_Metric_002
Definition: tmop.hpp:298
mfem::TMOP_Metric_252::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.cpp:763
mfem::TMOP_Metric_352::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:1265
mfem::TMOP_Integrator::metric_normal
double metric_normal
Definition: tmop.hpp:1655
mfem::TMOP_Metric_098::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:717
mfem::TMOP_Integrator::EnableAdaptiveLimiting
void EnableAdaptiveLimiting(const GridFunction &z0, Coefficient &coeff, AdaptivityEvaluator &ae)
Restriction of the node positions to certain regions.
Definition: tmop.cpp:2811
mfem::TMOP_Metric_347::sz_metric
TMOP_QualityMetric * sz_metric
Definition: tmop.hpp:919
mfem::TMOP_Metric_056::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.cpp:616
mfem::TMOP_Metric_315
3D non-barrier metric without a type.
Definition: tmop.hpp:734
mfem::TMOP_Integrator::X0
Vector X0
Definition: tmop.hpp:1744
mfem::TMOP_WorstCaseUntangleOptimizer_Metric
Definition: tmop.hpp:149
mfem::TMOP_Metric_077
Definition: tmop.hpp:502
mfem::TMOP_Metric_001::Id
virtual int Id() const
Return the metric ID.
Definition: tmop.hpp:233
mfem::TMOP_Integrator::SetIntegrationRules
void SetIntegrationRules(IntegrationRules &irules, int order)
Prescribe a set of integration rules; relevant for mixed meshes.
Definition: tmop.hpp:1896
mfem::TMOP_AMetric_107a::ie
InvariantsEvaluator3D< double > ie
Definition: tmop.hpp:1035
mfem::TMOP_Metric_360::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.cpp:1334
mfem::TMOP_Integrator::integ_order
int integ_order
Definition: tmop.hpp:1650
mfem::TMOPComboIntegrator::EnableNormalization
void EnableNormalization(const GridFunction &x)
Normalization factor that considers all integrators in the combination.
Definition: tmop.cpp:4377
mfem::TMOP_Metric_302::EvalWMatrixForm
virtual double EvalWMatrixForm(const DenseMatrix &Jpt) const
Evaluates the metric in matrix form (opposed to invariant form). Used for validating the invariant ev...
Definition: tmop.cpp:853
mfem::TMOP_WorstCaseUntangleOptimizer_Metric::tmop_metric
TMOP_QualityMetric & tmop_metric
Definition: tmop.hpp:166
mfem::TMOP_AMetric_126
2D barrier Shape+Size (VS) metric (polyconvex).
Definition: tmop.hpp:1050
mfem::TMOP_Metric_001::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:200
mfem::TMOP_Metric_301::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:802
mfem::TMOP_Integrator::IsSurfaceFittingEnabled
bool IsSurfaceFittingEnabled()
Definition: tmop.hpp:1973
mfem::TMOP_Metric_313::min_detT
double & min_detT
Definition: tmop.hpp:716
mfem::TMOP_Integrator::nq
int nq
Definition: tmop.hpp:1740
mfem::TMOP_Metric_323
3D barrier Shape+Size (VS) metric, well-posed (invex).
Definition: tmop.hpp:813
mfem::DiscreteAdaptTC::GetAdaptivityEvaluator
const AdaptivityEvaluator * GetAdaptivityEvaluator() const
Definition: tmop.hpp:1569
mfem::ParFiniteElementSpace
Abstract parallel finite element space.
Definition: pfespace.hpp:28
mfem::TMOPComboIntegrator::AssemblePA
virtual void AssemblePA(const FiniteElementSpace &)
Method defining partial assembly.
Definition: tmop.cpp:4409
mfem::TMOP_Metric_080::TMOP_Metric_080
TMOP_Metric_080(double gamma)
Definition: tmop.hpp:528
mfem::TMOP_Metric_009::ie
InvariantsEvaluator2D< double > ie
Definition: tmop.hpp:359
mfem::TMOP_Metric_085::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.hpp:552
mfem::AdaptivityEvaluator::SetSerialMetaInfo
void SetSerialMetaInfo(const Mesh &m, const FiniteElementSpace &f)
Definition: tmop.cpp:2719
mfem::GeometricFactors
Structure for storing mesh geometric factors: coordinates, Jacobians, and determinants of the Jacobia...
Definition: mesh.hpp:1915
mfem::TMOP_Metric_007::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.cpp:399
mfem::DiscreteAdaptTC::UpdateGradientTargetSpecification
void UpdateGradientTargetSpecification(const Vector &x, double dx, bool use_flag=false, int x_ordering=Ordering::byNODES)
Definition: tmop.cpp:2607
mfem::TMOP_Metric_360::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.cpp:1325
mfem::TMOP_Integrator::ir
const IntegrationRule * ir
Definition: tmop.hpp:1749
mfem::TMOP_Integrator::SetExactActionFlag
void SetExactActionFlag(bool flag_)
Flag to control if exact action of Integration is effected.
Definition: tmop.hpp:2051
mfem::TMOP_Integrator::ne
int ne
Definition: tmop.hpp:1740
mfem::TMOP_Metric_058::ie
InvariantsEvaluator2D< double > ie
Definition: tmop.hpp:463
mfem::TMOP_Integrator::AssembleElementVectorFD
void AssembleElementVectorFD(const FiniteElement &el, ElementTransformation &T, const Vector &elfun, Vector &elvect)
Definition: tmop.cpp:3740
mfem::TargetConstructor::nodes
const GridFunction * nodes
Definition: tmop.hpp:1258
mfem::TMOP_WorstCaseUntangleOptimizer_Metric::TMOP_WorstCaseUntangleOptimizer_Metric
TMOP_WorstCaseUntangleOptimizer_Metric(TMOP_QualityMetric &tmop_metric_, int exponent_=1, double alpha_=1.5, double detT_ep_=0.0001, double muT_ep_=0.0001, BarrierType btype_=BarrierType::None, WorstCaseType wctype_=WorstCaseType::None)
Definition: tmop.hpp:177
mfem::TMOP_Metric_334::Id
virtual int Id() const
Return the metric ID.
Definition: tmop.hpp:908
mfem::TMOP_Metric_302::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.cpp:880
mfem::DiscreteAdaptTC::SetSerialDiscreteTargetSkew
virtual void SetSerialDiscreteTargetSkew(const GridFunction &tspec_)
Definition: tmop.cpp:1878
mfem::TMOP_Metric_211::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:733
mfem::TMOP_Integrator::UpdateSurfaceFittingWeight
void UpdateSurfaceFittingWeight(double factor)
Update the surface fitting weight as surf_fit_coeff *= factor;.
Definition: tmop.cpp:3903
mfem::DiscreteAdaptTC::SetRefinementSubElement
void SetRefinementSubElement(int amr_el_)
Definition: tmop.hpp:1626
mfem::TMOP_Metric_aspratio2D
2D non-barrier Aspect ratio metric.
Definition: tmop.hpp:267
mfem::TMOP_Metric_skew3D::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.hpp:261
mfem::TMOP_Metric_aspratio3D::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.hpp:291
mfem::TMOP_Metric_077::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.cpp:686
mfem::TMOP_Metric_333::ie
InvariantsEvaluator2D< double > ie
Definition: tmop.hpp:877
mfem::TMOP_Integrator::GetLocalStateEnergyPA
virtual double GetLocalStateEnergyPA(const Vector &) const
Compute the local (to the MPI rank) energy with partial assembly.
Definition: tmop_pa.cpp:297
mfem::TMOP_Metric_007
2D barrier Shape+Size (VS) metric (not polyconvex).
Definition: tmop.hpp:338
mfem::TMOP_Metric_333::sh_metric
TMOP_QualityMetric * sh_metric
Definition: tmop.hpp:878
mfem::TMOP_QuadraticLimiter
Default limiter function in TMOP_Integrator.
Definition: tmop.hpp:1093
mfem::TMOPComboIntegrator::GetLocalStateEnergyPA
virtual double GetLocalStateEnergyPA(const Vector &) const
Compute the local (to the MPI rank) energy with partial assembly.
Definition: tmop.cpp:4450
mfem::TMOP_Metric_098::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.hpp:564
mfem::TMOP_Metric_001::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.cpp:206
mfem::TMOP_Integrator::AssembleElementGradExact
void AssembleElementGradExact(const FiniteElement &el, ElementTransformation &T, const Vector &elfun, DenseMatrix &elmat)
Definition: tmop.cpp:3383
mfem::TMOPComboIntegrator::AddMultGradPA
virtual void AddMultGradPA(const Vector &, Vector &) const
Method for partially assembled gradient action.
Definition: tmop.cpp:4442
mfem::TMOP_Integrator::ElemDer
Array< Vector * > ElemDer
Definition: tmop.hpp:1698
mfem::TMOP_Metric_322
3D barrier Shape+Size (VS) metric, well-posed (invex).
Definition: tmop.hpp:792
mfem::TMOP_AMetric_126::~TMOP_AMetric_126
virtual ~TMOP_AMetric_126()
Definition: tmop.hpp:1065
mfem::DiscreteAdaptTC::GetTspecPertMixH
const Vector & GetTspecPertMixH()
Definition: tmop.hpp:1576
mfem::TMOP_AMetric_011::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.hpp:990
mfem::TMOPComboIntegrator::EnableLimiting
void EnableLimiting(const GridFunction &n0, const GridFunction &dist, Coefficient &w0, TMOP_LimiterFunction *lfunc=NULL)
Adds the limiting term to the first integrator. Disables it for the rest.
Definition: tmop.cpp:4278
mfem::TMOP_Metric_328::ie
InvariantsEvaluator2D< double > ie
Definition: tmop.hpp:837
mfem::TMOP_Metric_066::sz_metric
TMOP_QualityMetric * sz_metric
Definition: tmop.hpp:484
mfem::TMOP_Metric_022
2D Shifted barrier form of shape metric (mu_2).
Definition: tmop.hpp:387
mfem::TMOP_Metric_313::TMOP_Metric_313
TMOP_Metric_313(double &mindet)
Definition: tmop.hpp:720
mfem::TMOP_Metric_352::TMOP_Metric_352
TMOP_Metric_352(double &t0)
Definition: tmop.hpp:944
mfem::AnalyticAdaptTC::scalar_tspec
Coefficient * scalar_tspec
Definition: tmop.hpp:1378
mfem::TMOP_Metric_252::tau0
double & tau0
Definition: tmop.hpp:595
mfem::DiscreteAdaptTC::SetSerialDiscreteTargetAspectRatio
virtual void SetSerialDiscreteTargetAspectRatio(const GridFunction &tspec_)
Definition: tmop.cpp:1888
mfem::TMOP_Metric_aspratio3D::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.hpp:288
mfem::TMOP_Metric_077::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.cpp:677
mfem::TMOP_Metric_055::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:571
mfem::IntRules
IntegrationRules IntRules(0, Quadrature1D::GaussLegendre)
A global object with all integration rules (defined in intrules.cpp)
Definition: intrules.hpp:379
mfem::TMOPMatrixCoefficient::TMOPMatrixCoefficient
TMOPMatrixCoefficient(int dim)
Definition: tmop.hpp:1363
mfem::TMOP_WorstCaseUntangleOptimizer_Metric::WorstCaseType::None
mfem::TMOP_Metric_301::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.cpp:809
mfem::TMOP_Metric_058
2D barrier shape (S) metric (not polyconvex).
Definition: tmop.hpp:460
mfem::TMOP_Integrator::maps
const DofToQuad * maps
Definition: tmop.hpp:1745
mfem::TMOP_QualityMetric::~TMOP_QualityMetric
virtual ~TMOP_QualityMetric()
Definition: tmop.hpp:35
mfem::TMOP_Metric_302::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.cpp:872
mfem::TMOP_Metric_058::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:641
mfem::TMOP_Integrator::EnergyIntegrationRule
const IntegrationRule & EnergyIntegrationRule(const FiniteElement &el) const
Definition: tmop.hpp:1810
mfem::TMOP_Integrator::AddMultPA
virtual void AddMultPA(const Vector &, Vector &) const
Method for partially assembled action.
Definition: tmop_pa.cpp:250
mfem::TMOP_Integrator::ComputeUntanglerMaxMuBarrier
double ComputeUntanglerMaxMuBarrier(const Vector &x, const FiniteElementSpace &fes)
Definition: tmop.cpp:4176
mfem::TMOP_Integrator::AddMultPA_C0_2D
void AddMultPA_C0_2D(const Vector &, Vector &) const
Definition: tmop_pa_p2_c0.cpp:152
mfem::TMOP_AMetric_107a::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.hpp:1041
mfem::TMOP_Integrator::geom
const GeometricFactors * geom
Definition: tmop.hpp:1747
mfem::TMOP_Metric_304
3D barrier Shape (S) metric, well-posed (polyconvex & invex).
Definition: tmop.hpp:673
mfem::TMOP_WorstCaseUntangleOptimizer_Metric::exponent
int exponent
Definition: tmop.hpp:169
mfem::FiniteElement::GetGeomType
Geometry::Type GetGeomType() const
Returns the Geometry::Type of the reference element.
Definition: fe_base.hpp:319
mfem::TargetConstructor::ComputeAllElementTargets
bool ComputeAllElementTargets(const FiniteElementSpace &fes, const IntegrationRule &ir, const Vector &xe, DenseTensor &Jtr) const
mfem::TMOP_Metric_004
Definition: tmop.hpp:320
mfem::TMOP_Integrator::GetLocalStateEnergyPA_C0_3D
double GetLocalStateEnergyPA_C0_3D(const Vector &) const
Definition: tmop_pa_w3_c0.cpp:143
mfem::TMOP_AMetric_014a
2D barrier Size (V) metric (polyconvex).
Definition: tmop.hpp:996
mfem::TMOP_QualityMetric
Abstract class for local mesh quality metrics in the target-matrix optimization paradigm (TMOP) by P...
Definition: tmop.hpp:23
mfem::TMOP_Integrator::AssembleGradPA_C0_2D
void AssembleGradPA_C0_2D(const Vector &) const
Definition: tmop_pa_h2s_c0.cpp:150
mfem::TMOP_Metric_322::EvalWMatrixForm
virtual double EvalWMatrixForm(const DenseMatrix &Jpt) const
Evaluates the metric in matrix form (opposed to invariant form). Used for validating the invariant ev...
Definition: tmop.cpp:1152
mfem::DiscreteAdaptTC::FinalizeSerialDiscreteTargetSpec
void FinalizeSerialDiscreteTargetSpec(const GridFunction &tspec_)
Definition: tmop.cpp:1908
mfem::TMOP_Metric_009::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:432
mfem::TMOP_Metric_001::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.cpp:212
mfem::TMOP_Integrator::adapt_lim_coeff
Coefficient * adapt_lim_coeff
Definition: tmop.hpp:1675
mfem::TMOPMatrixCoefficient::~TMOPMatrixCoefficient
virtual ~TMOPMatrixCoefficient()
Definition: tmop.hpp:1371
mfem::AdaptivityEvaluator::~AdaptivityEvaluator
virtual ~AdaptivityEvaluator()
Definition: tmop.cpp:2750
mfem::TMOP_AMetric_107a::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:1405
mfem::TMOP_Metric_skew3D::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:246
mfem::TMOP_Metric_315::ie
InvariantsEvaluator3D< double > ie
Definition: tmop.hpp:737
mfem::TMOP_Combo_QualityMetric::AddQualityMetric
virtual void AddQualityMetric(TMOP_QualityMetric *tq, double wt=1.0)
Definition: tmop.hpp:92
mfem::TMOP_Metric_002::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.cpp:352
mfem::TMOPComboIntegrator::SetLimitingNodes
void SetLimitingNodes(const GridFunction &n0)
Update the original/reference nodes used for limiting.
Definition: tmop.cpp:4299
mfem::TMOP_Integrator::C0
Vector C0
Definition: tmop.hpp:1744
mfem::TMOP_Metric_080::~TMOP_Metric_080
virtual ~TMOP_Metric_080()
Definition: tmop.hpp:539
mfem::DiscreteAdaptTC::SetDiscreteTargetBase
void SetDiscreteTargetBase(const GridFunction &tspec_)
Definition: tmop.cpp:1831
mfem::TMOP_Metric_066::~TMOP_Metric_066
virtual ~TMOP_Metric_066()
Definition: tmop.hpp:497
mfem::TMOP_Integrator::adapt_lim_eval
AdaptivityEvaluator * adapt_lim_eval
Definition: tmop.hpp:1676
mfem::TMOP_Integrator::AssembleGradPA
virtual void AssembleGradPA(const Vector &, const FiniteElementSpace &)
Prepare the integrator for partial assembly (PA) gradient evaluations on the given FE space fes at th...
Definition: tmop_pa.cpp:23
mfem::f
double f(const Vector &xvec)
Definition: lor_mms.hpp:32
mfem::TMOP_Metric_055::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.cpp:587
mfem::TMOP_WorstCaseUntangleOptimizer_Metric::EvalWBarrier
virtual double EvalWBarrier(const DenseMatrix &Jpt) const
Definition: tmop.cpp:184
mfem::TMOP_Integrator::AddMultGradPA_3D
void AddMultGradPA_3D(const Vector &, Vector &) const
Definition: tmop_pa_h3m.cpp:117
mfem::TMOP_Integrator::discr_tc
DiscreteAdaptTC * discr_tc
Definition: tmop.hpp:1685
mfem::TMOP_Integrator::EnableLimiting
void EnableLimiting(const GridFunction &n0, const GridFunction &dist, Coefficient &w0, TMOP_LimiterFunction *lfunc=NULL)
Limiting of the mesh displacements (general version).
Definition: tmop.cpp:2786
mfem::TMOP_Combo_QualityMetric::EvalWMatrixForm
virtual double EvalWMatrixForm(const DenseMatrix &Jpt) const
Evaluates the metric in matrix form (opposed to invariant form). Used for validating the invariant ev...
Definition: tmop.cpp:23
mfem::TMOP_Integrator::AssembleDiagonalPA_3D
void AssembleDiagonalPA_3D(Vector &) const
Definition: tmop_pa_h3d.cpp:136
mfem::TMOP_Metric_352::tau0
double & tau0
Definition: tmop.hpp:940
mfem::TMOP_WorstCaseUntangleOptimizer_Metric::GetWorstCaseType
virtual WorstCaseType GetWorstCaseType()
Definition: tmop.hpp:215
mfem::TMOP_AMetric_011::ie
InvariantsEvaluator3D< double > ie
Definition: tmop.hpp:981
mfem::TMOP_Integrator::SetCoefficient
void SetCoefficient(Coefficient &w1)
Sets a scaling Coefficient for the quality metric term of the integrator.
Definition: tmop.hpp:1908
mfem::TMOP_Metric_skew3D::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.hpp:258
mfem::TMOP_Metric_056::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.cpp:608
mfem::TMOP_Metric_055
Definition: tmop.hpp:424
mfem::DiscreteAdaptTC::UpdateTargetSpecificationAtNode
void UpdateTargetSpecificationAtNode(const FiniteElement &el, ElementTransformation &T, int nodenum, int idir, const Vector &IntData)
Definition: tmop.cpp:1980
mfem::TMOP_Metric_334::sh_metric
TMOP_QualityMetric * sh_metric
Definition: tmop.hpp:897
mfem::DiscreteAdaptTC::SetTspecFromIntRule
void SetTspecFromIntRule(int e_id, const IntegrationRule &intrule)
Definition: tmop.cpp:2011
mfem::TMOP_QualityMetric::Id
virtual int Id() const
Return the metric ID.
Definition: tmop.hpp:78
mfem::Array::Append
int Append(const T &el)
Append element &#39;el&#39; to array, resize if necessary.
Definition: array.hpp:756
mfem::TargetConstructor::TargetConstructor
TargetConstructor(TargetType ttype)
Constructor for use in serial.
Definition: tmop.hpp:1286
mfem::TMOP_Metric_skew2D::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.hpp:246
mfem::TMOP_Integrator::UpdateAfterMeshPositionChange
void UpdateAfterMeshPositionChange(const Vector &new_x, int new_x_ordering=Ordering::byNODES)
Definition: tmop.cpp:4054
mfem::TMOP_Metric_022::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:482
mfem::TMOP_Metric_316
3D barrier metric without a type.
Definition: tmop.hpp:752
mfem::TMOP_WorstCaseUntangleOptimizer_Metric::WorstCaseType
WorstCaseType
Definition: tmop.hpp:158
mfem::DiscreteAdaptTC::DiscreteAdaptTC
DiscreteAdaptTC(TargetType ttype)
Definition: tmop.hpp:1473
mfem::TMOP_Integrator::AddMultGradPA_C0_2D
void AddMultGradPA_C0_2D(const Vector &, Vector &) const
Definition: tmop_pa_h2m_c0.cpp:94
mfem::TMOP_Metric_347::sh_metric
TMOP_QualityMetric * sh_metric
Definition: tmop.hpp:919
mfem::DiscreteAdaptTC::ResetRefinementTspecData
void ResetRefinementTspecData()
Definition: tmop.hpp:1611
mfem::TMOP_Metric_211::ie
InvariantsEvaluator2D< double > ie
Definition: tmop.hpp:577
mfem::TMOP_Metric_skew2D::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.hpp:243
mfem::TMOP_Metric_aspratio3D::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:306
mfem::TMOP_Metric_323::EvalWMatrixForm
virtual double EvalWMatrixForm(const DenseMatrix &Jpt) const
Evaluates the metric in matrix form (opposed to invariant form). Used for validating the invariant ev...
Definition: tmop.cpp:1226
mfem::TargetConstructor::SetNodes
void SetNodes(const GridFunction &n)
Set the nodes to be used in the target-matrix construction.
Definition: tmop.hpp:1314
mfem::TMOP_Integrator::AssembleElementVectorExact
void AssembleElementVectorExact(const FiniteElement &el, ElementTransformation &T, const Vector &elfun, Vector &elvect)
Definition: tmop.cpp:3244
mfem::TMOP_Integrator::E
Vector E
Definition: tmop.hpp:1744
mfem::TMOP_Metric_077::Id
virtual int Id() const
Return the metric ID.
Definition: tmop.hpp:516
mfem::TMOP_Metric_328::sz_metric
TMOP_QualityMetric * sz_metric
Definition: tmop.hpp:838
mfem::TMOP_Integrator::targetC
const TargetConstructor * targetC
Definition: tmop.hpp:1646
mfem::TMOP_Integrator::ElemPertEnergy
Array< Vector * > ElemPertEnergy
Definition: tmop.hpp:1699
mfem::TMOP_Integrator::lim_nodes0
const GridFunction * lim_nodes0
Definition: tmop.hpp:1660
mfem::TMOP_Integrator::adapt_lim_pgf0
const ParGridFunction * adapt_lim_pgf0
Definition: tmop.hpp:1672
mfem::TMOP_Metric_333::sz_metric
TMOP_QualityMetric * sz_metric
Definition: tmop.hpp:878
mfem::TMOP_Metric_332::sh_metric
TMOP_QualityMetric * sh_metric
Definition: tmop.hpp:856
mfem::TMOP_Metric_066::sh_metric
TMOP_QualityMetric * sh_metric
Definition: tmop.hpp:484
mfem::TMOP_Metric_313::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.cpp:1016
mfem::NonlinearFormIntegrator::AssemblePA
virtual void AssemblePA(const FiniteElementSpace &fes)
Method defining partial assembly.
Definition: nonlininteg.cpp:25
mfem::TMOP_Metric_347
3D barrier Shape+Size (VS) metric, well-posed (polyconvex).
Definition: tmop.hpp:915
mfem::TMOP_Combo_QualityMetric
Definition: tmop.hpp:85
mfem::TMOP_Metric_022::ie
InvariantsEvaluator2D< double > ie
Definition: tmop.hpp:391
mfem::TMOP_WorstCaseUntangleOptimizer_Metric::WorstCaseType::PMean
mfem::TMOP_QuadraticLimiter::Eval_d2
virtual void Eval_d2(const Vector &x, const Vector &x0, double dist, DenseMatrix &d2) const
Returns the Hessian of the limiting function f(x, x0, d) with respect to x.
Definition: tmop.hpp:1112
mfem::TMOP_Metric_302::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:862
mfem::TMOP_Metric_322::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.cpp:1173
mfem::TMOPComboIntegrator::AssembleGradPA
virtual void AssembleGradPA(const Vector &, const FiniteElementSpace &)
Prepare the integrator for partial assembly (PA) gradient evaluations on the given FE space fes at th...
Definition: tmop.cpp:4417
mfem::TMOP_Metric_323::ie
InvariantsEvaluator3D< double > ie
Definition: tmop.hpp:816
mfem::DiscreteAdaptTC::SetParDiscreteTargetAspectRatio
virtual void SetParDiscreteTargetAspectRatio(const ParGridFunction &tspec_)
Definition: tmop.cpp:1805
mfem::TMOP_Integrator::AssemblePA
virtual void AssemblePA(const FiniteElementSpace &)
Method defining partial assembly.
Definition: tmop_pa.cpp:179
mfem::TMOP_Integrator::AssembleGradPA_C0_3D
void AssembleGradPA_C0_3D(const Vector &) const
Definition: tmop_pa_h3s_c0.cpp:169
mfem::TMOP_ExponentialLimiter::~TMOP_ExponentialLimiter
virtual ~TMOP_ExponentialLimiter()
Definition: tmop.hpp:1173
mfem::TMOP_Metric_004::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.cpp:380
mfem::TargetConstructor::~TargetConstructor
virtual ~TargetConstructor()
Definition: tmop.hpp:1300
mfem::TargetConstructor::ComputeElementTargetsGradient
virtual void ComputeElementTargetsGradient(const IntegrationRule &ir, const Vector &elfun, IsoparametricTransformation &Tpr, DenseTensor &dJtr) const
Definition: tmop.cpp:1625
mfem::TMOPComboIntegrator::ParEnableNormalization
void ParEnableNormalization(const ParGridFunction &x)
Definition: tmop.cpp:4393
mfem::TMOP_Metric_252::ie
InvariantsEvaluator2D< double > ie
Definition: tmop.hpp:596
mfem::TMOP_Integrator::AssembleElementVector
virtual void AssembleElementVector(const FiniteElement &el, ElementTransformation &T, const Vector &elfun, Vector &elvect)
Perform the local action of the NonlinearFormIntegrator.
Definition: tmop.cpp:3215
mfem::TMOP_Metric_004::ie
InvariantsEvaluator2D< double > ie
Definition: tmop.hpp:323
mfem::TMOP_Metric_098
2D barrier Shape+Size+Orientation (VOS) metric (polyconvex).
Definition: tmop.hpp:558
mfem::DiscreteAdaptTC::GetTSpecData
GridFunction * GetTSpecData()
Get the entire tspec.
Definition: tmop.hpp:1523
mfem::DiscreteAdaptTC::tspec_fesv
FiniteElementSpace * tspec_fesv
Definition: tmop.hpp:1443
mfem::TMOP_Integrator::metric_coeff
Coefficient * metric_coeff
Definition: tmop.hpp:1653
mfem::TMOP_Integrator::AssembleElemGradSurfFit
void AssembleElemGradSurfFit(const FiniteElement &el_x, IsoparametricTransformation &Tpr, DenseMatrix &mat)
Definition: tmop.cpp:3642
mfem::TMOP_WorstCaseUntangleOptimizer_Metric::max_muT
double max_muT
Definition: tmop.hpp:168
mfem::TMOP_Integrator::h_metric
TMOP_QualityMetric * h_metric
Definition: tmop.hpp:1644
mfem::TMOP_Combo_QualityMetric::tmop_q_arr
Array< TMOP_QualityMetric * > tmop_q_arr
Definition: tmop.hpp:88
mfem::TMOP_Metric_360::Id
virtual int Id() const
Return the metric ID.
Definition: tmop.hpp:973
mfem::TMOP_Metric_321::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.cpp:1115
mfem::TMOP_Metric_004::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:368
mfem::TMOP_WorstCaseUntangleOptimizer_Metric::GetBarrierType
virtual BarrierType GetBarrierType()
Definition: tmop.hpp:213
mfem::TMOP_Integrator::AssembleDiagonalPA_2D
void AssembleDiagonalPA_2D(Vector &) const
Definition: tmop_pa_h2d.cpp:147
mfem::DiscreteAdaptTC::RestoreTargetSpecificationAtNode
void RestoreTargetSpecificationAtNode(ElementTransformation &T, int nodenum)
Definition: tmop.cpp:1997
mfem::TargetConstructor::Parallel
bool Parallel() const
Definition: tmop.hpp:1303
mfem::TMOP_Metric_315::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.cpp:1037
mfem::TMOP_WorstCaseUntangleOptimizer_Metric::BarrierType::Pseudo
mfem::TMOP_Integrator::AssemblePA_Limiting
void AssemblePA_Limiting()
Definition: tmop_pa.cpp:51
mfem::TMOP_Metric_080::sh_metric
TMOP_QualityMetric * sh_metric
Definition: tmop.hpp:525
mfem::TMOP_AMetric_107a
2D barrier Shape+Orientation (OS) metric (polyconvex).
Definition: tmop.hpp:1032
mfem::TMOP_QualityMetric::TMOP_QualityMetric
TMOP_QualityMetric()
Definition: tmop.hpp:34
mfem::DiscreteAdaptTC::SetTspecAtIndex
void SetTspecAtIndex(int idx, const GridFunction &tspec_)
Definition: tmop.cpp:1855
mfem::TMOP_Integrator::GetRefinementElementEnergy
virtual double GetRefinementElementEnergy(const FiniteElement &el, ElementTransformation &T, const Vector &elfun, const IntegrationRule &irule)
Computes the mean of the energies of the given element&#39;s children.
Definition: tmop.cpp:3075
mfem::TMOP_Combo_QualityMetric::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.cpp:43
mfem::TMOP_Metric_002::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.cpp:358
mfem::TMOP_Integrator::~TMOP_Integrator
~TMOP_Integrator()
Definition: tmop.cpp:2774
mfem::TMOP_Integrator::GetLocalStateEnergyPA_3D
double GetLocalStateEnergyPA_3D(const Vector &) const
Definition: tmop_pa_w3.cpp:155
mfem::TMOP_Integrator::dxscale
double dxscale
Definition: tmop.hpp:1690
mfem::TMOP_Integrator::lim_coeff
Coefficient * lim_coeff
Definition: tmop.hpp:1661
mfem::TMOP_Metric_022::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.cpp:502
mfem::TMOP_Metric_328
3D barrier Shape+Size (VS) metric (polyconvex).
Definition: tmop.hpp:834
mfem::TMOP_Metric_080::ie
InvariantsEvaluator2D< double > ie
Definition: tmop.hpp:524
mfem::TMOP_Integrator::surf_fit_eval
AdaptivityEvaluator * surf_fit_eval
Definition: tmop.hpp:1682
mfem::TMOP_Metric_009::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.cpp:449
mfem::TMOP_WorstCaseUntangleOptimizer_Metric::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.hpp:199
mfem::TMOP_AMetric_011
Definition: tmop.hpp:978
mfem::TMOP_Metric_066::TMOP_Metric_066
TMOP_Metric_066(double gamma)
Definition: tmop.hpp:487
mfem::TMOP_ExponentialLimiter::Eval_d1
virtual void Eval_d1(const Vector &x, const Vector &x0, double dist, Vector &d1) const
Returns the gradient of the limiting function f(x, x0, d) with respect to x.
Definition: tmop.hpp:1134
mfem::TMOP_Metric_058::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.cpp:649
mfem::TMOP_Metric_304::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.cpp:952
mfem::TMOP_QuadraticLimiter::~TMOP_QuadraticLimiter
virtual ~TMOP_QuadraticLimiter()
Definition: tmop.hpp:1120
mfem::TMOP_Metric_315::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.cpp:1045
mfem::DiscreteAdaptTC::GetTSpecFESpace
FiniteElementSpace * GetTSpecFESpace()
Get the FESpace associated with tspec.
Definition: tmop.hpp:1521
mfem::TMOP_WorstCaseUntangleOptimizer_Metric::min_detT
double min_detT
Definition: tmop.hpp:167
mfem::TMOP_Metric_050
Definition: tmop.hpp:407
mfem::TMOP_AMetric_126::sz_metric
TMOP_QualityMetric * sz_metric
Definition: tmop.hpp:1054
mfem::TMOP_QualityMetric::SetTargetJacobian
virtual void SetTargetJacobian(const DenseMatrix &Jtr_)
Specify the reference-element -> target-element Jacobian matrix for the point of interest.
Definition: tmop.hpp:43
mfem::TMOP_Metric_347::ie
InvariantsEvaluator2D< double > ie
Definition: tmop.hpp:918
mfem::TMOP_Metric_211::TMOP_Metric_211
TMOP_Metric_211(double epsilon=1e-4)
Definition: tmop.hpp:580
mfem::TMOP_Integrator::GetFDh
double GetFDh() const
Definition: tmop.hpp:2048
mfem::TMOP_Integrator::AssembleElemGradAdaptLim
void AssembleElemGradAdaptLim(const FiniteElement &el, IsoparametricTransformation &Tpr, const IntegrationRule &ir, const Vector &weights, DenseMatrix &m)
Definition: tmop.cpp:3527
mfem::TMOP_WorstCaseUntangleOptimizer_Metric::muT_ep
double muT_ep
Definition: tmop.hpp:172
mfem::TMOP_Metric_aspratio2D::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:286
mfem::TMOP_Integrator::AssembleElementGrad
virtual void AssembleElementGrad(const FiniteElement &el, ElementTransformation &T, const Vector &elfun, DenseMatrix &elmat)
Assemble the local gradient matrix.
Definition: tmop.cpp:3229
mfem::TMOP_Integrator::maps_lim
const DofToQuad * maps_lim
Definition: tmop.hpp:1746
mfem::TMOP_Metric_211
2D untangling metric.
Definition: tmop.hpp:573
mfem::TMOP_Metric_315::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:1029
mfem::TMOP_Metric_321::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.cpp:1126
mfem::FiniteElementSpace
Class FiniteElementSpace - responsible for providing FEM view of the mesh, mainly managing the set of...
Definition: fespace.hpp:96
mfem::TMOP_Metric_311
3D Size (V) untangling metric.
Definition: tmop.hpp:694
mfem::TMOP_Metric_323::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.cpp:1249
mfem::TMOP_Metric_322::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:1162
mfem::TMOP_Metric_211::eps
const double eps
Definition: tmop.hpp:576
mfem::TMOP_Combo_QualityMetric::SetTargetJacobian
virtual void SetTargetJacobian(const DenseMatrix &Jtr_)
Specify the reference-element -> target-element Jacobian matrix for the point of interest.
Definition: tmop.hpp:98
mfem::TMOP_Metric_056
Definition: tmop.hpp:442
mfem::TMOP_Integrator::SetLimitingNodes
void SetLimitingNodes(const GridFunction &n0)
Update the original/reference nodes used for limiting.
Definition: tmop.hpp:1976
mfem::DiscreteAdaptTC::tspec_refine
DenseMatrix tspec_refine
Definition: tmop.hpp:1432
mfem::TMOP_Metric_321::EvalWMatrixForm
virtual double EvalWMatrixForm(const DenseMatrix &Jpt) const
Evaluates the metric in matrix form (opposed to invariant form). Used for validating the invariant ev...
Definition: tmop.cpp:1094
mfem::TMOP_AMetric_126::TMOP_AMetric_126
TMOP_AMetric_126(double gamma)
Definition: tmop.hpp:1057
mfem::Coefficient
Base class Coefficients that optionally depend on space and time. These are used by the BilinearFormI...
Definition: coefficient.hpp:41
mfem::TMOP_Metric_085::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.hpp:549
mfem::TMOP_Metric_352::ie
InvariantsEvaluator3D< double > ie
Definition: tmop.hpp:941
mfem::TMOP_WorstCaseUntangleOptimizer_Metric::WorstCaseType::Beta
mfem::TMOP_Combo_QualityMetric::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:33
mfem::TMOP_Integrator::AddMultPA_C0_3D
void AddMultPA_C0_3D(const Vector &, Vector &) const
Definition: tmop_pa_p3_c0.cpp:160
mfem::subtract
void subtract(const Vector &x, const Vector &y, Vector &z)
Definition: vector.cpp:461
mfem::AnalyticAdaptTC::matrix_tspec
TMOPMatrixCoefficient * matrix_tspec
Definition: tmop.hpp:1380
mfem::TMOP_Integrator::AssembleDiagonalPA_C0_2D
void AssembleDiagonalPA_C0_2D(Vector &) const
Definition: tmop_pa_h2d_c0.cpp:84
mfem::TMOP_Metric_002::EvalWMatrixForm
virtual double EvalWMatrixForm(const DenseMatrix &Jpt) const
Evaluates the metric in matrix form (opposed to invariant form). Used for validating the invariant ev...
Definition: tmop.cpp:341
mfem::TargetConstructor::GetNodes
const GridFunction * GetNodes() const
Get the nodes to be used in the target-matrix construction.
Definition: tmop.hpp:1317
mfem::TMOP_Metric_066::ie
InvariantsEvaluator2D< double > ie
Definition: tmop.hpp:483
mfem::TMOP_Metric_322::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.cpp:1189
mfem::TMOP_Metric_313::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:996
mfem::TMOP_Integrator::GetFDFlag
bool GetFDFlag() const
Definition: tmop.hpp:2047
mfem::TMOP_AMetric_011::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.hpp:987
mfem::TargetConstructor::ContainsVolumeInfo
virtual bool ContainsVolumeInfo() const
Checks if the target matrices contain non-trivial size specification.
Definition: tmop.cpp:1540
mfem::TMOP_Metric_056::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:600
mfem::MatrixCoefficient
Base class for Matrix Coefficients that optionally depend on time and space.
Definition: coefficient.hpp:906
mfem::TMOP_Metric_050::ie
InvariantsEvaluator2D< double > ie
Definition: tmop.hpp:410
mfem::TMOP_Metric_321::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:1104
mfem::TMOP_Integrator::ReleasePADeviceMemory
void ReleasePADeviceMemory(bool copy_to_host=true)
Definition: tmop.cpp:2760
mfem::TMOP_Metric_321::Id
virtual int Id() const
Return the metric ID.
Definition: tmop.hpp:788
mfem::TMOP_QuadraticLimiter::Eval_d1
virtual void Eval_d1(const Vector &x, const Vector &x0, double dist, Vector &d1) const
Returns the gradient of the limiting function f(x, x0, d) with respect to x.
Definition: tmop.hpp:1103
mfem::DenseMatrix::Clear
void Clear()
Delete the matrix data array (if owned) and reset the matrix state.
Definition: densemat.hpp:98
mfem::TMOP_AMetric_014a::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.hpp:1005
mfem::TMOP_Integrator::DisableLimiting
void DisableLimiting()
Definition: tmop.hpp:1804
mfem::TMOPComboIntegrator::AssembleElementGrad
virtual void AssembleElementGrad(const FiniteElement &el, ElementTransformation &T, const Vector &elfun, DenseMatrix &elmat)
Assemble the local gradient matrix.
Definition: tmop.cpp:4335
mfem::DofToQuad
Structure representing the matrices/tensors needed to evaluate (in reference space) the values...
Definition: fe_base.hpp:135
mfem::TMOP_Metric_252::TMOP_Metric_252
TMOP_Metric_252(double &t0)
Note that t0 is stored by reference.
Definition: tmop.hpp:600
mfem::TMOP_Metric_328::TMOP_Metric_328
TMOP_Metric_328(double gamma)
Definition: tmop.hpp:841
mfem::TMOP_Metric_014::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.hpp:378
mfem::DiscreteAdaptTC::Jtrcomp
DenseTensor Jtrcomp
Definition: tmop.hpp:1439
mfem::AdaptivityEvaluator::SetParMetaInfo
void SetParMetaInfo(const ParMesh &m, const ParFiniteElementSpace &f)
Parallel version of SetSerialMetaInfo.
Definition: tmop.cpp:2730
mfem::NonlinearFormIntegrator::IntRule
const IntegrationRule * IntRule
Definition: nonlininteg.hpp:30
mfem::DiscreteAdaptTC::ResetUpdateFlags
void ResetUpdateFlags()
Used in combination with the Update methods to avoid extra computations.
Definition: tmop.hpp:1515
mfem::TMOP_Metric_080::Id
virtual int Id() const
Return the metric ID.
Definition: tmop.hpp:536
mfem::AnalyticAdaptTC::AnalyticAdaptTC
AnalyticAdaptTC(TargetType ttype)
Definition: tmop.hpp:1383
mfem::TMOP_AMetric_036::ie
InvariantsEvaluator3D< double > ie
Definition: tmop.hpp:1017
mfem::TMOPComboIntegrator::AddTMOPIntegrator
void AddTMOPIntegrator(TMOP_Integrator *ti)
Adds a new TMOP_Integrator to the combination.
Definition: tmop.hpp:2081
mfem::TMOP_Metric_085::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:699
mfem::DiscreteAdaptTC::tspec_gf
GridFunction * tspec_gf
Definition: tmop.hpp:1445
mfem::TMOP_Metric_skew2D
2D non-barrier Skew metric.
Definition: tmop.hpp:237
mfem::TMOP_Integrator::AssembleGradDiagonalPA
virtual void AssembleGradDiagonalPA(Vector &) const
Method for computing the diagonal of the gradient with partial assembly.
Definition: tmop_pa.cpp:225
mfem::TMOP_Metric_323::Id
virtual int Id() const
Return the metric ID.
Definition: tmop.hpp:830
mfem::TMOP_Metric_058::EvalWMatrixForm
virtual double EvalWMatrixForm(const DenseMatrix &Jpt) const
Evaluates the metric in matrix form (opposed to invariant form). Used for validating the invariant ev...
Definition: tmop.cpp:630
mfem::TMOP_Integrator::UpdateAfterMeshTopologyChange
void UpdateAfterMeshTopologyChange()
Definition: tmop.cpp:2912
mfem::TMOP_WorstCaseUntangleOptimizer_Metric::SetMaxMuT
virtual void SetMaxMuT(double max_muT_)
Definition: tmop.hpp:211
mfem::TMOP_Integrator::PMatI
DenseMatrix PMatI
Definition: tmop.hpp:1711
mfem::TMOP_WorstCaseUntangleOptimizer_Metric::SetMinDetT
virtual void SetMinDetT(double min_detT_)
Definition: tmop.hpp:209
mfem::TMOP_Metric_316::ie
InvariantsEvaluator3D< double > ie
Definition: tmop.hpp:755
mfem::TMOP_Metric_009
2D barrier Shape+Size (VS) metric (not polyconvex).
Definition: tmop.hpp:356
mfem::TMOP_QualityMetric::SetTransformation
void SetTransformation(ElementTransformation &)
The method HyperelasticModel::SetTransformation() is hidden for TMOP_QualityMetrics, because it is not used.
Definition: tmop.hpp:31
mfem::TargetConstructor::ComputeElementTargets
virtual void ComputeElementTargets(int e_id, const FiniteElement &fe, const IntegrationRule &ir, const Vector &elfun, DenseTensor &Jtr) const
Given an element and quadrature rule, computes ref->target transformation Jacobians for each quadratu...
Definition: tmop.cpp:1554
mfem::TMOP_Integrator::GetLocalStateEnergyPA_C0_2D
double GetLocalStateEnergyPA_C0_2D(const Vector &) const
Definition: tmop_pa_w2_c0.cpp:131
mfem::TMOP_Integrator::ComputeFDh
void ComputeFDh(const Vector &x, const FiniteElementSpace &fes)
Determines the perturbation, h, for FD-based approximation.
Definition: tmop.cpp:4074
mfem::TMOP_Integrator::Jtr_debug_grad
bool Jtr_debug_grad
Definition: tmop.hpp:1743
mfem::TMOP_Metric_360::EvalWMatrixForm
virtual double EvalWMatrixForm(const DenseMatrix &Jpt) const
Evaluates the metric in matrix form (opposed to invariant form). Used for validating the invariant ev...
Definition: tmop.cpp:1311
mfem::TMOP_Integrator::ComputeNormalizationEnergies
void ComputeNormalizationEnergies(const GridFunction &x, double &metric_energy, double &lim_energy, double &surf_fit_gf_energy)
Definition: tmop.cpp:3949
mfem::TMOP_LimiterFunction::Eval
virtual double Eval(const Vector &x, const Vector &x0, double d) const =0
Returns the limiting function, f(x, x0, d).
mfem::TMOP_Integrator::surf_fit_coeff
Coefficient * surf_fit_coeff
Definition: tmop.hpp:1681
mfem::IntegrationPoint
Class for integration point with weight.
Definition: intrules.hpp:25
mfem::TMOP_QualityMetric::EvalWMatrixForm
virtual double EvalWMatrixForm(const DenseMatrix &Jpt) const
Evaluates the metric in matrix form (opposed to invariant form). Used for validating the invariant ev...
Definition: tmop.hpp:47
mfem::TMOP_Metric_050::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.cpp:550
mfem::DiscreteAdaptTC::UpdateHessianTargetSpecification
void UpdateHessianTargetSpecification(const Vector &x, double dx, bool use_flag=false, int x_ordering=Ordering::byNODES)
Definition: tmop.cpp:2642
mfem::TMOP_Metric_347::~TMOP_Metric_347
virtual ~TMOP_Metric_347()
Definition: tmop.hpp:933
mfem::TMOP_Metric_332::GetGamma
double GetGamma() const
Definition: tmop.hpp:868
mfem::DiscreteAdaptTC::adapt_eval
AdaptivityEvaluator * adapt_eval
Definition: tmop.hpp:1462
mfem::TMOP_Combo_QualityMetric::SetWeights
void SetWeights(const Vector &weights)
Changes the weights of the metrics in the combination.
Definition: tmop.hpp:128
mfem::TMOP_Metric_252::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.cpp:775
mfem::DiscreteAdaptTC::ptspec_fesv
ParFiniteElementSpace * ptspec_fesv
Definition: tmop.hpp:1448
mfem::TMOP_Integrator::dx
double dx
Definition: tmop.hpp:1689
mfem::TMOP_Metric_301::ie
InvariantsEvaluator3D< double > ie
Definition: tmop.hpp:615
mfem::TMOP_Integrator::fes
const FiniteElementSpace * fes
Definition: tmop.hpp:1748
mfem::TMOPComboIntegrator::tmopi
Array< TMOP_Integrator * > tmopi
Definition: tmop.hpp:2070
mfem::IsoparametricTransformation
A standard isoparametric element transformation.
Definition: eltrans.hpp:361
mfem::TMOP_Integrator::ComputeMinJac
void ComputeMinJac(const Vector &x, const FiniteElementSpace &fes)
Definition: tmop.cpp:4020
mfem::TMOP_Integrator::AssembleDiagonalPA_C0_3D
void AssembleDiagonalPA_C0_3D(Vector &) const
Definition: tmop_pa_h3d_c0.cpp:111
mfem::TMOP_Integrator::TMOP_Integrator
TMOP_Integrator(TMOP_QualityMetric *m, TargetConstructor *tc, TMOP_QualityMetric *hm)
Definition: tmop.hpp:1870
mfem::TMOP_AMetric_011::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:1347
mfem::TMOP_Integrator::ActionIntegrationRule
const IntegrationRule & ActionIntegrationRule(const FiniteElement &el) const
Definition: tmop.hpp:1819
mfem::DenseMatrix::Diag
void Diag(double c, int n)
Creates n x n diagonal matrix with diagonal elements c.
Definition: densemat.cpp:1390
mfem::TargetConstructor::GetComm
MPI_Comm GetComm() const
Definition: tmop.hpp:1304
mfem::NonlinearFormIntegrator
This class is used to express the local action of a general nonlinear finite element operator...
Definition: nonlininteg.hpp:27
mfem::TMOP_Integrator::AddMultGradPA
virtual void AddMultGradPA(const Vector &, Vector &) const
Method for partially assembled gradient action.
Definition: tmop_pa.cpp:272
mfem::TMOP_Integrator::GetFDDerivative
double GetFDDerivative(const FiniteElement &el, ElementTransformation &T, Vector &elfun, const int nodenum, const int idir, const double baseenergy, bool update_stored)
Definition: tmop.cpp:3718
mfem::TMOP_ExponentialLimiter
Exponential limiter function in TMOP_Integrator.
Definition: tmop.hpp:1124
mfem::TMOP_Metric_aspratio2D::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.hpp:276
mfem::TMOP_AMetric_036
2D barrier Shape+Size+Orientation (VOS) metric (polyconvex).
Definition: tmop.hpp:1014
mfem::TMOP_Metric_303::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.cpp:918
mfem::TMOP_Metric_311::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.cpp:973
mfem::TMOP_Integrator::fdflag
bool fdflag
Definition: tmop.hpp:1688
mfem::TMOP_Integrator::surf_fit_normal
double surf_fit_normal
Definition: tmop.hpp:1683
mfem::TMOP_Metric_313
3D Shape (S) metric, untangling version of 303.
Definition: tmop.hpp:713
dim
int dim
Definition: ex24.cpp:53
mfem::TMOP_Metric_315::Id
virtual int Id() const
Return the metric ID.
Definition: tmop.hpp:748
mfem::TMOP_Integrator::GetElementEnergy
virtual double GetElementEnergy(const FiniteElement &el, ElementTransformation &T, const Vector &elfun)
Computes the integral of W(Jacobian(Trt)) over a target zone.
Definition: tmop.cpp:2938
mfem::TMOP_AMetric_036::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.hpp:1026
mfem::TMOP_Integrator::AssembleElemVecAdaptLim
void AssembleElemVecAdaptLim(const FiniteElement &el, IsoparametricTransformation &Tpr, const IntegrationRule &ir, const Vector &weights, DenseMatrix &mat)
Definition: tmop.cpp:3491
mfem::TMOP_Integrator::H0
Vector H0
Definition: tmop.hpp:1744
mfem::TMOP_Integrator::ParUpdateAfterMeshTopologyChange
void ParUpdateAfterMeshTopologyChange()
Definition: tmop.cpp:2925
mfem::TMOPComboIntegrator::GetDerefinementElementEnergy
virtual double GetDerefinementElementEnergy(const FiniteElement &el, ElementTransformation &T, const Vector &elfun)
Definition: tmop.cpp:4364
mfem::TMOP_AMetric_014a::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.hpp:1008
mfem::TargetConstructor::ComputeAvgVolume
void ComputeAvgVolume() const
Definition: tmop.cpp:1426
mfem::Vector::Destroy
void Destroy()
Destroy a vector.
Definition: vector.hpp:589
mfem::TMOP_LimiterFunction::Eval_d1
virtual void Eval_d1(const Vector &x, const Vector &x0, double dist, Vector &d1) const =0
Returns the gradient of the limiting function f(x, x0, d) with respect to x.
mfem::TMOP_Metric_347::TMOP_Metric_347
TMOP_Metric_347(double gamma)
Definition: tmop.hpp:922
mfem::TMOP_Metric_002::Id
virtual int Id() const
Return the metric ID.
Definition: tmop.hpp:315
mfem::TMOP_Metric_211::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.cpp:742
mfem::TMOP_Metric_aspratio3D
3D non-barrier Aspect ratio metric.
Definition: tmop.hpp:282
mfem::DiscreteAdaptTC::GetTspecPert2H
const Vector & GetTspecPert2H()
Definition: tmop.hpp:1575
mfem::TMOP_Metric_058::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.cpp:657
mfem::DiscreteAdaptTC::GetTspecPert1H
const Vector & GetTspecPert1H()
Definition: tmop.hpp:1574
mfem::TMOP_Integrator::AssembleElementGradFD
void AssembleElementGradFD(const FiniteElement &el, ElementTransformation &T, const Vector &elfun, DenseMatrix &elmat)
Definition: tmop.cpp:3806
mfem::DiscreteAdaptTC::GetTSpecParFESpace
ParFiniteElementSpace * GetTSpecParFESpace()
Definition: tmop.hpp:1528
mfem::TMOP_Metric_334::sz_metric
TMOP_QualityMetric * sz_metric
Definition: tmop.hpp:897
mfem::TMOP_Metric_009::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.cpp:440
mfem::TMOP_Metric_002::ie
InvariantsEvaluator2D< double > ie
Definition: tmop.hpp:301
mfem::TMOP_Integrator::O
Vector O
Definition: tmop.hpp:1744
mfem::DiscreteAdaptTC::SetParDiscreteTargetSpec
virtual void SetParDiscreteTargetSpec(const ParGridFunction &tspec_)
Definition: tmop.cpp:1825
mfem::TMOP_Metric_007::ie
InvariantsEvaluator2D< double > ie
Definition: tmop.hpp:341
mfem::TMOP_Metric_328::sh_metric
TMOP_QualityMetric * sh_metric
Definition: tmop.hpp:838
mfem::HyperelasticModel
Abstract class for hyperelastic models.
Definition: nonlininteg.hpp:193
mfem::TMOP_Metric_304::Id
virtual int Id() const
Return the metric ID.
Definition: tmop.hpp:690
mfem::TMOP_Metric_323::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.cpp:1240
mfem::TMOP_Integrator::adapt_lim_gf
GridFunction * adapt_lim_gf
Definition: tmop.hpp:1674
mfem::TMOP_WorstCaseUntangleOptimizer_Metric::BarrierType::Shifted
mfem::TMOP_Metric_333::TMOP_Metric_333
TMOP_Metric_333(double gamma)
Definition: tmop.hpp:881
mfem::TargetConstructor::TargetConstructor
TargetConstructor(TargetType ttype, MPI_Comm mpicomm)
Constructor for use in parallel.
Definition: tmop.hpp:1296
mfem::TMOP_Metric_313::Id
virtual int Id() const
Return the metric ID.
Definition: tmop.hpp:730
mfem::TMOP_Integrator::surf_fit_gf
GridFunction * surf_fit_gf
Definition: tmop.hpp:1679
mfem::TMOP_Integrator::AssembleGradPA_3D
void AssembleGradPA_3D(const Vector &) const
Definition: tmop_pa_h3s.cpp:337
mfem::TMOP_WorstCaseUntangleOptimizer_Metric::btype
BarrierType btype
Definition: tmop.hpp:173
mfem::TMOP_Integrator::GetLocalStateEnergyPA_2D
double GetLocalStateEnergyPA_2D(const Vector &) const
Definition: tmop_pa_w2.cpp:145
mfem::TMOP_Integrator::TMOP_Integrator
TMOP_Integrator(TMOP_QualityMetric *m, TargetConstructor *tc)
Definition: tmop.hpp:1885
mfem::DiscreteAdaptTC::FinalizeParDiscreteTargetSpec
void FinalizeParDiscreteTargetSpec(const ParGridFunction &tspec_)
Definition: tmop.cpp:1729
mfem::DiscreteAdaptTC::tspec_pgf
ParGridFunction * tspec_pgf
Definition: tmop.hpp:1450
mfem::Vector
Vector data type.
Definition: vector.hpp:60
mfem::DiscreteAdaptTC::GetDiscreteTargetSpec
void GetDiscreteTargetSpec(GridFunction &tspec_, int idx)
Get one of the discrete fields from tspec.
Definition: tmop.cpp:1929
mfem::TMOP_Integrator::DSh
DenseMatrix DSh
Definition: tmop.hpp:1711
mfem::TMOP_WorstCaseUntangleOptimizer_Metric::alpha
double alpha
Definition: tmop.hpp:170
mfem::TMOP_Metric_334::GetGamma
double GetGamma() const
Definition: tmop.hpp:909
mfem::TMOP_Integrator::surf_fit_marker
const Array< bool > * surf_fit_marker
Definition: tmop.hpp:1680
mfem::TMOP_Metric_301::EvalWMatrixForm
virtual double EvalWMatrixForm(const DenseMatrix &Jpt) const
Evaluates the metric in matrix form (opposed to invariant form). Used for validating the invariant ev...
Definition: tmop.cpp:793
mfem::TMOP_Metric_332::TMOP_Metric_332
TMOP_Metric_332(double gamma)
Definition: tmop.hpp:859
mfem::TMOP_Metric_347::Id
virtual int Id() const
Return the metric ID.
Definition: tmop.hpp:930
mfem::TMOP_Integrator::DS
DenseMatrix DS
Definition: tmop.hpp:1711
mfem::TMOP_Metric_022::TMOP_Metric_022
TMOP_Metric_022(double &t0)
Definition: tmop.hpp:394
mfem::TMOP_Metric_333
3D barrier Shape+Size (VS) metric, well-posed (polyconvex).
Definition: tmop.hpp:874
mfem::TMOP_Metric_303::ie
InvariantsEvaluator3D< double > ie
Definition: tmop.hpp:655
mfem::TMOPComboIntegrator::AssembleGradDiagonalPA
virtual void AssembleGradDiagonalPA(Vector &) const
Method for computing the diagonal of the gradient with partial assembly.
Definition: tmop.cpp:4426
mfem::DiscreteAdaptTC::SetTspecDataForDerefinement
void SetTspecDataForDerefinement(FiniteElementSpace *fes)
Computes target specification data with respect to the coarse FE space.
Definition: tmop.cpp:2037
mfem::TargetConstructor::TargetType
TargetType
Target-matrix construction algorithms supported by this class.
Definition: tmop.hpp:1238
mfem::DiscreteAdaptTC::UpdateTargetSpecification
void UpdateTargetSpecification(const Vector &new_x, bool use_flag=false, int new_x_ordering=Ordering::byNODES)
Definition: tmop.cpp:1960
mfem::TMOP_Integrator::EnableSurfaceFitting
void EnableSurfaceFitting(const GridFunction &s0, const Array< bool > &smarker, Coefficient &coeff, AdaptivityEvaluator &ae)
Fitting of certain DOFs to the zero level set of a function.
Definition: tmop.cpp:2846
mfem::TMOP_Metric_360::ie
InvariantsEvaluator3D< double > ie
Definition: tmop.hpp:959
mfem::TMOP_Metric_252::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:755
mfem::TMOP_WorstCaseUntangleOptimizer_Metric::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:167
mfem::TMOP_Metric_311::TMOP_Metric_311
TMOP_Metric_311(double epsilon=1e-4)
Definition: tmop.hpp:701
mfem::DiscreteAdaptTC::SetSerialDiscreteTargetSpec
virtual void SetSerialDiscreteTargetSpec(const GridFunction &tspec_)
Definition: tmop.cpp:1954
mfem::TMOP_AMetric_014a::ie
InvariantsEvaluator3D< double > ie
Definition: tmop.hpp:999
mfem::DiscreteAdaptTC::SetParDiscreteTargetSkew
virtual void SetParDiscreteTargetSkew(const ParGridFunction &tspec_)
Definition: tmop.cpp:1795
mfem::TMOP_Metric_303::EvalWMatrixForm
virtual double EvalWMatrixForm(const DenseMatrix &Jpt) const
Evaluates the metric in matrix form (opposed to invariant form). Used for validating the invariant ev...
Definition: tmop.cpp:896
mfem::AnalyticAdaptTC::ComputeElementTargetsGradient
virtual void ComputeElementTargetsGradient(const IntegrationRule &ir, const Vector &elfun, IsoparametricTransformation &Tpr, DenseTensor &dJtr) const
Definition: tmop.cpp:1682
mfem::TMOPComboIntegrator::GetRefinementElementEnergy
virtual double GetRefinementElementEnergy(const FiniteElement &el, ElementTransformation &T, const Vector &elfun, const IntegrationRule &irule)
Definition: tmop.cpp:4351
mfem::TMOP_AMetric_126::ie
InvariantsEvaluator2D< double > ie
Definition: tmop.hpp:1053
mfem::TMOP_Integrator::exact_action
bool exact_action
Definition: tmop.hpp:1696
mfem::DiscreteAdaptTC::SetParDiscreteTargetOrientation
virtual void SetParDiscreteTargetOrientation(const ParGridFunction &tspec_)
Definition: tmop.cpp:1815
mfem::AnalyticAdaptTC::ComputeAllElementTargets
virtual void ComputeAllElementTargets(const FiniteElementSpace &fes, const IntegrationRule &ir, const Vector &xe, DenseTensor &Jtr) const
Computes reference-to-target transformation Jacobians for all quadrature points in all elements...
Definition: tmop_pa.cpp:138
mfem::ParGridFunction
Class for parallel grid function.
Definition: pgridfunc.hpp:32
mfem::TMOP_Metric_004::Id
virtual int Id() const
Return the metric ID.
Definition: tmop.hpp:334
mfem::TargetConstructor
Base class representing target-matrix construction algorithms for mesh optimization via the target-ma...
Definition: tmop.hpp:1234
mfem::DenseMatrix::SetSize
void SetSize(int s)
Change the size of the DenseMatrix to s x s.
Definition: densemat.hpp:105
mfem::DiscreteAdaptTC::~DiscreteAdaptTC
virtual ~DiscreteAdaptTC()
Definition: tmop.cpp:2709
mfem::TMOP_Metric_334::TMOP_Metric_334
TMOP_Metric_334(double gamma)
Definition: tmop.hpp:900
mfem::TMOP_Integrator::AddMultPA_2D
void AddMultPA_2D(const Vector &, Vector &) const
Definition: tmop_pa_p2.cpp:167
mfem::AnalyticAdaptTC::SetAnalyticTargetSpec
virtual void SetAnalyticTargetSpec(Coefficient *sspec, VectorCoefficient *vspec, TMOPMatrixCoefficient *mspec)
Definition: tmop.cpp:1639
mfem::TMOP_Metric_332
3D barrier Shape+Size (VS) metric (polyconvex).
Definition: tmop.hpp:853
mfem::DenseTensor
Rank 3 tensor (array of matrices)
Definition: densemat.hpp:978
mfem::TMOP_Metric_007::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:392
mfem::TMOP_Metric_316::EvalWMatrixForm
virtual double EvalWMatrixForm(const DenseMatrix &Jpt) const
Evaluates the metric in matrix form (opposed to invariant form). Used for validating the invariant ev...
Definition: tmop.cpp:1058
mfem::ParMesh
Class for parallel meshes.
Definition: pmesh.hpp:32
mfem::DiscreteAdaptTC::SetSerialDiscreteTargetSize
virtual void SetSerialDiscreteTargetSize(const GridFunction &tspec_)
Definition: tmop.cpp:1868
mfem::TMOP_Metric_332::sz_metric
TMOP_QualityMetric * sz_metric
Definition: tmop.hpp:856
mfem::TMOP_Metric_352::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.cpp:1285
mfem::TMOP_Integrator::lim_func
TMOP_LimiterFunction * lim_func
Definition: tmop.hpp:1665
mfem::TMOP_Integrator::Jtr_needs_update
bool Jtr_needs_update
Definition: tmop.hpp:1742
mfem::TMOP_Metric_080::GetGamma
double GetGamma() const
Definition: tmop.hpp:537
mfem::TMOP_Metric_302::ie
InvariantsEvaluator3D< double > ie
Definition: tmop.hpp:634
mfem::TMOP_Integrator::adapt_lim_gf0
const GridFunction * adapt_lim_gf0
Definition: tmop.hpp:1670
mfem::TMOPComboIntegrator::AssembleElementVector
virtual void AssembleElementVector(const FiniteElement &el, ElementTransformation &T, const Vector &elfun, Vector &elvect)
Perform the local action of the NonlinearFormIntegrator.
Definition: tmop.cpp:4319
mfem::TMOP_Integrator::ComputeMinDetT
double ComputeMinDetT(const Vector &x, const FiniteElementSpace &fes)
Definition: tmop.cpp:4134
mfem::TMOPComboIntegrator::AddMultPA
virtual void AddMultPA(const Vector &, Vector &) const
Method for partially assembled action.
Definition: tmop.cpp:4434
mfem::TMOP_Integrator::dim
int dim
Definition: tmop.hpp:1740
mfem::Vector::DistanceSquaredTo
double DistanceSquaredTo(const double *p) const
Compute the square of the Euclidean distance to another vector.
Definition: vector.hpp:653
mfem::TMOP_Integrator::Jpt
DenseMatrix Jpt
Definition: tmop.hpp:1711
mfem::TMOP_WorstCaseUntangleOptimizer_Metric::BarrierType::None
mfem::TMOP_Metric_085
2D barrier Shape+Orientation (OS) metric (polyconvex).
Definition: tmop.hpp:543
mfem::FiniteElement::GetOrder
int GetOrder() const
Returns the order of the finite element. In the case of anisotropic orders, returns the maximum order...
Definition: fe_base.hpp:326
mfem::TMOP_Combo_QualityMetric::wt_arr
Array< double > wt_arr
Definition: tmop.hpp:89
mfem::TMOP_Integrator::ParEnableNormalization
void ParEnableNormalization(const ParGridFunction &x)
Definition: tmop.cpp:3936
mfem::TargetConstructor::ComputeAllElementTargets_Fallback
void ComputeAllElementTargets_Fallback(const FiniteElementSpace &fes, const IntegrationRule &ir, const Vector &xe, DenseTensor &Jtr) const
Definition: tmop.cpp:1468
mfem::TMOP_Integrator::P
DenseMatrix P
Definition: tmop.hpp:1711
mfem::TMOP_Metric_316::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:1064
mfem::TMOP_WorstCaseUntangleOptimizer_Metric::wctype
WorstCaseType wctype
Definition: tmop.hpp:174
mfem::DiscreteAdaptTC::UpdateAfterMeshTopologyChange
void UpdateAfterMeshTopologyChange()
Update all discrete fields based on tspec and update for AMR.
Definition: tmop.cpp:1943
mfem::DiscreteAdaptTC::ResetDerefinementTspecData
void ResetDerefinementTspecData()
Definition: tmop.hpp:1618
mfem::TMOP_Metric_303::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:903
mfem::TMOP_Metric_050::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.cpp:558
mfem::TMOP_Metric_098::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.hpp:567
mfem::TMOP_Metric_aspratio2D::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.hpp:273
mfem::TMOP_Integrator::fd_call_flag
bool fd_call_flag
Definition: tmop.hpp:1693
mfem::TMOP_Metric_301
3D barrier Shape (S) metric, well-posed (polyconvex & invex).
Definition: tmop.hpp:612
mfem::TMOP_QuadraticLimiter::Eval
virtual double Eval(const Vector &x, const Vector &x0, double dist) const
Returns the limiting function, f(x, x0, d).
Definition: tmop.hpp:1096
mfem::TMOP_Metric_304::EvalW
virtual double EvalW(const DenseMatrix &Jpt) const
Evaluate the strain energy density function, W = W(Jpt), by using the 2D or 3D matrix invariants...
Definition: tmop.cpp:937
mfem::TMOP_Metric_301::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.cpp:818
mfem::TMOP_Metric_316::EvalP
virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
Evaluate the 1st Piola-Kirchhoff stress tensor, P = P(Jpt).
Definition: tmop.cpp:1072
mfem::TMOP_Integrator::AddMultGradPA_C0_3D
void AddMultGradPA_C0_3D(const Vector &, Vector &) const
Definition: tmop_pa_h3m_c0.cpp:98
mfem::TMOP_Metric_066::Id
virtual int Id() const
Return the metric ID.
Definition: tmop.hpp:494
mfem::TMOP_Metric_001
2D non-barrier metric without a type.
Definition: tmop.hpp:219
mfem::AdaptivityEvaluator::fes
FiniteElementSpace * fes
Definition: tmop.hpp:1185
mfem::TargetConstructor::GetTargetType
TargetType GetTargetType() const
Definition: tmop.hpp:1322
mfem::TMOP_Metric_304::ie
InvariantsEvaluator3D< double > ie
Definition: tmop.hpp:676
mfem::TMOP_Metric_313::AssembleH
virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS, const double weight, DenseMatrix &A) const
Evaluate the derivative of the 1st Piola-Kirchhoff stress tensor and assemble its contribution to the...
Definition: tmop.cpp:1021
mfem::TMOP_Metric_328::~TMOP_Metric_328
virtual ~TMOP_Metric_328()
Definition: tmop.hpp:849
mfem::DiscreteAdaptTC::coarse_tspec_fesv
FiniteElementSpace * coarse_tspec_fesv
Definition: tmop.hpp:1444
mfem::TMOP_Integrator
A TMOP integrator class based on any given TMOP_QualityMetric and TargetConstructor.
Definition: tmop.hpp:1638
mfem::TMOP_Metric_014
2D non-barrier Shape+Size+Orientation (VOS) metric (polyconvex).
Definition: tmop.hpp:372
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