MFEM v4.7.0 Finite element discretization library
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ode.hpp
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1// Copyright (c) 2010-2024, Lawrence Livermore National Security, LLC. Produced
2// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
3// LICENSE and NOTICE for details. LLNL-CODE-806117.
4//
5// This file is part of the MFEM library. For more information and source code
6// availability visit https://mfem.org.
7//
8// MFEM is free software; you can redistribute it and/or modify it under the
9// terms of the BSD-3 license. We welcome feedback and contributions, see file
10// CONTRIBUTING.md for details.
11
12#ifndef MFEM_ODE
13#define MFEM_ODE
14
15#include "../config/config.hpp"
16#include "operator.hpp"
18
19namespace mfem
20{
21
22/// Abstract class for solving systems of ODEs: dx/dt = f(x,t)
24{
25protected:
26 /// Pointer to the associated TimeDependentOperator.
27 TimeDependentOperator *f; // f(.,t) : R^n --> R^n
29
30public:
32
33 /// Associate a TimeDependentOperator with the ODE solver.
34 /** This method has to be called:
35 - Before the first call to Step().
36 - When the dimensions of the associated TimeDependentOperator change.
37 - When a time stepping sequence has to be restarted.
38 - To change the associated TimeDependentOperator. */
39 virtual void Init(TimeDependentOperator &f_);
40
41 /** @brief Perform a time step from time @a t [in] to time @a t [out] based
42 on the requested step size @a dt [in]. */
43 /** @param[in,out] x Approximate solution.
44 @param[in,out] t Time associated with the approximate solution @a x.
45 @param[in,out] dt Time step size.
46
47 The following rules describe the common behavior of the method:
48 - The input @a x [in] is the approximate solution for the input time
49 @a t [in].
50 - The input @a dt [in] is the desired time step size, defining the desired
51 target time: t [target] = @a t [in] + @a dt [in].
52 - The output @a x [out] is the approximate solution for the output time
53 @a t [out].
54 - The output @a dt [out] is the last time step taken by the method which
55 may be smaller or larger than the input @a dt [in] value, e.g. because
56 of time step control.
57 - The method may perform more than one time step internally; in this case
58 @a dt [out] is the last internal time step size.
59 - The output value of @a t [out] may be smaller or larger than
60 t [target], however, it is not smaller than @a t [in] + @a dt [out], if
61 at least one internal time step was performed.
62 - The value @a x [out] may be obtained by interpolation using internally
63 stored data.
64 - In some cases, the contents of @a x [in] may not be used, e.g. when
65 @a x [out] from a previous Step() call was obtained by interpolation.
66 - In consecutive calls to this method, the output @a t [out] of one
67 Step() call has to be the same as the input @a t [in] to the next
68 Step() call.
69 - If the previous rule has to be broken, e.g. to restart a time stepping
70 sequence, then the ODE solver must be re-initialized by calling Init()
71 between the two Step() calls. */
72 virtual void Step(Vector &x, real_t &t, real_t &dt) = 0;
73
74 /// Perform time integration from time @a t [in] to time @a tf [in].
75 /** @param[in,out] x Approximate solution.
76 @param[in,out] t Time associated with the approximate solution @a x.
77 @param[in,out] dt Time step size.
78 @param[in] tf Requested final time.
79
80 The default implementation makes consecutive calls to Step() until
81 reaching @a tf.
82 The following rules describe the common behavior of the method:
83 - The input @a x [in] is the approximate solution for the input time
84 @a t [in].
85 - The input @a dt [in] is the initial time step size.
86 - The output @a dt [out] is the last time step taken by the method which
87 may be smaller or larger than the input @a dt [in] value, e.g. because
88 of time step control.
89 - The output value of @a t [out] is not smaller than @a tf [in]. */
90 virtual void Run(Vector &x, real_t &t, real_t &dt, real_t tf)
91 {
92 while (t < tf) { Step(x, t, dt); }
93 }
94
95 /// Function for getting and setting the state vectors
96 virtual int GetMaxStateSize() { return 0; }
97 virtual int GetStateSize() { return 0; }
98 virtual const Vector &GetStateVector(int i)
99 {
100 mfem_error("ODESolver has no state vectors");
101 Vector *s = NULL; return *s; // Make some compiler happy
102 }
103 virtual void GetStateVector(int i, Vector &state)
104 {
105 mfem_error("ODESolver has no state vectors");
106 }
107 virtual void SetStateVector(int i, Vector &state)
108 {
109 mfem_error("ODESolver has no state vectors");
110 }
111
112 virtual ~ODESolver() { }
113};
114
115
116/// The classical forward Euler method
118{
119private:
120 Vector dxdt;
121
122public:
123 void Init(TimeDependentOperator &f_) override;
124
125 void Step(Vector &x, real_t &t, real_t &dt) override;
126};
127
128
129/** A family of explicit second-order RK2 methods. Some choices for the
130 parameter 'a' are:
131 a = 1/2 - the midpoint method
132 a = 1 - Heun's method
133 a = 2/3 - default, has minimal truncation error. */
134class RK2Solver : public ODESolver
135{
136private:
137 real_t a;
138 Vector dxdt, x1;
139
140public:
141 RK2Solver(const real_t a_ = 2./3.) : a(a_) { }
142
143 void Init(TimeDependentOperator &f_) override;
144
145 void Step(Vector &x, real_t &t, real_t &dt) override;
146};
147
148
149/// Third-order, strong stability preserving (SSP) Runge-Kutta method
151{
152private:
153 Vector y, k;
154
155public:
156 void Init(TimeDependentOperator &f_) override;
157
158 void Step(Vector &x, real_t &t, real_t &dt) override;
159};
160
161
162/// The classical explicit forth-order Runge-Kutta method, RK4
163class RK4Solver : public ODESolver
164{
165private:
166 Vector y, k, z;
167
168public:
169 void Init(TimeDependentOperator &f_) override;
170
171 void Step(Vector &x, real_t &t, real_t &dt) override;
172};
173
174
175/** An explicit Runge-Kutta method corresponding to a general Butcher tableau
176 +--------+----------------------+
177 | c[0] | a[0] |
178 | c[1] | a[1] a[2] |
179 | ... | ... |
180 | c[s-2] | ... a[s(s-1)/2-1] |
181 +--------+----------------------+
182 | | b[0] b[1] ... b[s-1] |
183 +--------+----------------------+ */
185{
186private:
187 int s;
188 const real_t *a, *b, *c;
189 Vector y, *k;
190
191public:
192 ExplicitRKSolver(int s_, const real_t *a_, const real_t *b_,
193 const real_t *c_);
194
195 void Init(TimeDependentOperator &f_) override;
196
197 void Step(Vector &x, real_t &t, real_t &dt) override;
198
199 virtual ~ExplicitRKSolver();
200};
201
202
203/** An 8-stage, 6th order RK method. From Verner's "efficient" 9-stage 6(5)
204 pair. */
206{
207private:
208 static MFEM_EXPORT const real_t a[28], b[8], c[7];
209
210public:
212};
213
214
215/** A 12-stage, 8th order RK method. From Verner's "efficient" 13-stage 8(7)
216 pair. */
218{
219private:
220 static const real_t a[66], b[12], c[11];
221
222public:
223 RK8Solver() : ExplicitRKSolver(12, a, b, c) { }
224};
225
226
227/** An explicit Adams-Bashforth method. */
229{
230private:
231 int s, smax;
232 const real_t *a;
233 Vector *k;
234 Array<int> idx;
235 ODESolver *RKsolver;
236 real_t dt_;
237
238 inline bool print()
239 {
240#ifdef MFEM_USE_MPI
241 return Mpi::IsInitialized() ? Mpi::Root() : true;
242#else
243 return true;
244#endif
245 }
246
247public:
248 AdamsBashforthSolver(int s_, const real_t *a_);
249
250 void Init(TimeDependentOperator &f_) override;
251
252 void Step(Vector &x, real_t &t, real_t &dt) override;
253
254 int GetMaxStateSize() override { return smax; };
255 int GetStateSize() override { return s; };
256 const Vector &GetStateVector(int i) override;
257 void GetStateVector(int i, Vector &state) override;
258 void SetStateVector(int i, Vector &state) override;
259
261 {
262 if (RKsolver) { delete RKsolver; }
263 delete [] k;
264 }
265};
266
267/** A 1-stage, 1st order AB method. */
269{
270private:
271 static MFEM_EXPORT const real_t a[1];
272
273public:
275};
276
277/** A 2-stage, 2nd order AB method. */
279{
280private:
281 static MFEM_EXPORT const real_t a[2];
282
283public:
285};
286
287/** A 3-stage, 3rd order AB method. */
289{
290private:
291 static MFEM_EXPORT const real_t a[3];
292
293public:
295};
296
297/** A 4-stage, 4th order AB method. */
299{
300private:
301 static MFEM_EXPORT const real_t a[4];
302
303public:
305};
306
307/** A 5-stage, 5th order AB method. */
309{
310private:
311 static MFEM_EXPORT const real_t a[5];
312
313public:
315};
316
317
318/** An implicit Adams-Moulton method. */
320{
321private:
322 int s, smax;
323 const real_t *a;
324 Vector *k;
325 Array<int> idx;
326 ODESolver *RKsolver;
327 real_t dt_;
328
329 inline bool print()
330 {
331#ifdef MFEM_USE_MPI
332 return Mpi::IsInitialized() ? Mpi::Root() : true;
333#else
334 return true;
335#endif
336 }
337
338public:
339 AdamsMoultonSolver(int s_, const real_t *a_);
340
341 void Init(TimeDependentOperator &f_) override;
342
343 void Step(Vector &x, real_t &t, real_t &dt) override;
344
345 int GetMaxStateSize() override { return smax-1; };
346 int GetStateSize() override { return s-1; };
347 const Vector &GetStateVector(int i) override;
348 void GetStateVector(int i, Vector &state) override;
349 void SetStateVector(int i, Vector &state) override;
350
352 {
353 if (RKsolver) { delete RKsolver; }
354 delete [] k;
355 };
356};
357
358/** A 0-stage, 1st order AM method. */
360{
361private:
362 static MFEM_EXPORT const real_t a[1];
363
364public:
366};
367
368
369/** A 1-stage, 2nd order AM method. */
371{
372private:
373 static MFEM_EXPORT const real_t a[2];
374
375public:
377};
378
379/** A 2-stage, 3rd order AM method. */
381{
382private:
383 static MFEM_EXPORT const real_t a[3];
384
385public:
387};
388
389/** A 3-stage, 4th order AM method. */
391{
392private:
393 static MFEM_EXPORT const real_t a[4];
394
395public:
397};
398
399/** A 4-stage, 5th order AM method. */
401{
402private:
403 static MFEM_EXPORT const real_t a[5];
404
405public:
407};
408
409
410/// Backward Euler ODE solver. L-stable.
412{
413protected:
415
416public:
417 void Init(TimeDependentOperator &f_) override;
418
419 void Step(Vector &x, real_t &t, real_t &dt) override;
420};
421
422
423/// Implicit midpoint method. A-stable, not L-stable.
425{
426protected:
428
429public:
430 void Init(TimeDependentOperator &f_) override;
431
432 void Step(Vector &x, real_t &t, real_t &dt) override;
433};
434
435
436/** Two stage, singly diagonal implicit Runge-Kutta (SDIRK) methods;
437 the choices for gamma_opt are:
438 0 - 3rd order method, not A-stable
439 1 - 3rd order method, A-stable, not L-stable (default)
440 2 - 2nd order method, L-stable
441 3 - 2nd order method, L-stable (has solves outside [t,t+dt]). */
443{
444protected:
447
448public:
449 SDIRK23Solver(int gamma_opt = 1);
450
451 void Init(TimeDependentOperator &f_) override;
452
453 void Step(Vector &x, real_t &t, real_t &dt) override;
454};
455
456
457/** Three stage, singly diagonal implicit Runge-Kutta (SDIRK) method of
458 order 4. A-stable, not L-stable. */
460{
461protected:
463
464public:
465 void Init(TimeDependentOperator &f_) override;
466
467 void Step(Vector &x, real_t &t, real_t &dt) override;
468};
469
470
471/** Three stage, singly diagonal implicit Runge-Kutta (SDIRK) method of
472 order 3. L-stable. */
474{
475protected:
477
478public:
479 void Init(TimeDependentOperator &f_) override;
480
481 void Step(Vector &x, real_t &t, real_t &dt) override;
482};
483
484
485/** Two stage, explicit singly diagonal implicit Runge-Kutta (ESDIRK) method
486 of order 2. A-stable. */
488{
489protected:
491
492public:
493 virtual void Init(TimeDependentOperator &f_);
494
495 virtual void Step(Vector &x, real_t &t, real_t &dt);
496};
497
498
499/** Three stage, explicit singly diagonal implicit Runge-Kutta (ESDIRK) method
500 of order 2. L-stable. */
502{
503protected:
505
506public:
507 virtual void Init(TimeDependentOperator &f_);
508
509 virtual void Step(Vector &x, real_t &t, real_t &dt);
510};
511
512
513/** Three stage, explicit singly diagonal implicit Runge-Kutta (ESDIRK) method
514 of order 3. A-stable. */
516{
517protected:
519
520public:
521 virtual void Init(TimeDependentOperator &f_);
522
523 virtual void Step(Vector &x, real_t &t, real_t &dt);
524};
525
526
527/// Generalized-alpha ODE solver from "A generalized-Î± method for integrating
528/// the filtered Navier-Stokes equations with a stabilized finite element
529/// method" by K.E. Jansen, C.H. Whiting and G.M. Hulbert.
531{
532protected:
533 mutable Vector xdot,k,y;
536
537 void SetRhoInf(real_t rho_inf);
538 void PrintProperties(std::ostream &out = mfem::out);
539public:
540
542
543 void Init(TimeDependentOperator &f_) override;
544
545 void Step(Vector &x, real_t &t, real_t &dt) override;
546
547 int GetMaxStateSize() override { return 1; };
548 int GetStateSize() override { return nstate; };
549 const Vector &GetStateVector(int i) override;
550 void GetStateVector(int i, Vector &state) override;
551 void SetStateVector(int i, Vector &state) override;
552};
553
554
555/// The SIASolver class is based on the Symplectic Integration Algorithm
556/// described in "A Symplectic Integration Algorithm for Separable Hamiltonian
557/// Functions" by J. Candy and W. Rozmus, Journal of Computational Physics,
558/// Vol. 92, pages 230-256 (1991).
559
560/** The Symplectic Integration Algorithm (SIA) is designed for systems of first
561 order ODEs derived from a Hamiltonian.
562 H(q,p,t) = T(p) + V(q,t)
563 Which leads to the equations:
564 dq/dt = dT/dp
565 dp/dt = -dV/dq
566 In the integrator the operators P and F are defined to be:
567 P = dT/dp
568 F = -dV/dq
569 */
571{
572public:
573 SIASolver() : F_(NULL), P_(NULL) {}
574
575 virtual void Init(Operator &P, TimeDependentOperator & F);
576
577 virtual void Step(Vector &q, Vector &p, real_t &t, real_t &dt) = 0;
578
579 virtual void Run(Vector &q, Vector &p, real_t &t, real_t &dt, real_t tf)
580 {
581 while (t < tf) { Step(q, p, t, dt); }
582 }
583
584 virtual ~SIASolver() {}
585
586protected:
587 TimeDependentOperator * F_; // p_{i+1} = p_{i} + dt F(q_{i})
588 Operator * P_; // q_{i+1} = q_{i} + dt P(p_{i+1})
589
590 mutable Vector dp_;
591 mutable Vector dq_;
592};
593
594/// First Order Symplectic Integration Algorithm
595class SIA1Solver : public SIASolver
596{
597public:
599 void Step(Vector &q, Vector &p, real_t &t, real_t &dt) override;
600};
601
602/// Second Order Symplectic Integration Algorithm
603class SIA2Solver : public SIASolver
604{
605public:
607 void Step(Vector &q, Vector &p, real_t &t, real_t &dt) override;
608};
609
610/// Variable order Symplectic Integration Algorithm (orders 1-4)
611class SIAVSolver : public SIASolver
612{
613public:
614 SIAVSolver(int order);
615 void Step(Vector &q, Vector &p, real_t &t, real_t &dt) override;
616
617private:
618 int order_;
619
620 Array<real_t> a_;
621 Array<real_t> b_;
622};
623
624
625
626/// Abstract class for solving systems of ODEs: d2x/dt2 = f(x,dx/dt,t)
628{
629protected:
630 /// Pointer to the associated TimeDependentOperator.
631 SecondOrderTimeDependentOperator *f; // f(.,.,t) : R^n x R^n --> R^n
633
634public:
636
637 /// Associate a TimeDependentOperator with the ODE solver.
638 /** This method has to be called:
639 - Before the first call to Step().
640 - When the dimensions of the associated TimeDependentOperator change.
641 - When a time stepping sequence has to be restarted.
642 - To change the associated TimeDependentOperator. */
644
645 /** @brief Perform a time step from time @a t [in] to time @a t [out] based
646 on the requested step size @a dt [in]. */
647 /** @param[in,out] x Approximate solution.
648 @param[in,out] dxdt Approximate rate.
649 @param[in,out] t Time associated with the
650 approximate solution @a x and rate @ dxdt
651 @param[in,out] dt Time step size.
652
653 The following rules describe the common behavior of the method:
654 - The input @a x [in] is the approximate solution for the input time
655 @a t [in].
656 - The input @a dxdt [in] is the approximate rate for the input time
657 @a t [in].
658 - The input @a dt [in] is the desired time step size, defining the desired
659 target time: t [target] = @a t [in] + @a dt [in].
660 - The output @a x [out] is the approximate solution for the output time
661 @a t [out].
662 - The output @a dxdt [out] is the approximate rate for the output time
663 @a t [out].
664 - The output @a dt [out] is the last time step taken by the method which
665 may be smaller or larger than the input @a dt [in] value, e.g. because
666 of time step control.
667 - The method may perform more than one time step internally; in this case
668 @a dt [out] is the last internal time step size.
669 - The output value of @a t [out] may be smaller or larger than
670 t [target], however, it is not smaller than @a t [in] + @a dt [out], if
671 at least one internal time step was performed.
672 - The value @a x [out] may be obtained by interpolation using internally
673 stored data.
674 - In some cases, the contents of @a x [in] may not be used, e.g. when
675 @a x [out] from a previous Step() call was obtained by interpolation.
676 - In consecutive calls to this method, the output @a t [out] of one
677 Step() call has to be the same as the input @a t [in] to the next
678 Step() call.
679 - If the previous rule has to be broken, e.g. to restart a time stepping
680 sequence, then the ODE solver must be re-initialized by calling Init()
681 between the two Step() calls. */
682 virtual void Step(Vector &x, Vector &dxdt, real_t &t, real_t &dt) = 0;
683
684 /// Perform time integration from time @a t [in] to time @a tf [in].
685 /** @param[in,out] x Approximate solution.
686 @param[in,out] dxdt Approximate rate.
687 @param[in,out] t Time associated with the approximate solution @a x.
688 @param[in,out] dt Time step size.
689 @param[in] tf Requested final time.
690
691 The default implementation makes consecutive calls to Step() until
692 reaching @a tf.
693 The following rules describe the common behavior of the method:
694 - The input @a x [in] is the approximate solution for the input time
695 @a t [in].
696 - The input @a dxdt [in] is the approximate rate for the input time
697 @a t [in].
698 - The input @a dt [in] is the initial time step size.
699 - The output @a dt [out] is the last time step taken by the method which
700 may be smaller or larger than the input @a dt [in] value, e.g. because
701 of time step control.
702 - The output value of @a t [out] is not smaller than @a tf [in]. */
703 virtual void Run(Vector &x, Vector &dxdt, real_t &t, real_t &dt, real_t tf)
704 {
705 while (t < tf) { Step(x, dxdt, t, dt); }
706 }
707
708 /// Function for getting and setting the state vectors
709 virtual int GetMaxStateSize() { return 0; };
710 virtual int GetStateSize() { return 0; }
711 virtual const Vector &GetStateVector(int i)
712 {
713 mfem_error("ODESolver has no state vectors");
714 Vector *s = NULL; return *s; // Make some compiler happy
715 }
716 virtual void GetStateVector(int i, Vector &state)
717 {
718 mfem_error("ODESolver has no state vectors");
719 }
720 virtual void SetStateVector(int i, Vector &state)
721 {
722 mfem_error("ODESolver has no state vectors");
723 }
724
726};
727
728/// The classical newmark method.
729/// Newmark, N. M. (1959) A method of computation for structural dynamics.
730/// Journal of Engineering Mechanics, ASCE, 85 (EM3) 67-94.
732{
733private:
734 Vector d2xdt2;
735
736 real_t beta, gamma;
737 bool first;
738
739public:
740 NewmarkSolver(real_t beta_ = 0.25, real_t gamma_ = 0.5) { beta = beta_; gamma = gamma_; };
741
742 void PrintProperties(std::ostream &out = mfem::out);
743
744 void Init(SecondOrderTimeDependentOperator &f_) override;
745
746 void Step(Vector &x, Vector &dxdt, real_t &t, real_t &dt) override;
747};
748
750{
751public:
753};
754
756{
757public:
759};
760
762{
763public:
764 FoxGoodwinSolver() : NewmarkSolver(1.0/12.0, 0.5) { };
765};
766
767/// Generalized-alpha ODE solver
768/// A Time Integration Algorithm for Structural Dynamics With Improved
769/// Numerical Dissipation: The Generalized-Î± Method
770/// J.Chung and G.M. Hulbert, J. Appl. Mech 60(2), 371-375, 1993
771/// https://doi.org/10.1115/1.2900803
772/// rho_inf in [0,1]
774{
775protected:
779
780public:
782 {
783 rho_inf = (rho_inf > 1.0) ? 1.0 : rho_inf;
784 rho_inf = (rho_inf < 0.0) ? 0.0 : rho_inf;
785
786 alpha_m = (2.0 - rho_inf)/(1.0 + rho_inf);
787 alpha_f = 1.0/(1.0 + rho_inf);
788 beta = 0.25*pow(1.0 + alpha_m - alpha_f,2);
789 gamma = 0.5 + alpha_m - alpha_f;
790 };
791
792 void PrintProperties(std::ostream &out = mfem::out);
793
794 void Init(SecondOrderTimeDependentOperator &f_) override;
795
796 void Step(Vector &x, Vector &dxdt, real_t &t, real_t &dt) override;
797
798 int GetMaxStateSize() override { return 1; };
799 int GetStateSize() override { return nstate; };
800 const Vector &GetStateVector(int i) override;
801 void GetStateVector(int i, Vector &state) override;
802 void SetStateVector(int i, Vector &state) override;
803};
804
805/// The classical midpoint method.
807{
808public:
810 {
811 alpha_m = 0.5;
812 alpha_f = 0.5;
813 beta = 0.25;
814 gamma = 0.5;
815 };
816};
817
818/// HHT-alpha ODE solver
819/// Improved numerical dissipation for time integration algorithms
820/// in structural dynamics
821/// H.M. Hilber, T.J.R. Hughes and R.L. Taylor 1977
822/// https://doi.org/10.1002/eqe.4290050306
823/// alpha in [2/3,1] --> Defined differently than in paper.
825{
826public:
828 {
829 alpha = (alpha > 1.0) ? 1.0 : alpha;
830 alpha = (alpha < 2.0/3.0) ? 2.0/3.0 : alpha;
831
832 alpha_m = 1.0;
833 alpha_f = alpha;
834 beta = (2-alpha)*(2-alpha)/4;
835 gamma = 0.5 + alpha_m - alpha_f;
836 };
837
838};
839
840/// WBZ-alpha ODE solver
841/// An alpha modification of Newmark's method
842/// W.L. Wood, M. Bossak and O.C. Zienkiewicz 1980
843/// https://doi.org/10.1002/nme.1620151011
844/// rho_inf in [0,1]
846{
847public:
848 WBZAlphaSolver(real_t rho_inf = 1.0)
849 {
850 rho_inf = (rho_inf > 1.0) ? 1.0 : rho_inf;
851 rho_inf = (rho_inf < 0.0) ? 0.0 : rho_inf;
852
853 alpha_f = 1.0;
854 alpha_m = 2.0/(1.0 + rho_inf);
855 beta = 0.25*pow(1.0 + alpha_m - alpha_f,2);
856 gamma = 0.5 + alpha_m - alpha_f;
857 };
858
859};
860
861}
862
863#endif
void Init(TimeDependentOperator &f_) override
Associate a TimeDependentOperator with the ODE solver.
Definition ode.cpp:396
void SetStateVector(int i, Vector &state) override
Definition ode.cpp:387
AdamsBashforthSolver(int s_, const real_t *a_)
Definition ode.cpp:347
const Vector & GetStateVector(int i) override
Definition ode.cpp:377
int GetMaxStateSize() override
Function for getting and setting the state vectors.
Definition ode.hpp:254
void Step(Vector &x, real_t &t, real_t &dt) override
Perform a time step from time t [in] to time t [out] based on the requested step size dt [in].
Definition ode.cpp:409
int GetStateSize() override
Definition ode.hpp:255
int GetMaxStateSize() override
Function for getting and setting the state vectors.
Definition ode.hpp:345
const Vector & GetStateVector(int i) override
Definition ode.cpp:476
void Step(Vector &x, real_t &t, real_t &dt) override
Perform a time step from time t [in] to time t [out] based on the requested step size dt [in].
Definition ode.cpp:515
int GetStateSize() override
Definition ode.hpp:346
AdamsMoultonSolver(int s_, const real_t *a_)
Definition ode.cpp:458
void Init(TimeDependentOperator &f_) override
Associate a TimeDependentOperator with the ODE solver.
Definition ode.cpp:501
void SetStateVector(int i, Vector &state) override
Definition ode.cpp:492
The classical midpoint method.
Definition ode.hpp:807
Backward Euler ODE solver. L-stable.
Definition ode.hpp:412
void Init(TimeDependentOperator &f_) override
Associate a TimeDependentOperator with the ODE solver.
Definition ode.cpp:572
void Step(Vector &x, real_t &t, real_t &dt) override
Perform a time step from time t [in] to time t [out] based on the requested step size dt [in].
Definition ode.cpp:578
static MemoryType GetHostMemoryType()
Get the current Host MemoryType. This is the MemoryType used by most MFEM classes when allocating mem...
Definition device.hpp:265
virtual void Step(Vector &x, real_t &t, real_t &dt)
Perform a time step from time t [in] to time t [out] based on the requested step size dt [in].
Definition ode.cpp:751
virtual void Init(TimeDependentOperator &f_)
Associate a TimeDependentOperator with the ODE solver.
Definition ode.cpp:743
virtual void Init(TimeDependentOperator &f_)
Associate a TimeDependentOperator with the ODE solver.
Definition ode.cpp:778
virtual void Step(Vector &x, real_t &t, real_t &dt)
Perform a time step from time t [in] to time t [out] based on the requested step size dt [in].
Definition ode.cpp:786
void Step(Vector &x, real_t &t, real_t &dt) override
Perform a time step from time t [in] to time t [out] based on the requested step size dt [in].
Definition ode.cpp:159
virtual ~ExplicitRKSolver()
Definition ode.cpp:189
ExplicitRKSolver(int s_, const real_t *a_, const real_t *b_, const real_t *c_)
Definition ode.cpp:138
void Init(TimeDependentOperator &f_) override
Associate a TimeDependentOperator with the ODE solver.
Definition ode.cpp:148
The classical forward Euler method.
Definition ode.hpp:118
void Step(Vector &x, real_t &t, real_t &dt) override
Perform a time step from time t [in] to time t [out] based on the requested step size dt [in].
Definition ode.cpp:30
void Init(TimeDependentOperator &f_) override
Associate a TimeDependentOperator with the ODE solver.
Definition ode.cpp:24
void Init(SecondOrderTimeDependentOperator &f_) override
Associate a TimeDependentOperator with the ODE solver.
Definition ode.cpp:1090
void Step(Vector &x, Vector &dxdt, real_t &t, real_t &dt) override
Perform a time step from time t [in] to time t [out] based on the requested step size dt [in].
Definition ode.cpp:1156
int GetStateSize() override
Definition ode.hpp:799
void SetStateVector(int i, Vector &state) override
Definition ode.cpp:1118
int GetMaxStateSize() override
Function for getting and setting the state vectors.
Definition ode.hpp:798
void PrintProperties(std::ostream &out=mfem::out)
Definition ode.cpp:1127
const Vector & GetStateVector(int i) override
Definition ode.cpp:1101
GeneralizedAlpha2Solver(real_t rho_inf=1.0)
Definition ode.hpp:781
void Init(TimeDependentOperator &f_) override
Associate a TimeDependentOperator with the ODE solver.
Definition ode.cpp:815
void SetRhoInf(real_t rho_inf)
Definition ode.cpp:850
void SetStateVector(int i, Vector &state) override
Definition ode.cpp:841
void Step(Vector &x, real_t &t, real_t &dt) override
Perform a time step from time t [in] to time t [out] based on the requested step size dt [in].
Definition ode.cpp:888
GeneralizedAlphaSolver(real_t rho=1.0)
Definition ode.hpp:541
int GetMaxStateSize() override
Function for getting and setting the state vectors.
Definition ode.hpp:547
const Vector & GetStateVector(int i) override
Definition ode.cpp:825
int GetStateSize() override
Definition ode.hpp:548
void PrintProperties(std::ostream &out=mfem::out)
Definition ode.cpp:861
HHTAlphaSolver(real_t alpha=1.0)
Definition ode.hpp:827
Implicit midpoint method. A-stable, not L-stable.
Definition ode.hpp:425
void Step(Vector &x, real_t &t, real_t &dt) override
Perform a time step from time t [in] to time t [out] based on the requested step size dt [in].
Definition ode.cpp:593
void Init(TimeDependentOperator &f_) override
Associate a TimeDependentOperator with the ODE solver.
Definition ode.cpp:587
static bool Root()
Return true if the rank in MPI_COMM_WORLD is zero.
static bool IsInitialized()
Return true if MPI has been initialized.
void Step(Vector &x, Vector &dxdt, real_t &t, real_t &dt) override
Perform a time step from time t [in] to time t [out] based on the requested step size dt [in].
Definition ode.cpp:1063
void PrintProperties(std::ostream &out=mfem::out)
Definition ode.cpp:1034
NewmarkSolver(real_t beta_=0.25, real_t gamma_=0.5)
Definition ode.hpp:740
void Init(SecondOrderTimeDependentOperator &f_) override
Associate a TimeDependentOperator with the ODE solver.
Definition ode.cpp:1026
Abstract class for solving systems of ODEs: dx/dt = f(x,t)
Definition ode.hpp:24
virtual const Vector & GetStateVector(int i)
Definition ode.hpp:98
TimeDependentOperator * f
Pointer to the associated TimeDependentOperator.
Definition ode.hpp:27
virtual void Init(TimeDependentOperator &f_)
Associate a TimeDependentOperator with the ODE solver.
Definition ode.cpp:18
virtual void GetStateVector(int i, Vector &state)
Definition ode.hpp:103
virtual void Step(Vector &x, real_t &t, real_t &dt)=0
Perform a time step from time t [in] to time t [out] based on the requested step size dt [in].
virtual ~ODESolver()
Definition ode.hpp:112
virtual void SetStateVector(int i, Vector &state)
Definition ode.hpp:107
MemoryType mem_type
Definition ode.hpp:28
virtual int GetMaxStateSize()
Function for getting and setting the state vectors.
Definition ode.hpp:96
virtual void Run(Vector &x, real_t &t, real_t &dt, real_t tf)
Perform time integration from time t [in] to time tf [in].
Definition ode.hpp:90
virtual int GetStateSize()
Definition ode.hpp:97
Abstract operator.
Definition operator.hpp:25
void Init(TimeDependentOperator &f_) override
Associate a TimeDependentOperator with the ODE solver.
Definition ode.cpp:39
void Step(Vector &x, real_t &t, real_t &dt) override
Perform a time step from time t [in] to time t [out] based on the requested step size dt [in].
Definition ode.cpp:47
RK2Solver(const real_t a_=2./3.)
Definition ode.hpp:141
Third-order, strong stability preserving (SSP) Runge-Kutta method.
Definition ode.hpp:151
void Init(TimeDependentOperator &f_) override
Associate a TimeDependentOperator with the ODE solver.
Definition ode.cpp:68
void Step(Vector &x, real_t &t, real_t &dt) override
Perform a time step from time t [in] to time t [out] based on the requested step size dt [in].
Definition ode.cpp:76
The classical explicit forth-order Runge-Kutta method, RK4.
Definition ode.hpp:164
void Init(TimeDependentOperator &f_) override
Associate a TimeDependentOperator with the ODE solver.
Definition ode.cpp:100
void Step(Vector &x, real_t &t, real_t &dt) override
Perform a time step from time t [in] to time t [out] based on the requested step size dt [in].
Definition ode.cpp:109
SDIRK23Solver(int gamma_opt=1)
Definition ode.cpp:602
void Step(Vector &x, real_t &t, real_t &dt) override
Perform a time step from time t [in] to time t [out] based on the requested step size dt [in].
Definition ode.cpp:629
void Init(TimeDependentOperator &f_) override
Associate a TimeDependentOperator with the ODE solver.
Definition ode.cpp:622
void Step(Vector &x, real_t &t, real_t &dt) override
Perform a time step from time t [in] to time t [out] based on the requested step size dt [in].
Definition ode.cpp:693
void Init(TimeDependentOperator &f_) override
Associate a TimeDependentOperator with the ODE solver.
Definition ode.cpp:686
void Step(Vector &x, real_t &t, real_t &dt) override
Perform a time step from time t [in] to time t [out] based on the requested step size dt [in].
Definition ode.cpp:657
void Init(TimeDependentOperator &f_) override
Associate a TimeDependentOperator with the ODE solver.
Definition ode.cpp:649
First Order Symplectic Integration Algorithm.
Definition ode.hpp:596
void Step(Vector &q, Vector &p, real_t &t, real_t &dt) override
Definition ode.cpp:925
Second Order Symplectic Integration Algorithm.
Definition ode.hpp:604
void Step(Vector &q, Vector &p, real_t &t, real_t &dt) override
Definition ode.cpp:938
TimeDependentOperator * F_
Definition ode.hpp:587
Vector dq_
Definition ode.hpp:591
Vector dp_
Definition ode.hpp:590
virtual void Init(Operator &P, TimeDependentOperator &F)
Definition ode.cpp:916
virtual void Step(Vector &q, Vector &p, real_t &t, real_t &dt)=0
virtual ~SIASolver()
Definition ode.hpp:584
virtual void Run(Vector &q, Vector &p, real_t &t, real_t &dt, real_t tf)
Definition ode.hpp:579
Operator * P_
Definition ode.hpp:588
Variable order Symplectic Integration Algorithm (orders 1-4)
Definition ode.hpp:612
void Step(Vector &q, Vector &p, real_t &t, real_t &dt) override
Definition ode.cpp:995
SIAVSolver(int order)
Definition ode.cpp:953
Abstract class for solving systems of ODEs: d2x/dt2 = f(x,dx/dt,t)
Definition ode.hpp:628
SecondOrderTimeDependentOperator * f
Pointer to the associated TimeDependentOperator.
Definition ode.hpp:631
virtual ~SecondOrderODESolver()
Definition ode.hpp:725
virtual const Vector & GetStateVector(int i)
Definition ode.hpp:711
virtual int GetMaxStateSize()
Function for getting and setting the state vectors.
Definition ode.hpp:709
virtual void GetStateVector(int i, Vector &state)
Definition ode.hpp:716
virtual void SetStateVector(int i, Vector &state)
Definition ode.hpp:720
virtual int GetStateSize()
Definition ode.hpp:710
virtual void Run(Vector &x, Vector &dxdt, real_t &t, real_t &dt, real_t tf)
Perform time integration from time t [in] to time tf [in].
Definition ode.hpp:703
virtual void Init(SecondOrderTimeDependentOperator &f)
Associate a TimeDependentOperator with the ODE solver.
Definition ode.cpp:1020
virtual void Step(Vector &x, Vector &dxdt, real_t &t, real_t &dt)=0
Perform a time step from time t [in] to time t [out] based on the requested step size dt [in].
Base abstract class for second order time dependent operators.
Definition operator.hpp:635
Base abstract class for first order time dependent operators.
Definition operator.hpp:317
virtual void Step(Vector &x, real_t &t, real_t &dt)
Perform a time step from time t [in] to time t [out] based on the requested step size dt [in].
Definition ode.cpp:726
virtual void Init(TimeDependentOperator &f_)
Associate a TimeDependentOperator with the ODE solver.
Definition ode.cpp:719
Vector data type.
Definition vector.hpp:80
WBZAlphaSolver(real_t rho_inf=1.0)
Definition ode.hpp:848
Vector beta
const real_t alpha
Definition ex15.cpp:369
real_t b
Definition lissajous.cpp:42
real_t a
Definition lissajous.cpp:41
void mfem_error(const char *msg)
Definition error.cpp:154
OutStream out(std::cout)
Global stream used by the library for standard output. Initially it uses the same std::streambuf as s...
Definition globals.hpp:66
float real_t
Definition config.hpp:43
MemoryType
Memory types supported by MFEM.
@ HOST
Host memory; using new[] and delete[].
real_t p(const Vector &x, real_t t)
RefCoord t[3]
RefCoord s[3]