bilininteg.hpp

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// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
// reserved. See file COPYRIGHT for details.
//
// This file is part of the MFEM library. For more information and source code
// availability see http://mfem.org.
//
// MFEM is free software; you can redistribute it and/or modify it under the
// terms of the GNU Lesser General Public License (as published by the Free
// Software Foundation) version 2.1 dated February 1999.

#ifndef MFEM_BILININTEG
#define MFEM_BILININTEG

#include "../config/config.hpp"
#include "nonlininteg.hpp"

namespace mfem
{

class BilinearFormIntegrator : public NonlinearFormIntegrator
{
protected:
   const IntegrationRule *IntRule;

   BilinearFormIntegrator(const IntegrationRule *ir = NULL)
   { IntRule = ir; }

public:
   virtual void AssembleElementMatrix(const FiniteElement &el,
                                      ElementTransformation &Trans,
                                      DenseMatrix &elmat);

   virtual void AssembleElementMatrix2(const FiniteElement &trial_fe,
                                       const FiniteElement &test_fe,
                                       ElementTransformation &Trans,
                                       DenseMatrix &elmat);

   virtual void AssembleFaceMatrix(const FiniteElement &el1,
                                   const FiniteElement &el2,
                                   FaceElementTransformations &Trans,
                                   DenseMatrix &elmat);

   virtual void AssembleFaceMatrix(const FiniteElement &trial_face_fe,
                                   const FiniteElement &test_fe1,
                                   const FiniteElement &test_fe2,
                                   FaceElementTransformations &Trans,
                                   DenseMatrix &elmat);

   virtual void AssembleElementVector(const FiniteElement &el,
                                      ElementTransformation &Tr,
                                      const Vector &elfun, Vector &elvect);

   virtual void AssembleElementGrad(const FiniteElement &el,
                                    ElementTransformation &Tr,
                                    const Vector &elfun, DenseMatrix &elmat)
   { AssembleElementMatrix(el, Tr, elmat); }

   virtual void ComputeElementFlux(const FiniteElement &el,
                                   ElementTransformation &Trans,
                                   Vector &u,
                                   const FiniteElement &fluxelem,
                                   Vector &flux, int with_coef = 1) { }

   virtual double ComputeFluxEnergy(const FiniteElement &fluxelem,
                                    ElementTransformation &Trans,
                                    Vector &flux, Vector *d_energy = NULL)
   { return 0.0; }

   void SetIntRule(const IntegrationRule *ir) { IntRule = ir; }

   virtual ~BilinearFormIntegrator() { }
};

class TransposeIntegrator : public BilinearFormIntegrator
{
private:
   int own_bfi;
   BilinearFormIntegrator *bfi;

   DenseMatrix bfi_elmat;

public:
   TransposeIntegrator (BilinearFormIntegrator *_bfi, int _own_bfi = 1)
   { bfi = _bfi; own_bfi = _own_bfi; }

   virtual void AssembleElementMatrix(const FiniteElement &el,
                                      ElementTransformation &Trans,
                                      DenseMatrix &elmat);

   virtual void AssembleElementMatrix2(const FiniteElement &trial_fe,
                                       const FiniteElement &test_fe,
                                       ElementTransformation &Trans,
                                       DenseMatrix &elmat);

   using BilinearFormIntegrator::AssembleFaceMatrix;
   virtual void AssembleFaceMatrix(const FiniteElement &el1,
                                   const FiniteElement &el2,
                                   FaceElementTransformations &Trans,
                                   DenseMatrix &elmat);

   virtual ~TransposeIntegrator() { if (own_bfi) { delete bfi; } }
};

class LumpedIntegrator : public BilinearFormIntegrator
{
private:
   int own_bfi;
   BilinearFormIntegrator *bfi;

public:
   LumpedIntegrator (BilinearFormIntegrator *_bfi, int _own_bfi = 1)
   { bfi = _bfi; own_bfi = _own_bfi; }

   virtual void AssembleElementMatrix(const FiniteElement &el,
                                      ElementTransformation &Trans,
                                      DenseMatrix &elmat);

   virtual ~LumpedIntegrator() { if (own_bfi) { delete bfi; } }
};

class InverseIntegrator : public BilinearFormIntegrator
{
private:
   int own_integrator;
   BilinearFormIntegrator *integrator;

public:
   InverseIntegrator(BilinearFormIntegrator *integ, int own_integ = 1)
   { integrator = integ; own_integrator = own_integ; }

   virtual void AssembleElementMatrix(const FiniteElement &el,
                                      ElementTransformation &Trans,
                                      DenseMatrix &elmat);

   virtual ~InverseIntegrator() { if (own_integrator) { delete integrator; } }
};

class SumIntegrator : public BilinearFormIntegrator
{
private:
   int own_integrators;
   DenseMatrix elem_mat;
   Array<BilinearFormIntegrator*> integrators;

public:
   SumIntegrator(int own_integs = 1) { own_integrators = own_integs; }

   void AddIntegrator(BilinearFormIntegrator *integ)
   { integrators.Append(integ); }

   virtual void AssembleElementMatrix(const FiniteElement &el,
                                      ElementTransformation &Trans,
                                      DenseMatrix &elmat);

   virtual ~SumIntegrator();
};

class DiffusionIntegrator: public BilinearFormIntegrator
{
private:
   Vector vec, pointflux, shape;
#ifndef MFEM_THREAD_SAFE
   DenseMatrix dshape, dshapedxt, invdfdx, mq;
   DenseMatrix te_dshape, te_dshapedxt;
#endif
   Coefficient *Q;
   MatrixCoefficient *MQ;

public:
   DiffusionIntegrator() { Q = NULL; MQ = NULL; }

   DiffusionIntegrator (Coefficient &q) : Q(&q) { MQ = NULL; }

   DiffusionIntegrator (MatrixCoefficient &q) : MQ(&q) { Q = NULL; }

   virtual void AssembleElementMatrix(const FiniteElement &el,
                                      ElementTransformation &Trans,
                                      DenseMatrix &elmat);
   virtual void AssembleElementMatrix2(const FiniteElement &trial_fe,
                                       const FiniteElement &test_fe,
                                       ElementTransformation &Trans,
                                       DenseMatrix &elmat);

   virtual void AssembleElementVector(const FiniteElement &el,
                                      ElementTransformation &Tr,
                                      const Vector &elfun, Vector &elvect);

   virtual void ComputeElementFlux(const FiniteElement &el,
                                   ElementTransformation &Trans,
                                   Vector &u, const FiniteElement &fluxelem,
                                   Vector &flux, int with_coef = 1);

   virtual double ComputeFluxEnergy(const FiniteElement &fluxelem,
                                    ElementTransformation &Trans,
                                    Vector &flux, Vector *d_energy = NULL);
};

class MassIntegrator: public BilinearFormIntegrator
{
protected:
   Vector shape, te_shape;
   Coefficient *Q;

public:
   MassIntegrator(const IntegrationRule *ir = NULL)
      : BilinearFormIntegrator(ir) { Q = NULL; }
   MassIntegrator(Coefficient &q, const IntegrationRule *ir = NULL)
      : BilinearFormIntegrator(ir), Q(&q) { }

   virtual void AssembleElementMatrix(const FiniteElement &el,
                                      ElementTransformation &Trans,
                                      DenseMatrix &elmat);
   virtual void AssembleElementMatrix2(const FiniteElement &trial_fe,
                                       const FiniteElement &test_fe,
                                       ElementTransformation &Trans,
                                       DenseMatrix &elmat);
};

class BoundaryMassIntegrator : public MassIntegrator
{
public:
   BoundaryMassIntegrator(Coefficient &q) : MassIntegrator(q) { }

   using BilinearFormIntegrator::AssembleFaceMatrix;

   virtual void AssembleFaceMatrix(const FiniteElement &el1,
                                   const FiniteElement &el2,
                                   FaceElementTransformations &Trans,
                                   DenseMatrix &elmat);
};

class ConvectionIntegrator : public BilinearFormIntegrator
{
private:
   DenseMatrix dshape, adjJ, Q_ir;
   Vector shape, vec2, BdFidxT;
   VectorCoefficient &Q;
   double alpha;

public:
   ConvectionIntegrator(VectorCoefficient &q, double a = 1.0)
      : Q(q) { alpha = a; }
   virtual void AssembleElementMatrix(const FiniteElement &,
                                      ElementTransformation &,
                                      DenseMatrix &);
};

class GroupConvectionIntegrator : public BilinearFormIntegrator
{
private:
   DenseMatrix dshape, adjJ, Q_nodal, grad;
   Vector shape;
   VectorCoefficient &Q;
   double alpha;

public:
   GroupConvectionIntegrator(VectorCoefficient &q, double a = 1.0)
      : Q(q) { alpha = a; }
   virtual void AssembleElementMatrix(const FiniteElement &,
                                      ElementTransformation &,
                                      DenseMatrix &);
};

class VectorMassIntegrator: public BilinearFormIntegrator
{
private:
   Vector shape, te_shape, vec;
   DenseMatrix partelmat;
   DenseMatrix mcoeff;
   Coefficient *Q;
   VectorCoefficient *VQ;
   MatrixCoefficient *MQ;

   int Q_order;

public:
   VectorMassIntegrator()
   { Q = NULL; VQ = NULL; MQ = NULL; Q_order = 0; }
   VectorMassIntegrator(Coefficient &q, int qo = 0)
      : Q(&q) { VQ = NULL; MQ = NULL; Q_order = qo; }
   VectorMassIntegrator(Coefficient &q, const IntegrationRule *ir)
      : BilinearFormIntegrator(ir), Q(&q)
   { VQ = NULL; MQ = NULL; Q_order = 0; }
   VectorMassIntegrator(VectorCoefficient &q, int qo = 0)
      : VQ(&q) { Q = NULL; MQ = NULL; Q_order = qo; }
   VectorMassIntegrator(MatrixCoefficient &q, int qo = 0)
      : MQ(&q) { Q = NULL; VQ = NULL; Q_order = qo; }

   virtual void AssembleElementMatrix(const FiniteElement &el,
                                      ElementTransformation &Trans,
                                      DenseMatrix &elmat);
   virtual void AssembleElementMatrix2(const FiniteElement &trial_fe,
                                       const FiniteElement &test_fe,
                                       ElementTransformation &Trans,
                                       DenseMatrix &elmat);
};


class VectorFEDivergenceIntegrator : public BilinearFormIntegrator
{
private:
   Coefficient *Q;
#ifndef MFEM_THREAD_SAFE
   Vector divshape, shape;
#endif
public:
   VectorFEDivergenceIntegrator() { Q = NULL; }
   VectorFEDivergenceIntegrator(Coefficient &q) { Q = &q; }
   virtual void AssembleElementMatrix(const FiniteElement &el,
                                      ElementTransformation &Trans,
                                      DenseMatrix &elmat) { }
   virtual void AssembleElementMatrix2(const FiniteElement &trial_fe,
                                       const FiniteElement &test_fe,
                                       ElementTransformation &Trans,
                                       DenseMatrix &elmat);
};


class VectorFECurlIntegrator: public BilinearFormIntegrator
{
private:
   Coefficient *Q;
#ifndef MFEM_THREAD_SAFE
   DenseMatrix curlshapeTrial;
   DenseMatrix vshapeTest;
   DenseMatrix curlshapeTrial_dFT;
#endif
public:
   VectorFECurlIntegrator() { Q = NULL; }
   VectorFECurlIntegrator(Coefficient &q) { Q = &q; }
   virtual void AssembleElementMatrix(const FiniteElement &el,
                                      ElementTransformation &Trans,
                                      DenseMatrix &elmat) { }
   virtual void AssembleElementMatrix2(const FiniteElement &trial_fe,
                                       const FiniteElement &test_fe,
                                       ElementTransformation &Trans,
                                       DenseMatrix &elmat);
};


class DerivativeIntegrator : public BilinearFormIntegrator
{
private:
   Coefficient & Q;
   int xi;
   DenseMatrix dshape, dshapedxt, invdfdx;
   Vector shape, dshapedxi;
public:
   DerivativeIntegrator(Coefficient &q, int i) : Q(q), xi(i) { }
   virtual void AssembleElementMatrix(const FiniteElement &el,
                                      ElementTransformation &Trans,
                                      DenseMatrix &elmat)
   { AssembleElementMatrix2(el,el,Trans,elmat); }
   virtual void AssembleElementMatrix2(const FiniteElement &trial_fe,
                                       const FiniteElement &test_fe,
                                       ElementTransformation &Trans,
                                       DenseMatrix &elmat);
};

class CurlCurlIntegrator: public BilinearFormIntegrator
{
private:
   Vector vec, pointflux;
#ifndef MFEM_THREAD_SAFE
   DenseMatrix curlshape, curlshape_dFt;
   DenseMatrix vshape, projcurl;
#endif
   Coefficient *Q;

public:
   CurlCurlIntegrator() { Q = NULL; }
   CurlCurlIntegrator(Coefficient &q) : Q(&q) { }

   /* Given a particular Finite Element, compute the
      element curl-curl matrix elmat */
   virtual void AssembleElementMatrix(const FiniteElement &el,
                                      ElementTransformation &Trans,
                                      DenseMatrix &elmat);

   virtual void ComputeElementFlux(const FiniteElement &el,
                                   ElementTransformation &Trans,
                                   Vector &u, const FiniteElement &fluxelem,
                                   Vector &flux, int with_coef);

   virtual double ComputeFluxEnergy(const FiniteElement &fluxelem,
                                    ElementTransformation &Trans,
                                    Vector &flux, Vector *d_energy = NULL);
};

class VectorCurlCurlIntegrator: public BilinearFormIntegrator
{
private:
#ifndef MFEM_THREAD_SAFE
   DenseMatrix dshape_hat, dshape, curlshape, Jadj, grad_hat, grad;
#endif
   Coefficient *Q;

public:
   VectorCurlCurlIntegrator() { Q = NULL; }

   VectorCurlCurlIntegrator(Coefficient &q) : Q(&q) { }

   virtual void AssembleElementMatrix(const FiniteElement &el,
                                      ElementTransformation &Trans,
                                      DenseMatrix &elmat);
   virtual double GetElementEnergy(const FiniteElement &el,
                                   ElementTransformation &Tr,
                                   const Vector &elfun);
};

class VectorFEMassIntegrator: public BilinearFormIntegrator
{
private:
   Coefficient *Q;
   VectorCoefficient *VQ;
   MatrixCoefficient *MQ;
   void Init(Coefficient *q, VectorCoefficient *vq, MatrixCoefficient *mq)
   { Q = q; VQ = vq; MQ = mq; }

#ifndef MFEM_THREAD_SAFE
   Vector shape;
   Vector D;
   DenseMatrix K;
   DenseMatrix test_vshape;
   DenseMatrix trial_vshape;
#endif

public:
   VectorFEMassIntegrator() { Init(NULL, NULL, NULL); }
   VectorFEMassIntegrator(Coefficient *_q) { Init(_q, NULL, NULL); }
   VectorFEMassIntegrator(Coefficient &q) { Init(&q, NULL, NULL); }
   VectorFEMassIntegrator(VectorCoefficient *_vq) { Init(NULL, _vq, NULL); }
   VectorFEMassIntegrator(VectorCoefficient &vq) { Init(NULL, &vq, NULL); }
   VectorFEMassIntegrator(MatrixCoefficient *_mq) { Init(NULL, NULL, _mq); }
   VectorFEMassIntegrator(MatrixCoefficient &mq) { Init(NULL, NULL, &mq); }

   virtual void AssembleElementMatrix(const FiniteElement &el,
                                      ElementTransformation &Trans,
                                      DenseMatrix &elmat);
   virtual void AssembleElementMatrix2(const FiniteElement &trial_fe,
                                       const FiniteElement &test_fe,
                                       ElementTransformation &Trans,
                                       DenseMatrix &elmat);
};

class VectorDivergenceIntegrator : public BilinearFormIntegrator
{
private:
   Coefficient *Q;

   Vector shape;
   Vector divshape;
   DenseMatrix dshape;
   DenseMatrix gshape;
   DenseMatrix Jadj;

public:
   VectorDivergenceIntegrator() { Q = NULL; }
   VectorDivergenceIntegrator(Coefficient *_q) { Q = _q; }
   VectorDivergenceIntegrator(Coefficient &q) { Q = &q; }

   virtual void AssembleElementMatrix2(const FiniteElement &trial_fe,
                                       const FiniteElement &test_fe,
                                       ElementTransformation &Trans,
                                       DenseMatrix &elmat);
};

class DivDivIntegrator: public BilinearFormIntegrator
{
private:
   Coefficient *Q;

#ifndef MFEM_THREAD_SAFE
   Vector divshape;
#endif

public:
   DivDivIntegrator() { Q = NULL; }
   DivDivIntegrator(Coefficient &q) : Q(&q) { }

   virtual void AssembleElementMatrix(const FiniteElement &el,
                                      ElementTransformation &Trans,
                                      DenseMatrix &elmat);
};

class VectorDiffusionIntegrator : public BilinearFormIntegrator
{
private:
   Coefficient *Q;

   DenseMatrix Jinv;
   DenseMatrix dshape;
   DenseMatrix gshape;
   DenseMatrix pelmat;

public:
   VectorDiffusionIntegrator() { Q = NULL; }
   VectorDiffusionIntegrator(Coefficient &q) { Q = &q; }

   virtual void AssembleElementMatrix(const FiniteElement &el,
                                      ElementTransformation &Trans,
                                      DenseMatrix &elmat);
};

class ElasticityIntegrator : public BilinearFormIntegrator
{
private:
   double q_lambda, q_mu;
   Coefficient *lambda, *mu;

#ifndef MFEM_THREAD_SAFE
   DenseMatrix dshape, Jinv, gshape, pelmat;
   Vector divshape;
#endif

public:
   ElasticityIntegrator(Coefficient &l, Coefficient &m)
   { lambda = &l; mu = &m; }
   ElasticityIntegrator(Coefficient &m, double q_l, double q_m)
   { lambda = NULL; mu = &m; q_lambda = q_l; q_mu = q_m; }

   virtual void AssembleElementMatrix(const FiniteElement &,
                                      ElementTransformation &,
                                      DenseMatrix &);
};

class DGTraceIntegrator : public BilinearFormIntegrator
{
private:
   Coefficient *rho;
   VectorCoefficient *u;
   double alpha, beta;

   Vector shape1, shape2;

public:
   DGTraceIntegrator(VectorCoefficient &_u, double a, double b)
   { rho = NULL; u = &_u; alpha = a; beta = b; }

   DGTraceIntegrator(Coefficient &_rho, VectorCoefficient &_u,
                     double a, double b)
   { rho = &_rho; u = &_u; alpha = a; beta = b; }

   using BilinearFormIntegrator::AssembleFaceMatrix;
   virtual void AssembleFaceMatrix(const FiniteElement &el1,
                                   const FiniteElement &el2,
                                   FaceElementTransformations &Trans,
                                   DenseMatrix &elmat);
};

class DGDiffusionIntegrator : public BilinearFormIntegrator
{
protected:
   Coefficient *Q;
   MatrixCoefficient *MQ;
   double sigma, kappa;

   // these are not thread-safe!
   Vector shape1, shape2, dshape1dn, dshape2dn, nor, nh, ni;
   DenseMatrix jmat, dshape1, dshape2, mq, adjJ;

public:
   DGDiffusionIntegrator(const double s, const double k)
      : Q(NULL), MQ(NULL), sigma(s), kappa(k) { }
   DGDiffusionIntegrator(Coefficient &q, const double s, const double k)
      : Q(&q), MQ(NULL), sigma(s), kappa(k) { }
   DGDiffusionIntegrator(MatrixCoefficient &q, const double s, const double k)
      : Q(NULL), MQ(&q), sigma(s), kappa(k) { }
   using BilinearFormIntegrator::AssembleFaceMatrix;
   virtual void AssembleFaceMatrix(const FiniteElement &el1,
                                   const FiniteElement &el2,
                                   FaceElementTransformations &Trans,
                                   DenseMatrix &elmat);
};

class TraceJumpIntegrator : public BilinearFormIntegrator
{
private:
   Vector face_shape, shape1, shape2;

public:
   TraceJumpIntegrator() { }
   using BilinearFormIntegrator::AssembleFaceMatrix;
   virtual void AssembleFaceMatrix(const FiniteElement &trial_face_fe,
                                   const FiniteElement &test_fe1,
                                   const FiniteElement &test_fe2,
                                   FaceElementTransformations &Trans,
                                   DenseMatrix &elmat);
};

class NormalTraceJumpIntegrator : public BilinearFormIntegrator
{
private:
   Vector face_shape, normal, shape1_n, shape2_n;
   DenseMatrix shape1, shape2;

public:
   NormalTraceJumpIntegrator() { }
   using BilinearFormIntegrator::AssembleFaceMatrix;
   virtual void AssembleFaceMatrix(const FiniteElement &trial_face_fe,
                                   const FiniteElement &test_fe1,
                                   const FiniteElement &test_fe2,
                                   FaceElementTransformations &Trans,
                                   DenseMatrix &elmat);
};

class DiscreteInterpolator : public BilinearFormIntegrator { };


class GradientInterpolator : public DiscreteInterpolator
{
public:
   virtual void AssembleElementMatrix2(const FiniteElement &h1_fe,
                                       const FiniteElement &nd_fe,
                                       ElementTransformation &Trans,
                                       DenseMatrix &elmat)
   { nd_fe.ProjectGrad(h1_fe, Trans, elmat); }
};


class IdentityInterpolator : public DiscreteInterpolator
{
public:
   virtual void AssembleElementMatrix2(const FiniteElement &dom_fe,
                                       const FiniteElement &ran_fe,
                                       ElementTransformation &Trans,
                                       DenseMatrix &elmat)
   { ran_fe.Project(dom_fe, Trans, elmat); }
};


class CurlInterpolator : public DiscreteInterpolator
{
public:
   virtual void AssembleElementMatrix2(const FiniteElement &dom_fe,
                                       const FiniteElement &ran_fe,
                                       ElementTransformation &Trans,
                                       DenseMatrix &elmat)
   { ran_fe.ProjectCurl(dom_fe, Trans, elmat); }
};


class DivergenceInterpolator : public DiscreteInterpolator
{
public:
   virtual void AssembleElementMatrix2(const FiniteElement &dom_fe,
                                       const FiniteElement &ran_fe,
                                       ElementTransformation &Trans,
                                       DenseMatrix &elmat)
   { ran_fe.ProjectDiv(dom_fe, Trans, elmat); }
};


class NormalInterpolator : public DiscreteInterpolator
{
public:
   virtual void AssembleElementMatrix2(const FiniteElement &dom_fe,
                                       const FiniteElement &ran_fe,
                                       ElementTransformation &Trans,
                                       DenseMatrix &elmat);
};

}

#endif