nonlininteg.cpp

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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.googlecode.com.
//
// 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.

#include "fem.hpp"

namespace mfem
{

void NonlinearFormIntegrator::AssembleElementGrad(
   const FiniteElement &el, ElementTransformation &Tr, const Vector &elfun,
   DenseMatrix &elmat)
{
   mfem_error("NonlinearFormIntegrator::AssembleElementGrad"
              " is not overloaded!");
}

double NonlinearFormIntegrator::GetElementEnergy(
   const FiniteElement &el, ElementTransformation &Tr, const Vector &elfun)
{
   mfem_error("NonlinearFormIntegrator::GetElementEnergy"
              " is not overloaded!");
   return 0.0;
}


double InverseHarmonicModel::EvalW(const DenseMatrix &J) const
{
   Z.SetSize(J.Width());
   CalcAdjugateTranspose(J, Z);
   return 0.5*(Z*Z)/J.Det();
}

void InverseHarmonicModel::EvalP(const DenseMatrix &J, DenseMatrix &P) const
{
   int dim = J.Width();
   double t;

   Z.SetSize(dim);
   S.SetSize(dim);
   CalcAdjugateTranspose(J, Z);
   MultAAt(Z, S);
   t = 0.5*S.Trace();
   for (int i = 0; i < dim; i++)
      S(i,i) -= t;
   t = J.Det();
   S *= -1.0/(t*t);
   Mult(S, Z, P);
}

void InverseHarmonicModel::AssembleH(
   const DenseMatrix &J, const DenseMatrix &DS, const double weight,
   DenseMatrix &A) const
{
   int dof = DS.Height(), dim = DS.Width();
   double t;

   Z.SetSize(dim);
   S.SetSize(dim);
   G.SetSize(dof, dim);
   C.SetSize(dof, dim);

   CalcAdjugateTranspose(J, Z);
   MultAAt(Z, S);

   t = 1.0/J.Det();
   Z *= t;  // Z = J^{-t}
   S *= t;  // S = |J| (J.J^t)^{-1}
   t = 0.5*S.Trace();

   MultABt(DS, Z, G);  // G = DS.J^{-1}
   Mult(G, S, C);

   // 1.
   for (int i = 0; i < dof; i++)
      for (int j = 0; j <= i; j++)
      {
         double a = 0.0;
         for (int d = 0; d < dim; d++)
            a += G(i,d)*G(j,d);
         a *= weight;
         for (int k = 0; k < dim; k++)
            for (int l = 0; l <= k; l++)
            {
               double b = a*S(k,l);
               A(i+k*dof,j+l*dof) += b;
               if (i != j)
                  A(j+k*dof,i+l*dof) += b;
               if (k != l)
               {
                  A(i+l*dof,j+k*dof) += b;
                  if (i != j)
                     A(j+l*dof,i+k*dof) += b;
               }
            }
      }

   // 2.
   for (int i = 0; i < dof; i++)
      for (int j = 0; j < i; j++)
      {
         for (int k = 0; k < dim; k++)
            for (int l = 0; l < k; l++)
            {
               double a =
                  weight*(C(i,l)*G(j,k) - C(i,k)*G(j,l) +
                          C(j,k)*G(i,l) - C(j,l)*G(i,k) +
                          t*(G(i,k)*G(j,l) - G(i,l)*G(j,k)));

               A(i+k*dof,j+l*dof) += a;
               A(j+l*dof,i+k*dof) += a;

               A(i+l*dof,j+k*dof) -= a;
               A(j+k*dof,i+l*dof) -= a;
            }
      }
}


inline void NeoHookeanModel::EvalCoeffs() const
{
   mu = c_mu->Eval(*T, T->GetIntPoint());
   K = c_K->Eval(*T, T->GetIntPoint());
   if (c_g)
      g = c_g->Eval(*T, T->GetIntPoint());
}

double NeoHookeanModel::EvalW(const DenseMatrix &J) const
{
   int dim = J.Width();

   if (have_coeffs)
      EvalCoeffs();

   double dJ = J.Det();
   double sJ = dJ/g;
   double bI1 = pow(dJ, -2.0/dim)*(J*J); // \bar{I}_1

   return 0.5*(mu*(bI1 - dim) + K*(sJ - 1.0)*(sJ - 1.0));
}

void NeoHookeanModel::EvalP(const DenseMatrix &J, DenseMatrix &P) const
{
   int dim = J.Width();

   if (have_coeffs)
      EvalCoeffs();

   Z.SetSize(dim);
   CalcAdjugateTranspose(J, Z);

   double dJ = J.Det();
   double a  = mu*pow(dJ, -2.0/dim);
   double b  = K*(dJ/g - 1.0)/g - a*(J*J)/(dim*dJ);

   P = 0.0;
   P.Add(a, J);
   P.Add(b, Z);
}

void NeoHookeanModel::AssembleH(const DenseMatrix &J, const DenseMatrix &DS,
                                const double weight, DenseMatrix &A) const
{
   int dof = DS.Height(), dim = DS.Width();

   if (have_coeffs)
      EvalCoeffs();

   Z.SetSize(dim);
   G.SetSize(dof, dim);
   C.SetSize(dof, dim);

   double dJ = J.Det();
   double sJ = dJ/g;
   double a  = mu*pow(dJ, -2.0/dim);
   double bc = a*(J*J)/dim;
   double b  = bc - K*sJ*(sJ - 1.0);
   double c  = 2.0*bc/dim + K*sJ*(2.0*sJ - 1.0);

   CalcAdjugateTranspose(J, Z);
   Z *= (1.0/dJ); // Z = J^{-t}

   MultABt(DS, J, C); // C = DS J^t
   MultABt(DS, Z, G); // G = DS J^{-1}

   a *= weight;
   b *= weight;
   c *= weight;

   // 1.
   for (int i = 0; i < dof; i++)
      for (int k = 0; k <= i; k++)
      {
         double s = 0.0;
         for (int d = 0; d < dim; d++)
            s += DS(i,d)*DS(k,d);
         s *= a;

         for (int d = 0; d < dim; d++)
            A(i+d*dof,k+d*dof) += s;

         if (k != i)
            for (int d = 0; d < dim; d++)
               A(k+d*dof,i+d*dof) += s;
      }

   a *= (-2.0/dim);

   // 2.
   for (int i = 0; i < dof; i++)
      for (int j = 0; j < dim; j++)
         for (int k = 0; k < dof; k++)
            for (int l = 0; l < dim; l++)
            {
               A(i+j*dof,k+l*dof) +=
                  a*(C(i,j)*G(k,l) + G(i,j)*C(k,l)) +
                  b*G(i,l)*G(k,j) + c*G(i,j)*G(k,l);
            }
}


double HyperelasticNLFIntegrator::GetElementEnergy(const FiniteElement &el,
                                                   ElementTransformation &Tr,
                                                   const Vector &elfun)
{
   int dof = el.GetDof(), dim = el.GetDim();
   double energy;

   DSh.SetSize(dof, dim);
   J0i.SetSize(dim);
   J1.SetSize(dim);
   J.SetSize(dim);
   PMatI.UseExternalData(elfun.GetData(), dof, dim);

   int intorder = 2*el.GetOrder() + 3; // <---
   const IntegrationRule &ir = IntRules.Get(el.GetGeomType(), intorder);

   energy = 0.0;
   model->SetTransformation(Tr);
   for (int i = 0; i < ir.GetNPoints(); i++)
   {
      const IntegrationPoint &ip = ir.IntPoint(i);
      Tr.SetIntPoint(&ip);
      CalcInverse(Tr.Jacobian(), J0i);

      el.CalcDShape(ip, DSh);
      MultAtB(PMatI, DSh, J1);
      Mult(J1, J0i, J);

      energy += ip.weight*Tr.Weight()*model->EvalW(J);
   }

   return energy;
}

void HyperelasticNLFIntegrator::AssembleElementVector(
   const FiniteElement &el, ElementTransformation &Tr, const Vector &elfun,
   Vector &elvect)
{
   int dof = el.GetDof(), dim = el.GetDim();

   DSh.SetSize(dof, dim);
   DS.SetSize(dof, dim);
   J0i.SetSize(dim);
   J.SetSize(dim);
   P.SetSize(dim);
   PMatI.UseExternalData(elfun.GetData(), dof, dim);
   elvect.SetSize(dof*dim);
   PMatO.UseExternalData(elvect.GetData(), dof, dim);

   int intorder = 2*el.GetOrder() + 3; // <---
   const IntegrationRule &ir = IntRules.Get(el.GetGeomType(), intorder);

   elvect = 0.0;
   model->SetTransformation(Tr);
   for (int i = 0; i < ir.GetNPoints(); i++)
   {
      const IntegrationPoint &ip = ir.IntPoint(i);
      Tr.SetIntPoint(&ip);
      CalcInverse(Tr.Jacobian(), J0i);

      el.CalcDShape(ip, DSh);
      Mult(DSh, J0i, DS);
      MultAtB(PMatI, DS, J);

      model->EvalP(J, P);

      P *= ip.weight*Tr.Weight();
      AddMultABt(DS, P, PMatO);
   }
}

void HyperelasticNLFIntegrator::AssembleElementGrad(
   const FiniteElement &el, ElementTransformation &Tr, const Vector &elfun,
   DenseMatrix &elmat)
{
   int dof = el.GetDof(), dim = el.GetDim();

   DSh.SetSize(dof, dim);
   DS.SetSize(dof, dim);
   J0i.SetSize(dim);
   J.SetSize(dim);
   PMatI.UseExternalData(elfun.GetData(), dof, dim);
   elmat.SetSize(dof*dim);

   int intorder = 2*el.GetOrder() + 3; // <---
   const IntegrationRule &ir = IntRules.Get(el.GetGeomType(), intorder);

   elmat = 0.0;
   model->SetTransformation(Tr);
   for (int i = 0; i < ir.GetNPoints(); i++)
   {
      const IntegrationPoint &ip = ir.IntPoint(i);
      Tr.SetIntPoint(&ip);
      CalcInverse(Tr.Jacobian(), J0i);

      el.CalcDShape(ip, DSh);
      Mult(DSh, J0i, DS);
      MultAtB(PMatI, DS, J);

      model->AssembleH(J, DS, ip.weight*Tr.Weight(), elmat);
   }
}

HyperelasticNLFIntegrator::~HyperelasticNLFIntegrator()
{
   PMatI.ClearExternalData();
   PMatO.ClearExternalData();
}

}