lininteg.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.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.


#include <cmath>
#include "fem.hpp"

namespace mfem
{

void LinearFormIntegrator::AssembleRHSElementVect(
   const FiniteElement &el, FaceElementTransformations &Tr, Vector &elvect)
{
   mfem_error("LinearFormIntegrator::AssembleRHSElementVect(...)");
}


void DomainLFIntegrator::AssembleRHSElementVect(const FiniteElement &el,
                                                ElementTransformation &Tr,
                                                Vector &elvect)
{
   int dof = el.GetDof();

   shape.SetSize(dof);       // vector of size dof
   elvect.SetSize(dof);
   elvect = 0.0;

   const IntegrationRule *ir = IntRule;
   if (ir == NULL)
   {
      // ir = &IntRules.Get(el.GetGeomType(),
      //                    oa * el.GetOrder() + ob + Tr.OrderW());
      ir = &IntRules.Get(el.GetGeomType(), oa * el.GetOrder() + ob);
   }

   for (int i = 0; i < ir->GetNPoints(); i++)
   {
      const IntegrationPoint &ip = ir->IntPoint(i);

      Tr.SetIntPoint (&ip);
      double val = Tr.Weight() * Q.Eval(Tr, ip);

      el.CalcShape(ip, shape);

      add(elvect, ip.weight * val, shape, elvect);
   }
}

void BoundaryLFIntegrator::AssembleRHSElementVect(
   const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
{
   int dof = el.GetDof();

   shape.SetSize(dof);        // vector of size dof
   elvect.SetSize(dof);
   elvect = 0.0;

   const IntegrationRule *ir = IntRule;
   if (ir == NULL)
   {
      int intorder = oa * el.GetOrder() + ob;  // <----------
      ir = &IntRules.Get(el.GetGeomType(), intorder);
   }

   for (int i = 0; i < ir->GetNPoints(); i++)
   {
      const IntegrationPoint &ip = ir->IntPoint(i);

      Tr.SetIntPoint (&ip);
      double val = Tr.Weight() * Q.Eval(Tr, ip);

      el.CalcShape(ip, shape);

      add(elvect, ip.weight * val, shape, elvect);
   }
}

void BoundaryNormalLFIntegrator::AssembleRHSElementVect(
   const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
{
   int dim = el.GetDim()+1;
   int dof = el.GetDof();
   Vector nor(dim), Qvec;

   shape.SetSize(dof);
   elvect.SetSize(dof);
   elvect = 0.0;

   const IntegrationRule *ir = IntRule;
   if (ir == NULL)
   {
      int intorder = oa * el.GetOrder() + ob;  // <----------
      ir = &IntRules.Get(el.GetGeomType(), intorder);
   }

   for (int i = 0; i < ir->GetNPoints(); i++)
   {
      const IntegrationPoint &ip = ir->IntPoint(i);

      Tr.SetIntPoint(&ip);
      CalcOrtho(Tr.Jacobian(), nor);
      Q.Eval(Qvec, Tr, ip);

      el.CalcShape(ip, shape);

      elvect.Add(ip.weight*(Qvec*nor), shape);
   }
}

void BoundaryTangentialLFIntegrator::AssembleRHSElementVect(
   const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
{
   int dim = el.GetDim()+1;
   int dof = el.GetDof();
   Vector tangent(dim), Qvec;

   shape.SetSize(dof);
   elvect.SetSize(dof);
   elvect = 0.0;

   if (dim != 2)
   {
      mfem_error("These methods make sense only in 2D problems.");
   }

   const IntegrationRule *ir = IntRule;
   if (ir == NULL)
   {
      int intorder = oa * el.GetOrder() + ob;  // <----------
      ir = &IntRules.Get(el.GetGeomType(), intorder);
   }

   for (int i = 0; i < ir->GetNPoints(); i++)
   {
      const IntegrationPoint &ip = ir->IntPoint(i);

      Tr.SetIntPoint(&ip);
      const DenseMatrix &Jac = Tr.Jacobian();
      tangent(0) =  Jac(0,0);
      tangent(1) = Jac(1,0);

      Q.Eval(Qvec, Tr, ip);

      el.CalcShape(ip, shape);

      add(elvect, ip.weight*(Qvec*tangent), shape, elvect);
   }
}

void VectorDomainLFIntegrator::AssembleRHSElementVect(
   const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
{
   int vdim = Q.GetVDim();
   int dof  = el.GetDof();

   double val,cf;

   shape.SetSize(dof);       // vector of size dof

   elvect.SetSize(dof * vdim);
   elvect = 0.0;

   const IntegrationRule *ir = IntRule;
   if (ir == NULL)
   {
      int intorder = el.GetOrder() + 1;
      ir = &IntRules.Get(el.GetGeomType(), intorder);
   }

   for (int i = 0; i < ir->GetNPoints(); i++)
   {
      const IntegrationPoint &ip = ir->IntPoint(i);

      Tr.SetIntPoint (&ip);
      val = Tr.Weight();

      el.CalcShape(ip, shape);
      Q.Eval (Qvec, Tr, ip);

      for (int k = 0; k < vdim; k++)
      {
         cf = val * Qvec(k);

         for (int s = 0; s < dof; s++)
         {
            elvect(dof*k+s) += ip.weight * cf * shape(s);
         }
      }
   }
}

void VectorBoundaryLFIntegrator::AssembleRHSElementVect(
   const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
{
   int vdim = Q.GetVDim();
   int dof  = el.GetDof();

   shape.SetSize(dof);
   vec.SetSize(vdim);

   elvect.SetSize(dof * vdim);
   elvect = 0.0;

   const IntegrationRule *ir = IntRule;
   if (ir == NULL)
   {
      int intorder = el.GetOrder() + 1;
      ir = &IntRules.Get(el.GetGeomType(), intorder);
   }

   for (int i = 0; i < ir->GetNPoints(); i++)
   {
      const IntegrationPoint &ip = ir->IntPoint(i);

      Q.Eval(vec, Tr, ip);
      Tr.SetIntPoint (&ip);
      vec *= Tr.Weight() * ip.weight;
      el.CalcShape(ip, shape);
      for (int k = 0; k < vdim; k++)
         for (int s = 0; s < dof; s++)
         {
            elvect(dof*k+s) += vec(k) * shape(s);
         }
   }
}

void VectorFEDomainLFIntegrator::AssembleRHSElementVect(
   const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
{
   int dof = el.GetDof();
   int spaceDim = Tr.GetSpaceDim();

   vshape.SetSize(dof,spaceDim);
   vec.SetSize(spaceDim);

   elvect.SetSize(dof);
   elvect = 0.0;

   const IntegrationRule *ir = IntRule;
   if (ir == NULL)
   {
      // int intorder = 2*el.GetOrder() - 1; // ok for O(h^{k+1}) conv. in L2
      int intorder = 2*el.GetOrder();
      ir = &IntRules.Get(el.GetGeomType(), intorder);
   }

   for (int i = 0; i < ir->GetNPoints(); i++)
   {
      const IntegrationPoint &ip = ir->IntPoint(i);

      Tr.SetIntPoint (&ip);
      el.CalcVShape(Tr, vshape);

      QF.Eval (vec, Tr, ip);
      vec *= ip.weight * Tr.Weight();

      vshape.AddMult (vec, elvect);
   }
}


void VectorBoundaryFluxLFIntegrator::AssembleRHSElementVect(
   const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
{
   int dim = el.GetDim()+1;
   int dof = el.GetDof();

   shape.SetSize (dof);
   nor.SetSize (dim);
   elvect.SetSize (dim*dof);

   const IntegrationRule *ir = IntRule;
   if (ir == NULL)
   {
      ir = &IntRules.Get(el.GetGeomType(), el.GetOrder() + 1);
   }

   elvect = 0.0;
   for (int i = 0; i < ir->GetNPoints(); i++)
   {
      const IntegrationPoint &ip = ir->IntPoint(i);
      Tr.SetIntPoint (&ip);
      CalcOrtho(Tr.Jacobian(), nor);
      el.CalcShape (ip, shape);
      nor *= Sign * ip.weight * F -> Eval (Tr, ip);
      for (int j = 0; j < dof; j++)
         for (int k = 0; k < dim; k++)
         {
            elvect(dof*k+j) += nor(k) * shape(j);
         }
   }
}


void VectorFEBoundaryFluxLFIntegrator::AssembleRHSElementVect(
   const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
{
   int dof = el.GetDof();

   shape.SetSize(dof);
   elvect.SetSize(dof);
   elvect = 0.0;

   const IntegrationRule *ir = IntRule;
   if (ir == NULL)
   {
      int intorder = 2*el.GetOrder();  // <----------
      ir = &IntRules.Get(el.GetGeomType(), intorder);
   }

   for (int i = 0; i < ir->GetNPoints(); i++)
   {
      const IntegrationPoint &ip = ir->IntPoint(i);

      Tr.SetIntPoint (&ip);
      double val = ip.weight*F.Eval(Tr, ip);

      el.CalcShape(ip, shape);

      add(elvect, val, shape, elvect);
   }
}


void VectorFEBoundaryTangentLFIntegrator::AssembleRHSElementVect(
   const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
{
   int dof = el.GetDof();
   DenseMatrix vshape(dof, 2);
   Vector f_loc(3);
   Vector f_hat(2);

   elvect.SetSize(dof);
   elvect = 0.0;

   const IntegrationRule *ir = IntRule;
   if (ir == NULL)
   {
      int intorder = 2*el.GetOrder();  // <----------
      ir = &IntRules.Get(el.GetGeomType(), intorder);
   }

   for (int i = 0; i < ir->GetNPoints(); i++)
   {
      const IntegrationPoint &ip = ir->IntPoint(i);

      Tr.SetIntPoint(&ip);
      f.Eval(f_loc, Tr, ip);
      Tr.Jacobian().MultTranspose(f_loc, f_hat);
      el.CalcVShape(ip, vshape);

      Swap<double>(f_hat(0), f_hat(1));
      f_hat(0) = -f_hat(0);
      f_hat *= ip.weight;
      vshape.AddMult(f_hat, elvect);
   }
}


void BoundaryFlowIntegrator::AssembleRHSElementVect(
   const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
{
   mfem_error("BoundaryFlowIntegrator::AssembleRHSElementVect\n"
              "  is not implemented as boundary integrator!\n"
              "  Use LinearForm::AddBdrFaceIntegrator instead of\n"
              "  LinearForm::AddBoundaryIntegrator.");
}

void BoundaryFlowIntegrator::AssembleRHSElementVect(
   const FiniteElement &el, FaceElementTransformations &Tr, Vector &elvect)
{
   int dim, ndof, order;
   double un, w, vu_data[3], nor_data[3];

   dim  = el.GetDim();
   ndof = el.GetDof();
   Vector vu(vu_data, dim), nor(nor_data, dim);

   const IntegrationRule *ir = IntRule;
   if (ir == NULL)
   {
      // Assuming order(u)==order(mesh)
      order = Tr.Elem1->OrderW() + 2*el.GetOrder();
      if (el.Space() == FunctionSpace::Pk)
      {
         order++;
      }
      ir = &IntRules.Get(Tr.FaceGeom, order);
   }

   shape.SetSize(ndof);
   elvect.SetSize(ndof);
   elvect = 0.0;

   for (int p = 0; p < ir->GetNPoints(); p++)
   {
      const IntegrationPoint &ip = ir->IntPoint(p);
      IntegrationPoint eip;
      Tr.Loc1.Transform(ip, eip);
      el.CalcShape(eip, shape);

      Tr.Face->SetIntPoint(&ip);

      u->Eval(vu, *Tr.Elem1, eip);

      if (dim == 1)
      {
         nor(0) = 2*eip.x - 1.0;
      }
      else
      {
         CalcOrtho(Tr.Face->Jacobian(), nor);
      }

      un = vu * nor;
      w = 0.5*alpha*un - beta*fabs(un);
      w *= ip.weight*f->Eval(*Tr.Elem1, eip);
      elvect.Add(w, shape);
   }
}


void DGDirichletLFIntegrator::AssembleRHSElementVect(
   const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
{
   mfem_error("DGDirichletLFIntegrator::AssembleRHSElementVect");
}

void DGDirichletLFIntegrator::AssembleRHSElementVect(
   const FiniteElement &el, FaceElementTransformations &Tr, Vector &elvect)
{
   int dim, ndof;
   bool kappa_is_nonzero = (kappa != 0.);
   double w;

   dim = el.GetDim();
   ndof = el.GetDof();

   nor.SetSize(dim);
   nh.SetSize(dim);
   ni.SetSize(dim);
   adjJ.SetSize(dim);
   if (MQ)
   {
      mq.SetSize(dim);
   }

   shape.SetSize(ndof);
   dshape.SetSize(ndof, dim);
   dshape_dn.SetSize(ndof);

   elvect.SetSize(ndof);
   elvect = 0.0;

   const IntegrationRule *ir = IntRule;
   if (ir == NULL)
   {
      // a simple choice for the integration order; is this OK?
      int order = 2*el.GetOrder();
      ir = &IntRules.Get(Tr.FaceGeom, order);
   }

   for (int p = 0; p < ir->GetNPoints(); p++)
   {
      const IntegrationPoint &ip = ir->IntPoint(p);
      IntegrationPoint eip;

      Tr.Loc1.Transform(ip, eip);
      Tr.Face->SetIntPoint(&ip);
      if (dim == 1)
      {
         nor(0) = 2*eip.x - 1.0;
      }
      else
      {
         CalcOrtho(Tr.Face->Jacobian(), nor);
      }

      el.CalcShape(eip, shape);
      el.CalcDShape(eip, dshape);
      Tr.Elem1->SetIntPoint(&eip);
      // compute uD through the face transformation
      w = ip.weight * uD->Eval(*Tr.Face, ip) / Tr.Elem1->Weight();
      if (!MQ)
      {
         if (Q)
         {
            w *= Q->Eval(*Tr.Elem1, eip);
         }
         ni.Set(w, nor);
      }
      else
      {
         nh.Set(w, nor);
         MQ->Eval(mq, *Tr.Elem1, eip);
         mq.MultTranspose(nh, ni);
      }
      CalcAdjugate(Tr.Elem1->Jacobian(), adjJ);
      adjJ.Mult(ni, nh);

      dshape.Mult(nh, dshape_dn);
      elvect.Add(sigma, dshape_dn);

      if (kappa_is_nonzero)
      {
         elvect.Add(kappa*(ni*nor), shape);
      }
   }
}

}