paramnonlinearform.cpp

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// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
// LICENSE and NOTICE for details. LLNL-CODE-806117.
//
// This file is part of the MFEM library. For more information and source code
// availability visit https://mfem.org.
//
// MFEM is free software; you can redistribute it and/or modify it under the
// terms of the BSD-3 license. We welcome feedback and contributions, see file
// CONTRIBUTING.md for details.
 
 
#include "mfem.hpp"
#include "paramnonlinearform.hpp"
 
 
namespace mfem
{
 
real_t ParametricBNLFormIntegrator::GetElementEnergy(const
                                                     Array<const FiniteElement *> &el,
                                                     const Array<const FiniteElement *> &pel,
                                                     ElementTransformation &Tr,
                                                     const Array<const Vector *> &elfun,
                                                     const Array<const Vector *> &pelfun)
{
   mfem_error("ParametricBNLFormIntegrator::GetElementEnergy"
              " is not overloaded!");
   return 0.0;
}
 
void ParametricBNLFormIntegrator::AssembleFaceGrad(const
                                                   Array<const FiniteElement *> &el1,
                                                   const Array<const FiniteElement *> &el2,
                                                   const Array<const FiniteElement *> &pel1,
                                                   const Array<const FiniteElement *> &pel2,
                                                   FaceElementTransformations &Tr,
                                                   const Array<const Vector *> &elfun,
                                                   const Array<const Vector *> &pelfun,
                                                   const Array2D<DenseMatrix *> &elmats)
{
   mfem_error("ParametricBNLFormIntegrator::AssembleFaceGrad"
              " is not overloaded!");
}
 
void ParametricBNLFormIntegrator::AssembleElementGrad(const
                                                      Array<const FiniteElement *> &el,
                                                      const Array<const FiniteElement *> &pel,
                                                      ElementTransformation &Tr,
                                                      const Array<const Vector *> &elfun,
                                                      const Array<const Vector *> &pelfun,
                                                      const Array2D<DenseMatrix *> &elmats)
{
   mfem_error("ParametricBNLFormIntegrator::AssembleElementGrad"
              " is not overloaded!");
}
 
void ParametricBNLFormIntegrator::AssembleElementVector(
   const Array<const FiniteElement *> &el,
   const Array<const FiniteElement *> &pel,
   ElementTransformation &Tr,
   const Array<const Vector *> &elfun,
   const Array<const Vector *> &pelfun,
   const Array<Vector *> &elvec)
{
   mfem_error("ParametricBNLFormIntegrator::AssembleElementVector"
              " is not overloaded!");
}
 
void ParametricBNLFormIntegrator::AssembleFaceVector(const
                                                     Array<const FiniteElement *> &el1,
                                                     const Array<const FiniteElement *> &el2,
                                                     const Array<const FiniteElement *> &pel1,
                                                     const Array<const FiniteElement *> &pel2,
                                                     FaceElementTransformations &Tr,
                                                     const Array<const Vector *> &elfun,
                                                     const Array<const Vector *> &pelfun,
                                                     const Array<Vector *> &elvect)
{
   mfem_error("ParametricBNLFormIntegrator::AssembleFaceVector"
              " is not overloaded!");
}
 
 
void ParametricBNLFormIntegrator::AssemblePrmElementVector(
   const Array<const FiniteElement *> &el,
   const Array<const FiniteElement *> &pel,
   ElementTransformation &Tr,
   const Array<const Vector *> &elfun,
   const Array<const Vector *> &alfun,
   const Array<const Vector *> &pelfun,
   const Array<Vector *> &elvec)
{
   mfem_error("ParametricBNLFormIntegrator::AssemblePrmElementVector"
              " is not overloaded!");
}
 
void ParametricBNLFormIntegrator::AssemblePrmFaceVector(
   const Array<const FiniteElement *> &el1,
   const Array<const FiniteElement *> &el2,
   const Array<const FiniteElement *> &pel1,
   const Array<const FiniteElement *> &pel2,
   FaceElementTransformations &Tr,
   const Array<const Vector *> &elfun,
   const Array<const Vector *> &alfun,
   const Array<const Vector *> &pelfun,
   const Array<Vector *> &elvect)
{
   mfem_error("ParametricBNLFormIntegrator::AssemblePrmFaceVector"
              " is not overloaded!");
}
 
 
ParametricBNLForm::ParametricBNLForm(): fes(0), paramfes(0), BlockGrad(nullptr)
{
   height = 0;
   width  = 0;
 
   paramheight = 0;
   paramwidth = 0;
}
 
ParametricBNLForm::ParametricBNLForm(Array<FiniteElementSpace *> &statef,
                                     Array<FiniteElementSpace *> &paramf):
   fes(0),paramfes(0), BlockGrad(nullptr)
{
   SetSpaces(statef,paramf);
}
 
void ParametricBNLForm::SetSpaces(Array<FiniteElementSpace *> &statef,
                                  Array<FiniteElementSpace *> &paramf)
{
   delete BlockGrad;
   BlockGrad = nullptr;
   for (int i=0; i<Grads.NumRows(); ++i)
   {
      for (int j=0; j<Grads.NumCols(); ++j)
      {
         delete Grads(i,j);
         delete cGrads(i,j);
      }
   }
   for (int i = 0; i < ess_tdofs.Size(); ++i)
   {
      delete ess_tdofs[i];
   }
   for (int i = 0; i < paramess_tdofs.Size(); ++i)
   {
      delete paramess_tdofs[i];
   }
 
   height = 0;
   width = 0;
   // set state feses
   statef.Copy(fes);
   // set the block sizes
   block_offsets.SetSize(statef.Size() + 1);
   block_trueOffsets.SetSize(statef.Size() + 1);
   block_offsets[0] = 0;
   block_trueOffsets[0] = 0;
   for (int i=0; i<fes.Size(); ++i)
   {
      block_offsets[i+1] = fes[i]->GetVSize();
      block_trueOffsets[i+1] = fes[i]->GetTrueVSize();
   }
   block_offsets.PartialSum();
   block_trueOffsets.PartialSum();
 
   // Set design/parametric feses
   paramf.Copy(paramfes);
   paramblock_offsets.SetSize(paramf.Size() + 1);
   paramblock_trueOffsets.SetSize(paramf.Size() + 1);
   paramblock_offsets[0] = 0;
   paramblock_trueOffsets[0] = 0;
   for (int i=0; i<paramfes.Size(); ++i)
   {
      paramblock_offsets[i+1] = paramfes[i]->GetVSize();
      paramblock_trueOffsets[i+1] = paramfes[i]->GetTrueVSize();
   }
   paramblock_offsets.PartialSum();
   paramblock_trueOffsets.PartialSum();
 
   // Set the size of the operator
   height = block_trueOffsets[fes.Size()];
   width = block_trueOffsets[fes.Size()];
 
   Grads.SetSize(fes.Size(), fes.Size());
   Grads = NULL;
 
   cGrads.SetSize(fes.Size(), fes.Size());
   cGrads = NULL;
 
   P.SetSize(fes.Size());
   cP.SetSize(fes.Size());
   ess_tdofs.SetSize(fes.Size());
 
   for (int s = 0; s < fes.Size(); ++s)
   {
      // Retrieve prolongation matrix for each FE space
      P[s] = fes[s]->GetProlongationMatrix();
      cP[s] = dynamic_cast<const SparseMatrix *>(P[s]);
 
      // If the P Operator exists and its type is not SparseMatrix, this
      // indicates the Operator is part of parallel run.
      if (P[s] && !cP[s])
      {
         is_serial = false;
      }
 
      // If the P Operator exists and its type is SparseMatrix, this indicates
      // the Operator is serial but needs prolongation on assembly.
      if (cP[s])
      {
         needs_prolongation = true;
      }
 
      ess_tdofs[s] = new Array<int>;
   }
 
   // Set the size of the design/parametric part.
   paramheight = paramblock_trueOffsets[paramfes.Size()];
   paramwidth = paramblock_trueOffsets[paramfes.Size()];
 
   Pparam.SetSize(paramfes.Size());
   cPparam.SetSize(paramfes.Size());
   paramess_tdofs.SetSize(paramfes.Size());
 
   for (int s = 0; s < paramfes.Size(); ++s)
   {
      // Retrieve prolongation matrix for each FE space.
      Pparam[s] = paramfes[s]->GetProlongationMatrix();
      cPparam[s] = dynamic_cast<const SparseMatrix *>(Pparam[s]);
 
      // If the P Operator exists and its type is SparseMatrix, this indicates
      // the Operator is serial but needs prolongation on assembly.
      if (cPparam[s])
      {
         prmneeds_prolongation = true;
      }
 
      paramess_tdofs[s] = new Array<int>;
   }
 
   xsv.Update(block_offsets);
   adv.Update(block_offsets);
   xdv.Update(paramblock_offsets);
 
}
 
void ParametricBNLForm::AddBdrFaceIntegrator(ParametricBNLFormIntegrator *nlfi,
                                             Array<int> &bdr_marker)
{
   bfnfi.Append(nlfi);
   bfnfi_marker.Append(&bdr_marker);
}
 
real_t ParametricBNLForm::GetEnergyBlocked(const BlockVector &bx,
                                           const BlockVector &dx) const
{
   Array<Array<int> *> vdofs(fes.Size());
   Array<Vector *> el_x(fes.Size());
   Array<const Vector *> el_x_const(fes.Size());
   Array<const FiniteElement *> fe(fes.Size());
   ElementTransformation *T;
 
   Array<Array<int> *> prmvdofs(paramfes.Size());
   Array<Vector *> prmel_x(paramfes.Size());
   Array<const Vector *> prmel_x_const(paramfes.Size());
   Array<const FiniteElement *> prmfe(paramfes.Size());
 
   real_t energy = 0.0;
 
   for (int i=0; i<fes.Size(); ++i)
   {
      el_x_const[i] = el_x[i] = new Vector();
      vdofs[i] = new Array<int>;
   }
 
   for (int i=0; i<paramfes.Size(); ++i)
   {
      prmel_x_const[i] = prmel_x[i] = new Vector();
      prmvdofs[i] = new Array<int>;
   }
 
 
   if (dnfi.Size())
   {
      for (int i = 0; i < fes[0]->GetNE(); ++i)
      {
         T = fes[0]->GetElementTransformation(i);
         for (int s=0; s<fes.Size(); ++s)
         {
            fe[s] = fes[s]->GetFE(i);
            fes[s]->GetElementVDofs(i, *vdofs[s]);
            bx.GetBlock(s).GetSubVector(*vdofs[s], *el_x[s]);
         }
 
         for (int s=0; s<paramfes.Size(); ++s)
         {
            prmfe[s] = paramfes[s]->GetFE(i);
            paramfes[s]->GetElementVDofs(i, *prmvdofs[s]);
            dx.GetBlock(s).GetSubVector(*prmvdofs[s], *prmel_x[s]);
         }
 
 
 
         for (int k = 0; k < dnfi.Size(); ++k)
         {
            energy += dnfi[k]->GetElementEnergy(fe, prmfe, *T, el_x_const, prmel_x_const);
         }
      }
   }
 
   // Free the allocated memory
   for (int i = 0; i < fes.Size(); ++i)
   {
      delete el_x[i];
      delete vdofs[i];
   }
 
   for (int i = 0; i < paramfes.Size(); ++i)
   {
      delete prmel_x[i];
      delete prmvdofs[i];
   }
 
   if (fnfi.Size())
   {
      MFEM_ABORT("TODO: add energy contribution from interior face terms");
   }
 
   if (bfnfi.Size())
   {
      MFEM_ABORT("TODO: add energy contribution from boundary face terms");
   }
 
   return energy;
}
 
void ParametricBNLForm::SetStateFields(const Vector &xv) const
{
   BlockVector bx(const_cast<Vector&>(xv), block_trueOffsets);
   if (needs_prolongation)
   {
      for (int s = 0; s < fes.Size(); s++)
      {
         P[s]->Mult(bx.GetBlock(s), xsv.GetBlock(s));
      }
   }
   else
   {
      xsv=bx;
   }
}
 
void ParametricBNLForm::SetAdjointFields(const Vector &av) const
{
   BlockVector bx(const_cast<Vector&>(av), block_trueOffsets);
   if (needs_prolongation)
   {
      for (int s = 0; s < fes.Size(); s++)
      {
         P[s]->Mult(bx.GetBlock(s), adv.GetBlock(s));
      }
   }
   else
   {
      adv=bx;
   }
 
}
 
void ParametricBNLForm::SetParamFields(const Vector &dv) const
{
   BlockVector bx(const_cast<Vector&>(dv), paramblock_trueOffsets);
   if (prmneeds_prolongation)
   {
      for (int s = 0; s < paramfes.Size(); s++)
      {
         Pparam[s]->Mult(bx.GetBlock(s), xdv.GetBlock(s));
      }
   }
   else
   {
      xdv=bx;
   }
}
 
real_t ParametricBNLForm::GetEnergy(const Vector &x) const
{
   xs.Update(const_cast<Vector&>(x),block_offsets);
   return GetEnergyBlocked(xs,xdv);
}
 
void ParametricBNLForm::SetEssentialBC(const Array<Array<int> *>
                                       &bdr_attr_is_ess,
                                       Array<Vector *> &rhs)
{
   for (int s = 0; s < fes.Size(); ++s)
   {
      ess_tdofs[s]->SetSize(ess_tdofs.Size());
 
      fes[s]->GetEssentialTrueDofs(*bdr_attr_is_ess[s], *ess_tdofs[s]);
 
      if (rhs[s])
      {
         rhs[s]->SetSubVector(*ess_tdofs[s], 0.0);
      }
   }
}
 
void ParametricBNLForm::SetParamEssentialBC(const Array<Array<int> *>
                                            &bdr_attr_is_ess,
                                            Array<Vector *> &rhs)
{
   for (int s = 0; s < paramfes.Size(); ++s)
   {
      paramess_tdofs[s]->SetSize(paramess_tdofs.Size());
 
      paramfes[s]->GetEssentialTrueDofs(*bdr_attr_is_ess[s], *paramess_tdofs[s]);
 
      if (rhs[s])
      {
         rhs[s]->SetSubVector(*paramess_tdofs[s], 0.0);
      }
   }
}
 
void ParametricBNLForm::MultParamBlocked(const BlockVector &bx,
                                         const BlockVector &ax,
                                         const BlockVector &dx,
                                         BlockVector &dy) const
{
   // State fields
   Array<Array<int> *>vdofs(fes.Size());
   Array<Array<int> *>vdofs2(fes.Size());
   Array<Vector *> el_x(fes.Size());
   Array<const Vector *> el_x_const(fes.Size());
   Array<const FiniteElement *> fe(fes.Size());
   Array<const FiniteElement *> fe2(fes.Size());
 
   ElementTransformation *T;
 
   // Adjoint fields
   Array<Vector *> ael_x(fes.Size());
   Array<const Vector *> ael_x_const(fes.Size());
 
   // Parametric fields
   Array<Array<int> *>prmvdofs(paramfes.Size());
   Array<Array<int> *>prmvdofs2(paramfes.Size());
   Array<Vector *> prmel_x(paramfes.Size());
   Array<const Vector *> prmel_x_const(paramfes.Size());
   Array<Vector *> prmel_y(paramfes.Size());
   Array<const FiniteElement *> prmfe(paramfes.Size());
   Array<const FiniteElement *> prmfe2(paramfes.Size());
 
   dy = 0.0;
 
   for (int s=0; s<fes.Size(); ++s)
   {
      el_x_const[s] = el_x[s] = new Vector();
      vdofs[s] = new Array<int>;
      vdofs2[s] = new Array<int>;
 
      ael_x_const[s] = ael_x[s] = new Vector();
   }
 
   for (int s=0; s<paramfes.Size(); ++s)
   {
      prmel_x_const[s] = prmel_x[s] = new Vector();
      prmel_y[s] = new Vector();
      prmvdofs[s] = new Array<int>;
      prmvdofs2[s] = new Array<int>;
   }
 
   if (dnfi.Size())
   {
      for (int i = 0; i < fes[0]->GetNE(); ++i)
      {
         T = fes[0]->GetElementTransformation(i);
         for (int s = 0; s < fes.Size(); ++s)
         {
            fes[s]->GetElementVDofs(i, *(vdofs[s]));
            fe[s] = fes[s]->GetFE(i);
            bx.GetBlock(s).GetSubVector(*(vdofs[s]), *el_x[s]);
            ax.GetBlock(s).GetSubVector(*(vdofs[s]), *ael_x[s]);
         }
 
         for (int s = 0; s < paramfes.Size(); ++s)
         {
            paramfes[s]->GetElementVDofs(i, *(prmvdofs[s]));
            prmfe[s] = paramfes[s]->GetFE(i);
            dx.GetBlock(s).GetSubVector(*(prmvdofs[s]), *prmel_x[s]);
         }
 
 
         for (int k = 0; k < dnfi.Size(); ++k)
         {
            dnfi[k]->AssemblePrmElementVector(fe,prmfe, *T,
                                              el_x_const, ael_x_const, prmel_x_const,
                                              prmel_y);
 
            for (int s=0; s<paramfes.Size(); ++s)
            {
               if (prmel_y[s]->Size() == 0) { continue; }
               dy.GetBlock(s).AddElementVector(*(prmvdofs[s]), *prmel_y[s]);
            }
         }
      }
   }
 
   if (fnfi.Size())
   {
      Mesh *mesh = fes[0]->GetMesh();
      FaceElementTransformations *tr;
 
      for (int i = 0; i < mesh->GetNumFaces(); ++i)
      {
         tr = mesh->GetInteriorFaceTransformations(i);
         if (tr != NULL)
         {
            for (int s=0; s<fes.Size(); ++s)
            {
               fe[s] = fes[s]->GetFE(tr->Elem1No);
               fe2[s] = fes[s]->GetFE(tr->Elem2No);
 
               fes[s]->GetElementVDofs(tr->Elem1No, *(vdofs[s]));
               fes[s]->GetElementVDofs(tr->Elem2No, *(vdofs2[s]));
 
               vdofs[s]->Append(*(vdofs2[s]));
 
               bx.GetBlock(s).GetSubVector(*(vdofs[s]), *el_x[s]);
               ax.GetBlock(s).GetSubVector(*(vdofs[s]), *ael_x[s]);
            }
 
            for (int s=0; s<paramfes.Size(); ++s)
            {
               prmfe[s] = paramfes[s]->GetFE(tr->Elem1No);
               prmfe2[s] = paramfes[s]->GetFE(tr->Elem2No);
 
               paramfes[s]->GetElementVDofs(tr->Elem1No, *(prmvdofs[s]));
               paramfes[s]->GetElementVDofs(tr->Elem2No, *(prmvdofs2[s]));
 
               prmvdofs[s]->Append(*(prmvdofs2[s]));
 
               dx.GetBlock(s).GetSubVector(*(prmvdofs[s]), *prmel_x[s]);
            }
 
            for (int k = 0; k < fnfi.Size(); ++k)
            {
 
               fnfi[k]->AssemblePrmFaceVector(fe, fe2, prmfe, prmfe2, *tr,
                                              el_x_const, ael_x_const, prmel_x_const, prmel_y);
 
               for (int s=0; s<paramfes.Size(); ++s)
               {
                  if (prmel_y[s]->Size() == 0) { continue; }
                  dy.GetBlock(s).AddElementVector(*(prmvdofs[s]), *prmel_y[s]);
               }
            }
         }
      }
   }
 
   if (bfnfi.Size())
   {
      Mesh *mesh = fes[0]->GetMesh();
      FaceElementTransformations *tr;
      // Which boundary attributes need to be processed?
      Array<int> bdr_attr_marker(mesh->bdr_attributes.Size() ?
                                 mesh->bdr_attributes.Max() : 0);
      bdr_attr_marker = 0;
      for (int k = 0; k < bfnfi.Size(); ++k)
      {
         if (bfnfi_marker[k] == NULL)
         {
            bdr_attr_marker = 1;
            break;
         }
         Array<int> &bdr_marker = *bfnfi_marker[k];
         MFEM_ASSERT(bdr_marker.Size() == bdr_attr_marker.Size(),
                     "invalid boundary marker for boundary face integrator #"
                     << k << ", counting from zero");
         for (int i = 0; i < bdr_attr_marker.Size(); ++i)
         {
            bdr_attr_marker[i] |= bdr_marker[i];
         }
      }
 
      for (int i = 0; i < mesh->GetNBE(); ++i)
      {
         const int bdr_attr = mesh->GetBdrAttribute(i);
         if (bdr_attr_marker[bdr_attr-1] == 0) { continue; }
 
         tr = mesh->GetBdrFaceTransformations(i);
         if (tr != NULL)
         {
            for (int s=0; s<fes.Size(); ++s)
            {
               fe[s] = fes[s]->GetFE(tr->Elem1No);
               fe2[s] = fes[s]->GetFE(tr->Elem1No);
 
               fes[s]->GetElementVDofs(tr->Elem1No, *(vdofs[s]));
               bx.GetBlock(s).GetSubVector(*(vdofs[s]), *el_x[s]);
               ax.GetBlock(s).GetSubVector(*(vdofs[s]), *ael_x[s]);
            }
 
            for (int s=0; s<paramfes.Size(); ++s)
            {
               prmfe[s] = paramfes[s]->GetFE(tr->Elem1No);
               prmfe2[s] = paramfes[s]->GetFE(tr->Elem1No);
 
               paramfes[s]->GetElementVDofs(tr->Elem1No, *(prmvdofs[s]));
               dx.GetBlock(s).GetSubVector(*(prmvdofs[s]), *prmel_x[s]);
            }
 
 
            for (int k = 0; k < bfnfi.Size(); ++k)
            {
               if (bfnfi_marker[k] &&
                   (*bfnfi_marker[k])[bdr_attr-1] == 0) { continue; }
 
               bfnfi[k]->AssemblePrmFaceVector(fe, fe2, prmfe, prmfe2, *tr,
                                               el_x_const, ael_x_const, prmel_x_const, prmel_y);
 
               for (int s=0; s<paramfes.Size(); ++s)
               {
                  if (prmel_y[s]->Size() == 0) { continue; }
                  dy.GetBlock(s).AddElementVector(*(prmvdofs[s]), *prmel_y[s]);
               }
            }
         }
      }
   }
 
   for (int s=0; s<fes.Size(); ++s)
   {
      delete vdofs2[s];
      delete vdofs[s];
      delete el_x[s];
      delete ael_x[s];
   }
 
   for (int s=0; s<paramfes.Size(); ++s)
   {
      delete prmvdofs2[s];
      delete prmvdofs[s];
      delete prmel_y[s];
      delete prmel_x[s];
   }
 
}
 
void ParametricBNLForm::MultBlocked(const BlockVector &bx,
                                    const BlockVector &dx,
                                    BlockVector &by) const
{
 
   Array<Array<int> *>vdofs(fes.Size());
   Array<Array<int> *>vdofs2(fes.Size());
   Array<Vector *> el_x(fes.Size());
   Array<const Vector *> el_x_const(fes.Size());
   Array<Vector *> el_y(fes.Size());
   Array<const FiniteElement *> fe(fes.Size());
   Array<const FiniteElement *> fe2(fes.Size());
 
   ElementTransformation *T;
 
   Array<Array<int> *>prmvdofs(paramfes.Size());
   Array<Array<int> *>prmvdofs2(paramfes.Size());
   Array<Vector *> prmel_x(paramfes.Size());
   Array<const Vector *> prmel_x_const(paramfes.Size());
   Array<const FiniteElement *> prmfe(paramfes.Size());
   Array<const FiniteElement *> prmfe2(paramfes.Size());
 
   by = 0.0;
   for (int s=0; s<fes.Size(); ++s)
   {
      el_x_const[s] = el_x[s] = new Vector();
      el_y[s] = new Vector();
      vdofs[s] = new Array<int>;
      vdofs2[s] = new Array<int>;
   }
 
   for (int s=0; s<paramfes.Size(); ++s)
   {
      prmel_x_const[s] = prmel_x[s] = new Vector();
      prmvdofs[s] = new Array<int>;
      prmvdofs2[s] = new Array<int>;
   }
 
   if (dnfi.Size())
   {
      for (int i = 0; i < fes[0]->GetNE(); ++i)
      {
         T = fes[0]->GetElementTransformation(i);
         for (int s = 0; s < fes.Size(); ++s)
         {
            fes[s]->GetElementVDofs(i, *(vdofs[s]));
            fe[s] = fes[s]->GetFE(i);
            bx.GetBlock(s).GetSubVector(*(vdofs[s]), *el_x[s]);
         }
 
         for (int s = 0; s < paramfes.Size(); ++s)
         {
            paramfes[s]->GetElementVDofs(i, *(prmvdofs[s]));
            prmfe[s] = paramfes[s]->GetFE(i);
            dx.GetBlock(s).GetSubVector(*(prmvdofs[s]), *prmel_x[s]);
         }
 
 
         for (int k = 0; k < dnfi.Size(); ++k)
         {
            dnfi[k]->AssembleElementVector(fe,prmfe, *T,
                                           el_x_const, prmel_x_const, el_y);
 
            for (int s=0; s<fes.Size(); ++s)
            {
               if (el_y[s]->Size() == 0) { continue; }
               by.GetBlock(s).AddElementVector(*(vdofs[s]), *el_y[s]);
            }
         }
      }
   }
 
   if (fnfi.Size())
   {
      Mesh *mesh = fes[0]->GetMesh();
      FaceElementTransformations *tr;
 
      for (int i = 0; i < mesh->GetNumFaces(); ++i)
      {
         tr = mesh->GetInteriorFaceTransformations(i);
         if (tr != NULL)
         {
            for (int s=0; s<fes.Size(); ++s)
            {
               fe[s] = fes[s]->GetFE(tr->Elem1No);
               fe2[s] = fes[s]->GetFE(tr->Elem2No);
 
               fes[s]->GetElementVDofs(tr->Elem1No, *(vdofs[s]));
               fes[s]->GetElementVDofs(tr->Elem2No, *(vdofs2[s]));
 
               vdofs[s]->Append(*(vdofs2[s]));
 
               bx.GetBlock(s).GetSubVector(*(vdofs[s]), *el_x[s]);
            }
 
            for (int s=0; s<paramfes.Size(); ++s)
            {
               prmfe[s] = paramfes[s]->GetFE(tr->Elem1No);
               prmfe2[s] = paramfes[s]->GetFE(tr->Elem2No);
 
               paramfes[s]->GetElementVDofs(tr->Elem1No, *(prmvdofs[s]));
               paramfes[s]->GetElementVDofs(tr->Elem2No, *(prmvdofs2[s]));
 
               prmvdofs[s]->Append(*(prmvdofs2[s]));
 
               dx.GetBlock(s).GetSubVector(*(prmvdofs[s]), *prmel_x[s]);
            }
 
            for (int k = 0; k < fnfi.Size(); ++k)
            {
 
               fnfi[k]->AssembleFaceVector(fe, fe2, prmfe, prmfe2, *tr, el_x_const,
                                           prmel_x_const, el_y);
 
               for (int s=0; s<fes.Size(); ++s)
               {
                  if (el_y[s]->Size() == 0) { continue; }
                  by.GetBlock(s).AddElementVector(*(vdofs[s]), *el_y[s]);
               }
            }
         }
      }
   }
 
   if (bfnfi.Size())
   {
      Mesh *mesh = fes[0]->GetMesh();
      FaceElementTransformations *tr;
      // Which boundary attributes need to be processed?
      Array<int> bdr_attr_marker(mesh->bdr_attributes.Size() ?
                                 mesh->bdr_attributes.Max() : 0);
      bdr_attr_marker = 0;
      for (int k = 0; k < bfnfi.Size(); ++k)
      {
         if (bfnfi_marker[k] == NULL)
         {
            bdr_attr_marker = 1;
            break;
         }
         Array<int> &bdr_marker = *bfnfi_marker[k];
         MFEM_ASSERT(bdr_marker.Size() == bdr_attr_marker.Size(),
                     "invalid boundary marker for boundary face integrator #"
                     << k << ", counting from zero");
         for (int i = 0; i < bdr_attr_marker.Size(); ++i)
         {
            bdr_attr_marker[i] |= bdr_marker[i];
         }
      }
 
      for (int i = 0; i < mesh->GetNBE(); ++i)
      {
         const int bdr_attr = mesh->GetBdrAttribute(i);
         if (bdr_attr_marker[bdr_attr-1] == 0) { continue; }
 
         tr = mesh->GetBdrFaceTransformations(i);
         if (tr != NULL)
         {
            for (int s=0; s<fes.Size(); ++s)
            {
               fe[s] = fes[s]->GetFE(tr->Elem1No);
               fe2[s] = fes[s]->GetFE(tr->Elem1No);
 
               fes[s]->GetElementVDofs(tr->Elem1No, *(vdofs[s]));
               bx.GetBlock(s).GetSubVector(*(vdofs[s]), *el_x[s]);
            }
 
            for (int s=0; s<paramfes.Size(); ++s)
            {
               prmfe[s] = paramfes[s]->GetFE(tr->Elem1No);
               prmfe2[s] = paramfes[s]->GetFE(tr->Elem1No);
 
               paramfes[s]->GetElementVDofs(tr->Elem1No, *(prmvdofs[s]));
               dx.GetBlock(s).GetSubVector(*(prmvdofs[s]), *prmel_x[s]);
            }
 
 
            for (int k = 0; k < bfnfi.Size(); ++k)
            {
               if (bfnfi_marker[k] &&
                   (*bfnfi_marker[k])[bdr_attr-1] == 0) { continue; }
 
               bfnfi[k]->AssembleFaceVector(fe, fe2, prmfe, prmfe2, *tr, el_x_const,
                                            prmel_x_const, el_y);
 
               for (int s=0; s<fes.Size(); ++s)
               {
                  if (el_y[s]->Size() == 0) { continue; }
                  by.GetBlock(s).AddElementVector(*(vdofs[s]), *el_y[s]);
               }
            }
         }
      }
   }
 
   for (int s=0; s<fes.Size(); ++s)
   {
      delete vdofs2[s];
      delete vdofs[s];
      delete el_y[s];
      delete el_x[s];
   }
 
   for (int s=0; s<paramfes.Size(); ++s)
   {
      delete prmvdofs2[s];
      delete prmvdofs[s];
      delete prmel_x[s];
   }
 
}
 
const BlockVector &ParametricBNLForm::Prolongate(const BlockVector &bx) const
{
   MFEM_VERIFY(bx.Size() == Width(), "invalid input BlockVector size");
 
   if (needs_prolongation)
   {
      aux1.Update(block_offsets);
      for (int s = 0; s < fes.Size(); s++)
      {
         P[s]->Mult(bx.GetBlock(s), aux1.GetBlock(s));
      }
      return aux1;
   }
   return bx;
}
 
const BlockVector &ParametricBNLForm::ParamProlongate(const BlockVector &bx)
const
{
   MFEM_VERIFY(bx.Size() == paramwidth, "invalid input BlockVector size");
 
   if (prmneeds_prolongation)
   {
      prmaux1.Update(paramblock_offsets);
      for (int s = 0; s < paramfes.Size(); s++)
      {
         Pparam[s]->Mult(bx.GetBlock(s), prmaux1.GetBlock(s));
      }
      return prmaux1;
   }
   return bx;
}
 
 
void ParametricBNLForm::ParamMult(const Vector &x, Vector &y) const
{
   BlockVector bx(const_cast<Vector&>(x), paramblock_trueOffsets);
   BlockVector by(y, paramblock_trueOffsets);
 
   const BlockVector &pbx = ParamProlongate(bx);
 
   if (prmneeds_prolongation)
   {
      prmaux2.Update(paramblock_offsets);
   }
   BlockVector &pby = prmneeds_prolongation ? prmaux2 : by;
 
   xs.Update(const_cast<BlockVector&>(pbx), paramblock_offsets);
   ys.Update(pby, paramblock_offsets);
 
   MultParamBlocked(xsv,adv,xs,ys);
 
   for (int s = 0; s < paramfes.Size(); s++)
   {
      if (cPparam[s])
      {
         cPparam[s]->MultTranspose(pby.GetBlock(s), by.GetBlock(s));
      }
      by.GetBlock(s).SetSubVector(*paramess_tdofs[s], 0.0);
   }
}
 
 
void ParametricBNLForm::Mult(const Vector &x, Vector &y) const
{
 
   BlockVector bx(const_cast<Vector&>(x), block_trueOffsets);
   BlockVector by(y, block_trueOffsets);
 
   const BlockVector &pbx = Prolongate(bx);
 
   if (needs_prolongation)
   {
      aux2.Update(block_offsets);
   }
   BlockVector &pby = needs_prolongation ? aux2 : by;
 
   xs.Update(const_cast<BlockVector&>(pbx), block_offsets);
   ys.Update(pby, block_offsets);
   MultBlocked(xs,xdv,ys);
 
   for (int s = 0; s < fes.Size(); s++)
   {
      if (cP[s])
      {
         cP[s]->MultTranspose(pby.GetBlock(s), by.GetBlock(s));
      }
      by.GetBlock(s).SetSubVector(*ess_tdofs[s], 0.0);
   }
}
 
void ParametricBNLForm::ComputeGradientBlocked(const BlockVector &bx,
                                               const BlockVector &dx) const
{
   const int skip_zeros = 0;
   Array<Array<int> *> vdofs(fes.Size());
   Array<Array<int> *> vdofs2(fes.Size());
   Array<Vector *> el_x(fes.Size());
   Array<const Vector *> el_x_const(fes.Size());
   Array2D<DenseMatrix *> elmats(fes.Size(), fes.Size());
   Array<const FiniteElement *>fe(fes.Size());
   Array<const FiniteElement *>fe2(fes.Size());
 
   ElementTransformation * T;
 
   Array<Array<int> *> prmvdofs(paramfes.Size());
   Array<Array<int> *> prmvdofs2(paramfes.Size());
   Array<Vector *> prmel_x(paramfes.Size());
   Array<const Vector *> prmel_x_const(paramfes.Size());
   Array<const FiniteElement *>prmfe(paramfes.Size());
   Array<const FiniteElement *>prmfe2(paramfes.Size());
 
   for (int i=0; i<fes.Size(); ++i)
   {
      el_x_const[i] = el_x[i] = new Vector();
      vdofs[i] = new Array<int>;
      vdofs2[i] = new Array<int>;
      for (int j=0; j<fes.Size(); ++j)
      {
         elmats(i,j) = new DenseMatrix();
      }
   }
 
   for (int i=0; i<fes.Size(); ++i)
   {
      for (int j=0; j<fes.Size(); ++j)
      {
         if (Grads(i,j) != NULL)
         {
            *Grads(i,j) = 0.0;
         }
         else
         {
            Grads(i,j) = new SparseMatrix(fes[i]->GetVSize(),
                                          fes[j]->GetVSize());
         }
      }
   }
 
   for (int i=0; i<paramfes.Size(); ++i)
   {
      prmel_x_const[i] = prmel_x[i] = new Vector();
      prmvdofs[i] = new Array<int>;
      prmvdofs2[i] = new Array<int>;
   }
 
   if (dnfi.Size())
   {
      for (int i = 0; i < fes[0]->GetNE(); ++i)
      {
         T = fes[0]->GetElementTransformation(i);
 
         for (int s = 0; s < fes.Size(); ++s)
         {
            fe[s] = fes[s]->GetFE(i);
            fes[s]->GetElementVDofs(i, *vdofs[s]);
            bx.GetBlock(s).GetSubVector(*vdofs[s], *el_x[s]);
         }
 
         for (int s = 0; s < paramfes.Size(); ++s)
         {
            prmfe[s] = paramfes[s]->GetFE(i);
            paramfes[s]->GetElementVDofs(i, *prmvdofs[s]);
            dx.GetBlock(s).GetSubVector(*prmvdofs[s], *prmel_x[s]);
         }
 
         for (int k = 0; k < dnfi.Size(); ++k)
         {
            dnfi[k]->AssembleElementGrad(fe,prmfe,*T, el_x_const, prmel_x_const, elmats);
 
            for (int j=0; j<fes.Size(); ++j)
            {
               for (int l=0; l<fes.Size(); ++l)
               {
                  if (elmats(j,l)->Height() == 0) { continue; }
                  Grads(j,l)->AddSubMatrix(*vdofs[j], *vdofs[l],
                                           *elmats(j,l), skip_zeros);
               }
            }
         }
      }
   }
 
   if (fnfi.Size())
   {
      FaceElementTransformations *tr;
      Mesh *mesh = fes[0]->GetMesh();
 
      for (int i = 0; i < mesh->GetNumFaces(); ++i)
      {
         tr = mesh->GetInteriorFaceTransformations(i);
 
         for (int s=0; s < fes.Size(); ++s)
         {
            fe[s] = fes[s]->GetFE(tr->Elem1No);
            fe2[s] = fes[s]->GetFE(tr->Elem2No);
 
            fes[s]->GetElementVDofs(tr->Elem1No, *vdofs[s]);
            fes[s]->GetElementVDofs(tr->Elem2No, *vdofs2[s]);
            vdofs[s]->Append(*(vdofs2[s]));
 
            bx.GetBlock(s).GetSubVector(*vdofs[s], *el_x[s]);
         }
 
         for (int s=0; s < paramfes.Size(); ++s)
         {
            prmfe[s] = paramfes[s]->GetFE(tr->Elem1No);
            prmfe2[s] = paramfes[s]->GetFE(tr->Elem2No);
 
            paramfes[s]->GetElementVDofs(tr->Elem1No, *prmvdofs[s]);
            paramfes[s]->GetElementVDofs(tr->Elem2No, *prmvdofs2[s]);
            prmvdofs[s]->Append(*(prmvdofs2[s]));
 
            dx.GetBlock(s).GetSubVector(*prmvdofs[s], *prmel_x[s]);
         }
 
         for (int k = 0; k < fnfi.Size(); ++k)
         {
            fnfi[k]->AssembleFaceGrad(fe, fe2, prmfe, prmfe2, *tr, el_x_const,
                                      prmel_x_const, elmats);
            for (int j=0; j<fes.Size(); ++j)
            {
               for (int l=0; l<fes.Size(); ++l)
               {
                  if (elmats(j,l)->Height() == 0) { continue; }
                  Grads(j,l)->AddSubMatrix(*vdofs[j], *vdofs[l],
                                           *elmats(j,l), skip_zeros);
               }
            }
         }
      }
   }
 
   if (bfnfi.Size())
   {
      FaceElementTransformations *tr;
      Mesh *mesh = fes[0]->GetMesh();
 
      // Which boundary attributes need to be processed?
      Array<int> bdr_attr_marker(mesh->bdr_attributes.Size() ?
                                 mesh->bdr_attributes.Max() : 0);
      bdr_attr_marker = 0;
      for (int k = 0; k < bfnfi.Size(); ++k)
      {
         if (bfnfi_marker[k] == NULL)
         {
            bdr_attr_marker = 1;
            break;
         }
         Array<int> &bdr_marker = *bfnfi_marker[k];
         MFEM_ASSERT(bdr_marker.Size() == bdr_attr_marker.Size(),
                     "invalid boundary marker for boundary face integrator #"
                     << k << ", counting from zero");
         for (int i = 0; i < bdr_attr_marker.Size(); ++i)
         {
            bdr_attr_marker[i] |= bdr_marker[i];
         }
      }
 
      for (int i = 0; i < mesh->GetNBE(); ++i)
      {
         const int bdr_attr = mesh->GetBdrAttribute(i);
         if (bdr_attr_marker[bdr_attr-1] == 0) { continue; }
 
         tr = mesh->GetBdrFaceTransformations(i);
         if (tr != NULL)
         {
            for (int s = 0; s < fes.Size(); ++s)
            {
               fe[s] = fes[s]->GetFE(tr->Elem1No);
               fe2[s] = fe[s];
 
               fes[s]->GetElementVDofs(i, *vdofs[s]);
               bx.GetBlock(s).GetSubVector(*vdofs[s], *el_x[s]);
            }
 
            for (int s = 0; s < paramfes.Size(); ++s)
            {
               prmfe[s] = paramfes[s]->GetFE(tr->Elem1No);
               prmfe2[s] = prmfe[s];
 
               paramfes[s]->GetElementVDofs(i, *prmvdofs[s]);
               dx.GetBlock(s).GetSubVector(*prmvdofs[s], *prmel_x[s]);
            }
 
 
            for (int k = 0; k < bfnfi.Size(); ++k)
            {
               bfnfi[k]->AssembleFaceGrad(fe, fe2, prmfe, prmfe2, *tr, el_x_const,
                                          prmel_x_const, elmats);
               for (int l=0; l<fes.Size(); ++l)
               {
                  for (int j=0; j<fes.Size(); ++j)
                  {
                     if (elmats(j,l)->Height() == 0) { continue; }
                     Grads(j,l)->AddSubMatrix(*vdofs[j], *vdofs[l],
                                              *elmats(j,l), skip_zeros);
                  }
               }
            }
         }
      }
   }
 
   if (!Grads(0,0)->Finalized())
   {
      for (int i=0; i<fes.Size(); ++i)
      {
         for (int j=0; j<fes.Size(); ++j)
         {
            Grads(i,j)->Finalize(skip_zeros);
         }
      }
   }
 
   for (int i=0; i<fes.Size(); ++i)
   {
      for (int j=0; j<fes.Size(); ++j)
      {
         delete elmats(i,j);
      }
      delete vdofs2[i];
      delete vdofs[i];
      delete el_x[i];
   }
 
   for (int i=0; i<paramfes.Size(); ++i)
   {
      delete prmvdofs2[i];
      delete prmvdofs[i];
      delete prmel_x[i];
   }
}
 
BlockOperator& ParametricBNLForm::GetGradient(const Vector &x) const
{
   BlockVector bx(const_cast<Vector&>(x), block_trueOffsets);
   const BlockVector &pbx = Prolongate(bx);
 
   ComputeGradientBlocked(pbx, xdv);
 
   Array2D<SparseMatrix *> mGrads(fes.Size(), fes.Size());
   mGrads = Grads;
   if (needs_prolongation)
   {
      for (int s1 = 0; s1 < fes.Size(); ++s1)
      {
         for (int s2 = 0; s2 < fes.Size(); ++s2)
         {
            delete cGrads(s1, s2);
            cGrads(s1, s2) = RAP(*cP[s1], *Grads(s1, s2), *cP[s2]);
            mGrads(s1, s2) = cGrads(s1, s2);
         }
      }
   }
 
   for (int s = 0; s < fes.Size(); ++s)
   {
      for (int i = 0; i < ess_tdofs[s]->Size(); ++i)
      {
         for (int j = 0; j < fes.Size(); ++j)
         {
            if (s == j)
            {
               mGrads(s, s)->EliminateRowCol((*ess_tdofs[s])[i],
                                             Matrix::DIAG_ONE);
            }
            else
            {
               mGrads(s, j)->EliminateRow((*ess_tdofs[s])[i]);
               mGrads(j, s)->EliminateCol((*ess_tdofs[s])[i]);
            }
         }
      }
   }
 
   delete BlockGrad;
   BlockGrad = new BlockOperator(block_trueOffsets);
   for (int i = 0; i < fes.Size(); ++i)
   {
      for (int j = 0; j < fes.Size(); ++j)
      {
         BlockGrad->SetBlock(i, j, mGrads(i, j));
      }
   }
   return *BlockGrad;
 
}
 
ParametricBNLForm::~ParametricBNLForm()
{
   delete BlockGrad;
   for (int i=0; i<fes.Size(); ++i)
   {
      for (int j=0; j<fes.Size(); ++j)
      {
         delete Grads(i,j);
         delete cGrads(i,j);
      }
      delete ess_tdofs[i];
   }
 
   for (int i=0; i<paramfes.Size(); ++i)
   {
      delete paramess_tdofs[i];
   }
 
   for (int i = 0; i < dnfi.Size(); ++i)
   {
      delete dnfi[i];
   }
 
   for (int i = 0; i < fnfi.Size(); ++i)
   {
      delete fnfi[i];
   }
 
   for (int i = 0; i < bfnfi.Size(); ++i)
   {
      delete bfnfi[i];
   }
 
}
 
}