DOFVector.cc

//
// Software License for AMDiS
//
// Copyright (c) 2010 Dresden University of Technology 
// All rights reserved.
// Authors: Simon Vey, Thomas Witkowski et al.
//
// This file is part of AMDiS
//
// See also license.opensource.txt in the distribution.


#include <boost/numeric/mtl/mtl.hpp>
#include "DOFVector.h"
#include "Traverse.h"
#include "DualTraverse.h"
#include "FixVec.h"

namespace AMDiS {

  template<>
  void DOFVector<double>::coarseRestrict(RCNeighbourList& list, int n)
  {
    FUNCNAME("DOFVector<double>::coarseRestrict()");

    switch (coarsenOperation) {
    case NO_OPERATION:
      return;
      break;
    case COARSE_RESTRICT:
      (const_cast<BasisFunction*>(feSpace->getBasisFcts()))->coarseRestr(this, &list, n);
      break;
    case COARSE_INTERPOL:
      TEST_EXIT_DBG(feSpace)("Should not happen!\n");
      TEST_EXIT_DBG(feSpace->getBasisFcts())("Shoud not happen!\n");

      (const_cast<BasisFunction*>(feSpace->getBasisFcts()))->coarseInter(this, &list, n);
      break;
    default:
      WARNING("Invalid coarsen operation \"%d\" in vector \"%s\"\n", 
	      coarsenOperation, this->name.c_str());
    }
  }


  template<>
  void DOFVector<double>::refineInterpol(RCNeighbourList& list, int n)
  {
    (const_cast<BasisFunction*>(feSpace->getBasisFcts()))->refineInter(this, &list, n);
  }


  template<>
  void DOFVector<WorldVector<double> >::refineInterpol(RCNeighbourList& list, int n)
  {
    if (n < 1) 
      return;

    Element *el = list.getElement(0);
    int n0 = feSpace->getAdmin()->getNumberOfPreDofs(VERTEX);
    DegreeOfFreedom dof0 = el->getDof(0, n0);
    DegreeOfFreedom dof1 = el->getDof(1, n0);
    DegreeOfFreedom dof_new = el->getChild(0)->getDof(feSpace->getMesh()->getDim(), n0);
    vec[dof_new] = vec[dof0];
    vec[dof_new] += vec[dof1];
    vec[dof_new] *= 0.5;
  }


  template<>
  const double& DOFVector<double>::evalAtPoint(WorldVector<double> &p, ElInfo *oldElInfo, double* values) const
  {
    FUNCNAME("DOFVector<double>::evalAtCoords()");
  
    Mesh *mesh = feSpace->getMesh();
    const BasisFunction *basFcts = feSpace->getBasisFcts();
  
    int dim = mesh->getDim();
    int nBasFcts = basFcts->getNumber();
  
    DegreeOfFreedom *localIndices = new DegreeOfFreedom[nBasFcts];
    DimVec<double> lambda(dim, NO_INIT);
  
    ElInfo *elInfo = mesh->createNewElInfo();
    static double value = 0.0;
    bool inside = false;
  
    if (oldElInfo && oldElInfo->getMacroElement()) {
      inside = mesh->findElInfoAtPoint(p, elInfo, lambda, oldElInfo->getMacroElement(), NULL, NULL);
      delete oldElInfo;
    } else
      inside = mesh->findElInfoAtPoint(p, elInfo, lambda, NULL, NULL, NULL);

    if (oldElInfo)
      oldElInfo = elInfo;

    if (inside) {
      basFcts->getLocalIndices(elInfo->getElement(), feSpace->getAdmin(), localIndices);
      ElementVector uh(lambda.size());
      for (int i = 0; i < lambda.size(); i++)
        uh[i] = operator[](localIndices[i]);
      value = basFcts->evalUh(lambda, uh);
    } else
      throw(std::runtime_error("Can not eval DOFVector at point p, because point is outside geometry."));

    delete [] localIndices;
    if (oldElInfo == NULL)
      delete elInfo;

    if (values != NULL)
      *values = value;
    return value;
  };


  template<>
  const WorldVector<double>& DOFVector<WorldVector<double> >::evalAtPoint(WorldVector<double> &p, ElInfo *oldElInfo, WorldVector<double>* values) const
  {
    FUNCNAME("DOFVector<double>::evalAtCoords()");
  
    Mesh *mesh = feSpace->getMesh();
    const BasisFunction *basFcts = feSpace->getBasisFcts();
  
    int dim = mesh->getDim();
    int nBasFcts = basFcts->getNumber();
  
    DegreeOfFreedom *localIndices = new DegreeOfFreedom[nBasFcts];
    DimVec<double> lambda(dim, NO_INIT);
  
    ElInfo *elInfo = mesh->createNewElInfo();

    static WorldVector<double> Values(DEFAULT_VALUE, 0.0);
    WorldVector<double> *val = (NULL != values) ? values : &Values;

    bool inside = false;
  
    if (oldElInfo && oldElInfo->getMacroElement()) {
      inside = mesh->findElInfoAtPoint(p, elInfo, lambda, oldElInfo->getMacroElement(), NULL, NULL);
      delete oldElInfo;
    } else
      inside = mesh->findElInfoAtPoint(p, elInfo, lambda, NULL, NULL, NULL);

    if (oldElInfo)
      oldElInfo = elInfo;

    if (inside) {
      basFcts->getLocalIndices(elInfo->getElement(), feSpace->getAdmin(), localIndices);
      mtl::dense_vector<WorldVector<double> > uh(lambda.size());
      for (int i = 0; i < lambda.size(); i++)
        uh[i] = operator[](localIndices[i]);
      basFcts->evalUh(lambda, uh, val);
    } else
      throw(std::runtime_error("Can not eval DOFVector at point p, because point is outside geometry."));

    delete [] localIndices;
    if (oldElInfo == NULL)
      delete elInfo;

    return ((*val));
  };


  template<>
  double DOFVector<double>::IntOnBoundary(BoundaryType boundaryType, 
                                          Quadrature* q) const
  {
    FUNCNAME("DOFVector<T>::IntOnBoundary()");
  
    Mesh* mesh = this->feSpace->getMesh();
    int dim = mesh->getDim();
  
    if (!q) {
      int deg = 2 * this->feSpace->getBasisFcts()->getDegree();
      q = Quadrature::provideQuadrature(dim - 1, deg);
    } else {
      TEST_EXIT(q->getDim() == dim-1)
        ("Provided quadrature has wrong dimension for surfaceQuadrature!\n");
    }
  
    // create barycentric coords for each vertex of each side
    const Element *refElement = Global::getReferenceElement(dim);
    VectorOfFixVecs<DimVec<double> >**coords;
    coords = new VectorOfFixVecs<DimVec<double> >*[dim + 1];
  
    // for all element sides
    for (int i = 0; i < dim + 1; i++) {
      coords[i] = new VectorOfFixVecs<DimVec<double> >(dim, dim, DEFAULT_VALUE,
        DimVec<double>(dim, DEFAULT_VALUE, 0.0));
      // for each vertex of the side
      for (int k = 0; k < dim; k++) {
        int index = refElement->getVertexOfPosition(INDEX_OF_DIM(dim - 1, dim), 
                                                    i, k);
        (*coords[i])[k][index] = 1.0;
      }
    }
  
    std::vector<SurfaceQuadrature*> quadSurfaces(dim + 1);
    for (int i = 0; i < dim + 1; i++)
      quadSurfaces[i] = new SurfaceQuadrature(q, *coords[i]);
  
    double result = 0.0;
    TraverseStack stack;
    ElInfo *elInfo = stack.traverseFirst(mesh, -1, 
      Mesh::CALL_LEAF_EL | Mesh::FILL_BOUND | Mesh::FILL_COORDS);
    while (elInfo) {
      for (int face = 0; face < dim + 1; face++) {
        if (elInfo->getBoundary(face) == boundaryType) {
          int nPoints = quadSurfaces[face]->getNumPoints();
          mtl::dense_vector<double> uh_vec(nPoints);
          double det = elInfo->calcSurfaceDet(*coords[face]);
          double normT = 0.0;
          this->getVecAtQPs(elInfo, quadSurfaces[face], NULL, uh_vec);
          for (int iq = 0; iq < nPoints; iq++)
            normT += quadSurfaces[face]->getWeight(iq) * (uh_vec[iq]);
          result += det * normT;
        }
      }
  
      elInfo = stack.traverseNext(elInfo);
    }
  
    #ifdef HAVE_PARALLEL_DOMAIN_AMDIS
    double localResult = result;
    MPI::COMM_WORLD.Allreduce(&localResult, &result, 1, MPI_DOUBLE, MPI_SUM);
    #endif
    
    return result;
  }


  template<>
  double DOFVector<WorldVector<double> >::IntOnBoundaryNormal(
    BoundaryType boundaryType, Quadrature* q) const
  {
    FUNCNAME("DOFVector<T>::IntOnBoundary()");
 
    Mesh* mesh = this->feSpace->getMesh();
    int dim = mesh->getDim();
  
    if (!q) {
      int deg = 2 * this->feSpace->getBasisFcts()->getDegree();
      q = Quadrature::provideQuadrature(dim - 1, deg);
    } else {
      TEST_EXIT(q->getDim() == dim-1)
        ("Provided quadrature has wrong dimension for surfaceQuadrature!\n");
    }
  
    // create barycentric coords for each vertex of each side
    const Element *refElement = Global::getReferenceElement(dim);
    VectorOfFixVecs<DimVec<double> >**coords;
    coords = new VectorOfFixVecs<DimVec<double> >*[dim + 1];
  
    // for all element sides
    for (int i = 0; i < dim + 1; i++) {
      coords[i] = new VectorOfFixVecs<DimVec<double> >(dim, dim, DEFAULT_VALUE,
        DimVec<double>(dim, DEFAULT_VALUE, 0.0));
      // for each vertex of the side
      for (int k = 0; k < dim; k++) {
        int index = refElement->getVertexOfPosition(INDEX_OF_DIM(dim - 1, dim), 
                                                    i, k);
        (*coords[i])[k][index] = 1.0;
      }
    }
  
    std::vector<SurfaceQuadrature*> quadSurfaces(dim + 1);
    for (int i = 0; i < dim + 1; i++)
      quadSurfaces[i] = new SurfaceQuadrature(q, *coords[i]);
  
    double result = 0.0;
    WorldVector<double> normal;
    TraverseStack stack;
    ElInfo *elInfo = stack.traverseFirst(mesh, -1, 
      Mesh::CALL_LEAF_EL | Mesh::FILL_BOUND | Mesh::FILL_COORDS);
    while (elInfo) {
      for (int face = 0; face < dim + 1; face++) {
        if (elInfo->getBoundary(face) == boundaryType) {
          elInfo->getNormal(face, normal);
          double det = elInfo->calcSurfaceDet(*coords[face]);
  
          int nPoints = quadSurfaces[face]->getNumPoints();
          mtl::dense_vector<WorldVector<double> > uh_vec(nPoints);
          WorldVector<double> normT; normT.set(0.0);
          this->getVecAtQPs(elInfo, quadSurfaces[face], NULL, uh_vec);
          for (int iq = 0; iq < nPoints; iq++)
            normT += quadSurfaces[face]->getWeight(iq) * (uh_vec[iq]);
          // scalar product between vector-valued solution and normal vector
          result += det * (normT * normal); 
        }
      }
  
      elInfo = stack.traverseNext(elInfo);
    }
  
    #ifdef HAVE_PARALLEL_DOMAIN_AMDIS
    double localResult = result;
    MPI::COMM_WORLD.Allreduce(&localResult, &result, 1, MPI_DOUBLE, MPI_SUM);
    #endif
    
    return result;
  }


  template<>
  DOFVector<WorldVector<double> >*
  DOFVector<double>::getGradient(DOFVector<WorldVector<double> > *grad) const 
  {
    FUNCNAME("DOFVector<double>::getGradient()");

    // define result vector
    static DOFVector<WorldVector<double> > *result = NULL;

    if (grad) {
      result = grad;
    } else {
      if(result && result->getFeSpace() != feSpace) {
	delete result;
	result = new DOFVector<WorldVector<double> >(feSpace, "gradient");
      }
    }

    Mesh *mesh = feSpace->getMesh();
    int dim = mesh->getDim();
    const BasisFunction *basFcts = feSpace->getBasisFcts();
    DOFAdmin *admin = feSpace->getAdmin();

    // count number of nodes and dofs per node
    std::vector<int> nNodeDOFs;
    std::vector<int> nNodePreDofs;
    std::vector<DimVec<double>*> bary;

    int nNodes = 0;
    int nDofs = 0;

    for (int i = 0; i < dim + 1; i++) {
      GeoIndex geoIndex = INDEX_OF_DIM(i, dim);
      int nPositions = mesh->getGeo(geoIndex);
      int numPreDofs = admin->getNumberOfPreDofs(i);
      for (int j = 0; j < nPositions; j++) {
	int dofs = basFcts->getNumberOfDofs(geoIndex);
	nNodeDOFs.push_back(dofs);
	nDofs += dofs;
	nNodePreDofs.push_back(numPreDofs);
      }
      nNodes += nPositions;
    }

    TEST_EXIT_DBG(nDofs == basFcts->getNumber())
      ("number of dofs != number of basis functions\n");
    
    for (int i = 0; i < nDofs; i++)
      bary.push_back(basFcts->getCoords(i));    

    ElementVector localUh(basFcts->getNumber());

    // traverse mesh
    std::vector<bool> visited(getUsedSize(), false);
    TraverseStack stack;
    Flag fillFlag = Mesh::CALL_LEAF_EL | Mesh::FILL_GRD_LAMBDA | Mesh::FILL_COORDS;
    ElInfo *elInfo = stack.traverseFirst(mesh, -1, fillFlag);

    while (elInfo) {
      const DegreeOfFreedom **dof = elInfo->getElement()->getDof();
      const DimVec<WorldVector<double> > &grdLambda = elInfo->getGrdLambda();
      getLocalVector(elInfo->getElement(), localUh);

      int localDOFNr = 0;
      for (int i = 0; i < nNodes; i++) { // for all nodes
	for (int j = 0; j < nNodeDOFs[i]; j++) { // for all dofs at this node
	  DegreeOfFreedom dofIndex = dof[i][nNodePreDofs[i] + j];
	  if (!visited[dofIndex]) {	  
	    basFcts->evalGrdUh(*(bary[localDOFNr]), grdLambda, 
			       localUh, &((*result)[dofIndex]));

	    visited[dofIndex] = true;
	  }
	  localDOFNr++;
	}
      }

      elInfo = stack.traverseNext(elInfo);
    }

    return result;
  }


  template<>
  DOFVector<WorldVector<double> >*
  DOFVector<double>::getRecoveryGradient(DOFVector<WorldVector<double> > *grad) const 
  {
    FUNCNAME("DOFVector<double>::getRecoveryGradient()");

    // define result vector
    static DOFVector<WorldVector<double> > *vec = NULL;

    DOFVector<WorldVector<double> > *result = grad;

    if (!result) {
      if (vec && vec->getFeSpace() != feSpace) {
	delete vec;
	vec = NULL;
      }
      if (!vec)
	vec = new DOFVector<WorldVector<double> >(feSpace, "gradient");
      
      result = vec;
    }

    result->set(WorldVector<double>(DEFAULT_VALUE, 0.0));

    DOFVector<double> volume(feSpace, "volume");
    volume.set(0.0);

    const BasisFunction *basFcts = feSpace->getBasisFcts();
    int nPreDofs = feSpace->getAdmin()->getNumberOfPreDofs(VERTEX);

    DimVec<double> bary(dim, DEFAULT_VALUE, (1.0 / (dim + 1.0)));
    WorldVector<double> grd;

    // traverse mesh
    Mesh *mesh = feSpace->getMesh();
    TraverseStack stack;
    ElInfo *elInfo = stack.traverseFirst(mesh, -1,
					 Mesh::CALL_LEAF_EL | Mesh::FILL_DET | 
					 Mesh::FILL_GRD_LAMBDA | Mesh::FILL_COORDS);

    ElementVector localUh(basFcts->getNumber());

    while (elInfo) {
      double det = elInfo->getDet();
      const DegreeOfFreedom **dof = elInfo->getElement()->getDof();
      const DimVec<WorldVector<double> > &grdLambda = elInfo->getGrdLambda();
      getLocalVector(elInfo->getElement(), localUh);
      basFcts->evalGrdUh(bary, grdLambda, localUh, &grd);

      for (int i = 0; i < dim + 1; i++) {
	DegreeOfFreedom dofIndex = dof[i][nPreDofs];
	(*result)[dofIndex] += grd * det;
	volume[dofIndex] += det;
      }

      elInfo = stack.traverseNext(elInfo);
    }

    DOFVector<double>::Iterator volIt(&volume, USED_DOFS);
    DOFVector<WorldVector<double> >::Iterator grdIt(result, USED_DOFS);

    for (volIt.reset(), grdIt.reset(); !volIt.end(); ++volIt, ++grdIt)
      if (*volIt != 0.0)
	*grdIt *= 1.0 / (*volIt);

    return result;
  }


  template<>
  const WorldVector<double> *DOFVectorBase<double>::getGrdAtQPs(const ElInfo *elInfo, 
								const Quadrature *quad,
								const FastQuadrature *quadFast,
								WorldVector<double> *grdAtQPs) const
  {
    FUNCNAME("DOFVector<double>::getGrdAtQPs()");
  
    TEST_EXIT_DBG(quad || quadFast)("neither quad nor quadFast defined\n");

    if (quad && quadFast) {
      TEST_EXIT_DBG(quad == quadFast->getQuadrature())
      	("quad != quadFast->quadrature\n");
    }

    TEST_EXIT_DBG(!quadFast || quadFast->getBasisFunctions() == feSpace->getBasisFcts())
      ("invalid basis functions");

    int dow = Global::getGeo(WORLD);
    int nPoints = quadFast ? quadFast->getQuadrature()->getNumPoints() : quad->getNumPoints();
    static WorldVector<double> *grd = NULL;
    WorldVector<double> *result;

    if (grdAtQPs) {
      result = grdAtQPs;
    } else {
      if (grd) 
	delete [] grd;

      grd = new WorldVector<double>[nPoints];
      for (int i = 0; i < nPoints; i++)
	grd[i].set(0.0);
      
      result = grd;
    }
  
    ElementVector localVec(nBasFcts);
    getLocalVector(elInfo->getElement(), localVec);

    mtl::dense_vector<double> grd1(dim + 1);
    int parts = Global::getGeo(PARTS, dim);
    const DimVec<WorldVector<double> > &grdLambda = elInfo->getGrdLambda();

    if (quadFast) {
      for (int i = 0; i < nPoints; i++) {
	grd1 = 0.0;

	for (int j = 0; j < nBasFcts; j++)
	  for (int k = 0; k < parts; k++)
	    grd1[k] += quadFast->getGradient(i, j, k) * localVec[j];
	  
	for (int l=0; l < dow; l++) {
	  result[i][l] = 0.0;
	  for (int k = 0; k < parts; k++)
	    result[i][l] += grdLambda[k][l] * grd1[k];
	}
      }

    } else {      
      const BasisFunction *basFcts = feSpace->getBasisFcts();
      mtl::dense_vector<double> grdPhi(dim + 1);

      for (int i = 0; i < nPoints; i++) {
	grd1 = 0.0;

	for (int j = 0; j < nBasFcts; j++) {
	  (*(basFcts->getGrdPhi(j)))(quad->getLambda(i), grdPhi);
	  for (int k = 0; k < parts; k++)
	    grd1[k] += grdPhi[k] * localVec[j];
	}

	for (int l = 0; l < dow; l++) {
	  result[i][l] = 0.0;
	  for (int k = 0; k < parts; k++)
	    result[i][l] += grdLambda[k][l] * grd1[k];
	}
      }
    }

    return const_cast<const WorldVector<double>*>(result);
  }


  template<>
  const WorldVector<double> *DOFVectorBase<double>::getGrdAtQPs(const ElInfo *smallElInfo,
								const ElInfo *largeElInfo,
								const Quadrature *quad,
								const FastQuadrature *quadFast,
								WorldVector<double> *grdAtQPs) const
  {
    FUNCNAME("DOFVector<double>::getGrdAtQPs()");
  
    TEST_EXIT_DBG(quad || quadFast)("neither quad nor quadFast defined\n");

    if (quad && quadFast) {
      TEST_EXIT_DBG(quad == quadFast->getQuadrature())("quad != quadFast->quadrature\n");
    }

    TEST_EXIT_DBG(!quadFast || quadFast->getBasisFunctions() == feSpace->getBasisFcts())
      ("invalid basis functions");

    int dow = Global::getGeo(WORLD);
    int nPoints = quadFast ? quadFast->getQuadrature()->getNumPoints() : quad->getNumPoints();
    static WorldVector<double> *grd = NULL;
    WorldVector<double> *result;

    if (grdAtQPs) {
      result = grdAtQPs;
    } else {
      if (grd) 
	delete [] grd;

      grd = new WorldVector<double>[nPoints];
      for (int i = 0; i < nPoints; i++)
	grd[i].set(0.0);

      result = grd;
    }
  
    ElementVector localVec(nBasFcts);
    getLocalVector(largeElInfo->getElement(), localVec);

    const BasisFunction *basFcts = feSpace->getBasisFcts();    
    mtl::dense2D<double> &m = smallElInfo->getSubElemCoordsMat(basFcts->getDegree());

    int parts = Global::getGeo(PARTS, dim);
    const DimVec<WorldVector<double> > &grdLambda = largeElInfo->getGrdLambda();

    mtl::dense_vector<double> grd1(dim + 1);
    mtl::dense_vector<double> grdPhi(dim + 1);
    mtl::dense_vector<double> tmp(dim + 1);
    
    for (int i = 0; i < nPoints; i++) {
      grd1 = 0.0;
      
      for (int j = 0; j < nBasFcts; j++) {
	grdPhi = 0.0;

	for (int k = 0; k < nBasFcts; k++) {
	  (*(basFcts->getGrdPhi(k)))(quad->getLambda(i), tmp);
	  tmp *= m[j][k];
	  grdPhi += tmp;
	}

	for (int k = 0; k < parts; k++)
	  grd1[k] += grdPhi[k] * localVec[j];
      }
      
      for (int l = 0; l < dow; l++) {
	result[i][l] = 0.0;
	for (int k = 0; k < parts; k++)
	  result[i][l] += grdLambda[k][l] * grd1[k];
      }
    }    
  
    return const_cast<const WorldVector<double>*>(result);
  }


  template<>
  const WorldMatrix<double> *DOFVectorBase<double>::getD2AtQPs(const ElInfo *elInfo, 
							       const Quadrature *quad,
							       const FastQuadrature *quadFast,
							       WorldMatrix<double>  *d2AtQPs) const
  {
    FUNCNAME("DOFVector<double>::getD2AtQPs()");
  
    TEST_EXIT_DBG(quad || quadFast)("neither quad nor quadFast defined\n");

    if (quad && quadFast) {
      TEST_EXIT_DBG(quad == quadFast->getQuadrature())
      	("quad != quadFast->quadrature\n");
    }

    TEST_EXIT_DBG(!quadFast || quadFast->getBasisFunctions() == feSpace->getBasisFcts())
      ("invalid basis functions");

    Element *el = elInfo->getElement(); 

    int dow = Global::getGeo(WORLD);
    int nPoints = quadFast ? quadFast->getQuadrature()->getNumPoints() : quad->getNumPoints();

    static WorldMatrix<double> *vec = NULL;
    WorldMatrix<double> *result;

    if (d2AtQPs) {
      result = d2AtQPs;
    } else {
      if(vec) delete [] vec;
      vec = new WorldMatrix<double>[nPoints];
      for (int i = 0; i < nPoints; i++) {
	vec[i].set(0.0);
      }
      result = vec;
    }
  
    ElementVector localVec(nBasFcts);
    getLocalVector(el, localVec);

    DimMat<double> D2Tmp(dim, DEFAULT_VALUE, 0.0);
    int parts = Global::getGeo(PARTS, dim);
    const DimVec<WorldVector<double> > &grdLambda = elInfo->getGrdLambda();

    if (quadFast) {
      for (int iq = 0; iq < nPoints; iq++) {
	for (int k = 0; k < parts; k++)
	  for (int l = 0; l < parts; l++)
	    D2Tmp[k][l] = 0.0;

	for (int i = 0; i < nBasFcts; i++) {
	  for (int k = 0; k < parts; k++)
	    for (int l = 0; l < parts; l++)
	      D2Tmp[k][l] += localVec[i] * quadFast->getSecDer(iq, i, k, l);
	}

	for (int i = 0; i < dow; i++)
	  for (int j = 0; j < dow; j++) {
	    result[iq][i][j] = 0.0;
	    for (int k = 0; k < parts; k++)
	      for (int l = 0; l < parts; l++)
		result[iq][i][j] += grdLambda[k][i]*grdLambda[l][j]*D2Tmp[k][l];
	  }
      }
    } else {
      const BasisFunction *basFcts = feSpace->getBasisFcts();
      DimMat<double> D2Phi(dim, NO_INIT);

      for (int iq = 0; iq < nPoints; iq++) {
	for (int k = 0; k < parts; k++)
	  for (int l = 0; l < parts; l++)
	    D2Tmp[k][l] = 0.0;

	for (int i = 0; i < nBasFcts; i++) {
	  WARNING("not tested after index correction\n");
	  (*(basFcts->getD2Phi(i)))(quad->getLambda(iq), D2Phi);

	  for (int k = 0; k < parts; k++)
	    for (int l = 0; l < parts; l++)
	      D2Tmp[k][l] += localVec[i] * D2Phi[k][l];
	}

	for (int i = 0; i < dow; i++)
	  for (int j = 0; j < dow; j++) {
	    result[iq][i][j] = 0.0;
	    for (int k = 0; k < parts; k++)
	      for (int l = 0; l < parts; l++)
		result[iq][i][j] += grdLambda[k][i] * grdLambda[l][j] * D2Tmp[k][l];
	  }
      }
    }

    return const_cast<const WorldMatrix<double>*>(result);
  }


  template<>
  void DOFVector<double>::interpol(DOFVector<double> *source, double factor) 
  {
    FUNCNAME("DOFVector<double>::interpol()");

    const FiniteElemSpace *sourceFeSpace = source->getFeSpace();
    const BasisFunction *basisFcts = feSpace->getBasisFcts();
    const BasisFunction *sourceBasisFcts = sourceFeSpace->getBasisFcts();

    int nBasisFcts = basisFcts->getNumber();
    int nSourceBasisFcts = sourceBasisFcts->getNumber();

    this->set(0.0);

    std::vector<DegreeOfFreedom> myLocalIndices(nBasisFcts);
    ElementVector sourceLocalCoeffs(nSourceBasisFcts);

    if (feSpace->getMesh() == sourceFeSpace->getMesh()) {
      DimVec<double> *coords = NULL;
      TraverseStack stack;
      ElInfo *elInfo = stack.traverseFirst(feSpace->getMesh(), -1,
					   Mesh::CALL_LEAF_EL | 
					   Mesh::FILL_COORDS);

      while (elInfo) {
	Element *el = elInfo->getElement();

	basisFcts->getLocalIndices(el, feSpace->getAdmin(), myLocalIndices);
	source->getLocalVector(el, sourceLocalCoeffs);

	for (int i = 0; i < nBasisFcts; i++) {
	  if (vec[myLocalIndices[i]] == 0.0) {
	    coords = basisFcts->getCoords(i);
	    vec[myLocalIndices[i]] = sourceBasisFcts->evalUh(*coords, sourceLocalCoeffs) * factor;
	  }
	}
	elInfo = stack.traverseNext(elInfo);
      }
    } else {
      DimVec<double> coords2(feSpace->getMesh()->getDim(), NO_INIT);
      DualTraverse dualStack;
      ElInfo *elInfo1, *elInfo2;
      ElInfo *elInfoSmall, *elInfoLarge;
      WorldVector<double> worldVec;

      bool nextTraverse = dualStack.traverseFirst(feSpace->getMesh(),
						  sourceFeSpace->getMesh(),
						  -1, -1,
						  Mesh::CALL_LEAF_EL | Mesh::FILL_COORDS,
						  Mesh::CALL_LEAF_EL | Mesh::FILL_COORDS,
						  &elInfo1, &elInfo2,
						  &elInfoSmall, &elInfoLarge);
      while (nextTraverse) {     
	basisFcts->getLocalIndices(elInfo1->getElement(), feSpace->getAdmin(), 
				   myLocalIndices);
	source->getLocalVector(elInfo2->getElement(), sourceLocalCoeffs);

	for (int i = 0; i < nBasisFcts; i++) {
	  if (vec[myLocalIndices[i]] == 0.0) {
            elInfo1->coordToWorld(*(basisFcts->getCoords(i)), worldVec);
	    elInfo2->worldToCoord(worldVec, &coords2);
	  
	    bool isPositive = true;
	    for (int j = 0; j < coords2.size(); j++) {
	      if (coords2[j] < -0.00001) {
		isPositive = false;
		break;
	      }
	    }
	  
	    if (isPositive)
	      vec[myLocalIndices[i]] = 
		sourceBasisFcts->evalUh(coords2, sourceLocalCoeffs);	   
	  }
	}
      
	nextTraverse = 
	  dualStack.traverseNext(&elInfo1, &elInfo2, &elInfoSmall, &elInfoLarge);
      }
    }
  }


  template<>
  void DOFVector<WorldVector<double> >::interpol(DOFVector<WorldVector<double> > *v, 
						 double factor) 
  {
    WorldVector<double> nul(DEFAULT_VALUE,0.0);

    this->set(nul);

    DimVec<double> *coords = NULL;
    const FiniteElemSpace *vFeSpace = v->getFeSpace();

    if (feSpace == vFeSpace)
      WARNING("same FE-spaces\n");

    const BasisFunction *basFcts = feSpace->getBasisFcts();
    const BasisFunction *vBasFcts = vFeSpace->getBasisFcts();

    int nBasFcts = basFcts->getNumber();
    int vNumBasFcts = vBasFcts->getNumber();

    if (feSpace->getMesh() == vFeSpace->getMesh()) {      
      std::vector<DegreeOfFreedom> myLocalIndices(nBasFcts);
      mtl::dense_vector<WorldVector<double> > vLocalCoeffs(vNumBasFcts);
      Mesh *mesh = feSpace->getMesh();
      TraverseStack stack;
      ElInfo *elInfo = 
	stack.traverseFirst(mesh, -1, Mesh::CALL_LEAF_EL | Mesh::FILL_COORDS);

      while (elInfo) {
	Element *el = elInfo->getElement();
	basFcts->getLocalIndices(el, feSpace->getAdmin(), myLocalIndices);
	v->getLocalVector(el, vLocalCoeffs);

	for (int i = 0; i < nBasFcts; i++) {
	  if (vec[myLocalIndices[i]] == nul) {
	    coords = basFcts->getCoords(i);
	    vec[myLocalIndices[i]] += vBasFcts->evalUh(*coords, vLocalCoeffs, NULL) * factor;
	  }
	}
	elInfo = stack.traverseNext(elInfo);
      }
    } else {
      ERROR_EXIT("not yet for dual traverse\n");
    }
  }


  template<>
  WorldVector<DOFVector<double>*> *DOFVector<double>::getGradient(WorldVector<DOFVector<double>*> *grad) const
  {
    FUNCNAME("DOFVector<double>::getGradient()");

    Mesh *mesh = feSpace->getMesh();
    int dim = mesh->getDim();
    int dow = Global::getGeo(WORLD);

    const BasisFunction *basFcts = feSpace->getBasisFcts();

    DOFAdmin *admin = feSpace->getAdmin();

    // define result vector
    static WorldVector<DOFVector<double>*> *result = NULL;

    if (grad) {
      result = grad;
    } else {
      if (!result) {
	result = new WorldVector<DOFVector<double>*>;

	result->set(NULL);
      }
      for (int i = 0; i < dow; i++) {
	if ((*result)[i] && (*result)[i]->getFeSpace() != feSpace) {
	  delete (*result)[i];
	  (*result)[i] = new DOFVector<double>(feSpace, "gradient");
	}
      }
    }

    // count number of nodes and dofs per node
    std::vector<int> nNodeDOFs;
    std::vector<int> nNodePreDofs;
    std::vector<DimVec<double>*> bary;

    int nNodes = 0;
    int nDofs = 0;

    for (int i = 0; i < dim + 1; i++) {
      GeoIndex geoIndex = INDEX_OF_DIM(i, dim);
      int numPositionNodes = mesh->getGeo(geoIndex);
      int numPreDofs = admin->getNumberOfPreDofs(i);
      for (int j = 0; j < numPositionNodes; j++) {
	int dofs = basFcts->getNumberOfDofs(geoIndex);
	nNodeDOFs.push_back(dofs);
	nDofs += dofs;
	nNodePreDofs.push_back(numPreDofs);
      }
      nNodes += numPositionNodes;
    }

    TEST_EXIT_DBG(nDofs == basFcts->getNumber())
      ("number of dofs != number of basis functions\n");
    
    for (int i = 0; i < nDofs; i++)
      bary.push_back(basFcts->getCoords(i));    

    // traverse mesh
    std::vector<bool> visited(getUsedSize(), false);
    TraverseStack stack;
    Flag fillFlag = Mesh::CALL_LEAF_EL | Mesh::FILL_GRD_LAMBDA | Mesh::FILL_COORDS;
    ElInfo *elInfo = stack.traverseFirst(mesh, -1, fillFlag);
    WorldVector<double> grd;
    ElementVector localUh(basFcts->getNumber());

    while (elInfo) {
      const DegreeOfFreedom **dof = elInfo->getElement()->getDof();
      getLocalVector(elInfo->getElement(), localUh);
      const DimVec<WorldVector<double> > &grdLambda = elInfo->getGrdLambda();

      int localDOFNr = 0;
      for (int i = 0; i < nNodes; i++) { // for all nodes
	for (int j = 0; j < nNodeDOFs[i]; j++) { // for all dofs at this node
	  DegreeOfFreedom dofIndex = dof[i][nNodePreDofs[i] + j];

	  if (!visited[dofIndex]) {
	    basFcts->evalGrdUh(*(bary[localDOFNr]), grdLambda, localUh, &grd);

	    for (int k = 0; k < dow; k++)
	      (*(*result)[k])[dofIndex] = grd[k];	    

	    visited[dofIndex] = true;
	  }
	  localDOFNr++;
	}
      }

      elInfo = stack.traverseNext(elInfo);
    }

    return result;
  }


  DOFVectorDOF::DOFVectorDOF() : 
    DOFVector<DegreeOfFreedom>() 
  {}


  void DOFVectorDOF::freeDOFContent(DegreeOfFreedom dof) 
  {}


  WorldVector<DOFVector<double>*> *transform(DOFVector<WorldVector<double> > *vec,
					     WorldVector<DOFVector<double>*> *res)
  {
    FUNCNAME("DOFVector<double>::transform()");

    TEST_EXIT_DBG(vec)("no vector\n");

    int dow = Global::getGeo(WORLD);
    static WorldVector<DOFVector<double>*> *result = NULL;

    if (!res && !result) {
      result = new WorldVector<DOFVector<double>*>;
      for (int i = 0; i < dow; i++)
	(*result)[i] = new DOFVector<double>(vec->getFeSpace(), "transform");
    }

    WorldVector<DOFVector<double>*> *r = res ? res : result;

    int vecSize = vec->getSize();
    for (int i = 0; i < vecSize; i++)
      for (int j = 0; j < dow; j++)
	(*((*r)[j]))[i] = (*vec)[i][j];

    return r;
  }


  template<>
  void DOFVectorBase<double>::getVecAtQPs(const ElInfo *smallElInfo, 
					  const ElInfo *largeElInfo,
					  const Quadrature *quad,
					  const FastQuadrature *quadFast,
					  mtl::dense_vector<double>& vecAtQPs) const
  {
    FUNCNAME("DOFVector<double>::getVecAtQPs()");
 
    TEST_EXIT_DBG(quad || quadFast)("neither quad nor quadFast defined\n");

    if (quad && quadFast) {
      TEST_EXIT_DBG(quad == quadFast->getQuadrature())
      	("quad != quadFast->quadrature\n");
    }

    TEST_EXIT_DBG(!quadFast || quadFast->getBasisFunctions() == feSpace->getBasisFcts())
      ("invalid basis functions");

    if (smallElInfo->getMesh() == feSpace->getMesh())
      return getVecAtQPs(smallElInfo, quad, quadFast, vecAtQPs);    

    const BasisFunction *basFcts = feSpace->getBasisFcts();
    int nPoints = 
      quadFast ? quadFast->getQuadrature()->getNumPoints() : quad->getNumPoints(); 

    vecAtQPs.change_dim(nPoints);
    
    ElementVector localVec(nBasFcts);
    getLocalVector(largeElInfo->getElement(), localVec);
    mtl::dense2D<double> &m = smallElInfo->getSubElemCoordsMat(basFcts->getDegree());

    for (int i = 0; i < nPoints; i++) {
      vecAtQPs[i] = 0.0;
      for (int j = 0; j < nBasFcts; j++) {
	double val = 0.0;
	for (int k = 0; k < nBasFcts; k++)
	  val += m[j][k] * (*(basFcts->getPhi(k)))(quad->getLambda(i));

	vecAtQPs[i] += localVec[j] * val;
      }
    }
  }


  template<>
  void DOFVectorBase<double>::assemble(double factor, ElInfo *elInfo,
				       const BoundaryType *bound, 
				       Operator *op)
  {
    FUNCNAME("DOFVector::assemble()");

    if (!(op || this->operators.size())) 
      return;

    set_to_zero(this->elementVector);
    bool addVector = false;

    if (op) {
      op->getElementVector(elInfo, this->elementVector);
      addVector = true;
    } else {
      std::vector<Operator*>::iterator it;
      std::vector<double*>::iterator factorIt;

      for (it = this->operators.begin(), factorIt = this->operatorFactor.begin();	
	   it != this->operators.end(); 
	   ++it, ++factorIt)
	if ((*it)->getNeedDualTraverse() == false) {
	  (*it)->getElementVector(elInfo, this->elementVector, 
				  *factorIt ? **factorIt : 1.0);      
	  addVector = true;
	}
    }

    if (addVector)
      addElementVector(factor, this->elementVector, bound, elInfo);
  }


  template<>
  void DOFVectorBase<double>::assemble2(double factor, 
					ElInfo *mainElInfo, ElInfo *auxElInfo,
					ElInfo *smallElInfo, ElInfo *largeElInfo,
					const BoundaryType *bound, 
					Operator *op)
  {
    FUNCNAME("DOFVector::assemble2()");

    if (!(op || this->operators.size())) 
      return;

    set_to_zero(this->elementVector);
    bool addVector = false;

    TEST_EXIT(!op)("Not yet implemented!\n");

    std::vector<Operator*>::iterator it;
    std::vector<double*>::iterator factorIt;
    for (it = this->operators.begin(), factorIt = this->operatorFactor.begin();	
	 it != this->operators.end(); 
	 ++it, ++factorIt)
      if ((*it)->getNeedDualTraverse()) {
	(*it)->getElementVector(mainElInfo, auxElInfo,
				smallElInfo, largeElInfo,
				this->elementVector, 
				*factorIt ? **factorIt : 1.0);
	addVector = true;
      }
  
    if (addVector)
      addElementVector(factor, this->elementVector, bound, mainElInfo);
  }


  double integrate(const DOFVector<double> &vec1,
		   const DOFVector<double> &vec2,
		   BinaryAbstractFunction<double, double, double> *fct)
  {
    if (vec1.getFeSpace()->getMesh() == vec2.getFeSpace()->getMesh())
      return intSingleMesh(vec1, vec2, fct);
    else
      return intDualMesh(vec1, vec2, fct);
  }


  double intSingleMesh(const DOFVector<double> &vec1,
		       const DOFVector<double> &vec2,
		       BinaryAbstractFunction<double, double, double> *fct)
  {
    FUNCNAME("intDualmesh()");
    
    TEST_EXIT(fct)("No function defined!\n");

    int deg = std::max(fct->getDegree(), 
		       2 * vec1.getFeSpace()->getBasisFcts()->getDegree());
    Quadrature* quad = 
      Quadrature::provideQuadrature(vec1.getFeSpace()->getMesh()->getDim(), deg);
    FastQuadrature *fastQuad =
      FastQuadrature::provideFastQuadrature(vec1.getFeSpace()->getBasisFcts(), *quad, INIT_PHI);

    mtl::dense_vector<double> qp1(fastQuad->getNumPoints());
    mtl::dense_vector<double> qp2(fastQuad->getNumPoints());

    double value = 0.0;
    Flag traverseFlag = Mesh::CALL_LEAF_EL | Mesh::FILL_COORDS | Mesh::FILL_DET;      
    TraverseStack stack;    
    ElInfo *elInfo = stack.traverseFirst(vec1.getFeSpace()->getMesh(), -1, traverseFlag);
    while (elInfo) {
      vec1.getVecAtQPs(elInfo, quad, fastQuad, qp1);
      vec2.getVecAtQPs(elInfo, quad, fastQuad, qp2);

      double tmp = 0.0;
      for (int iq = 0; iq < fastQuad->getNumPoints(); iq++)
 	tmp += fastQuad->getWeight(iq) * (*fct)(qp1[iq], qp2[iq]);     
      value += tmp * elInfo->getDet();
      
      elInfo = stack.traverseNext(elInfo);
    }

#ifdef HAVE_PARALLEL_DOMAIN_AMDIS
    double localValue = value;
    MPI::COMM_WORLD.Allreduce(&localValue, &value, 1, MPI_DOUBLE, MPI_SUM);
#endif
    
    return value;
  }


  double intDualMesh(const DOFVector<double> &vec1,
		     const DOFVector<double> &vec2,
		     BinaryAbstractFunction<double, double, double> *fct)
  {
    FUNCNAME("intDualmesh()");
    
    TEST_EXIT(fct)("No function defined!\n");

    int deg = std::max(fct->getDegree(), 
		       2 * vec1.getFeSpace()->getBasisFcts()->getDegree());
    Quadrature* quad = 
      Quadrature::provideQuadrature(vec1.getFeSpace()->getMesh()->getDim(), deg);
    FastQuadrature *fastQuad =
      FastQuadrature::provideFastQuadrature(vec1.getFeSpace()->getBasisFcts(), *quad, INIT_PHI);

    mtl::dense_vector<double> qp1(fastQuad->getNumPoints());
    mtl::dense_vector<double> qp2(fastQuad->getNumPoints());

    double value = 0.0;
    Flag traverseFlag = Mesh::CALL_LEAF_EL | Mesh::FILL_COORDS | Mesh::FILL_DET;      
    DualTraverse dualTraverse;    
    DualElInfo dualElInfo;
    bool cont = dualTraverse.traverseFirst(vec1.getFeSpace()->getMesh(),
					   vec2.getFeSpace()->getMesh(),
					   -1, -1, traverseFlag, traverseFlag,
					   dualElInfo);
    while (cont) {
      vec1.getVecAtQPs(dualElInfo.smallElInfo, dualElInfo.largeElInfo, quad, NULL, qp1);
      vec2.getVecAtQPs(dualElInfo.smallElInfo, dualElInfo.largeElInfo, quad, NULL, qp2);

      double tmp = 0.0;
      for (int iq = 0; iq < quad->getNumPoints(); iq++)
 	tmp += quad->getWeight(iq) * (*fct)(qp1[iq], qp2[iq]);      
      value += tmp * dualElInfo.smallElInfo->getDet();
      
      cont = dualTraverse.traverseNext(dualElInfo);
    }

#ifdef HAVE_PARALLEL_DOMAIN_AMDIS
    double localValue = value;
    MPI::COMM_WORLD.Allreduce(&localValue, &value, 1, MPI_DOUBLE, MPI_SUM);
#endif

    return value;
  }

  
  double integrate(const DOFVector<double> &vec,
		   AbstractFunction<double, WorldVector<double> > *fct)
  {
    FUNCNAME("integrate()");
    
    TEST_EXIT(fct)("No function defined!\n");

    const FiniteElemSpace *feSpace = vec.getFeSpace();
    Mesh *mesh = feSpace->getMesh();

    int deg = std::max(fct->getDegree(), 2 * feSpace->getBasisFcts()->getDegree());
    Quadrature* quad = Quadrature::provideQuadrature(mesh->getDim(), deg);
    FastQuadrature *fastQuad =
      FastQuadrature::provideFastQuadrature(feSpace->getBasisFcts(), *quad, INIT_PHI);

    mtl::dense_vector<double> qp(fastQuad->getNumPoints());
    WorldVector<double> coords;

    double value = 0.0;
    Flag traverseFlag = Mesh::CALL_LEAF_EL | Mesh::FILL_COORDS | Mesh::FILL_DET;      
    TraverseStack stack;    
    ElInfo *elInfo = stack.traverseFirst(mesh, -1, traverseFlag);
    while (elInfo) {
      vec.getVecAtQPs(elInfo, quad, fastQuad, qp);

      double tmp = 0.0;
      for (int iq = 0; iq < fastQuad->getNumPoints(); iq++) {
	elInfo->coordToWorld(fastQuad->getLambda(iq), coords);
 	tmp += fastQuad->getWeight(iq) * (qp[iq] * (*fct)(coords));
      }

      value += tmp * elInfo->getDet();
      
      elInfo = stack.traverseNext(elInfo);
    }

#ifdef HAVE_PARALLEL_DOMAIN_AMDIS
    double localValue = value;
    MPI::COMM_WORLD.Allreduce(&localValue, &value, 1, MPI_DOUBLE, MPI_SUM);
#endif

    return value;
  }


  double integrate(const FiniteElemSpace* feSpace,
		   AbstractFunction<double, WorldVector<double> > *fct)
  {
    FUNCNAME("integrate()");
    
    TEST_EXIT(fct)("No function defined!\n");

    int deg = std::max(fct->getDegree(), feSpace->getBasisFcts()->getDegree());
    Quadrature* quad = 
      Quadrature::provideQuadrature(feSpace->getMesh()->getDim(), deg);
    FastQuadrature *fastQuad =
      FastQuadrature::provideFastQuadrature(feSpace->getBasisFcts(), *quad, INIT_PHI);

    WorldVector<double> coords;

    double value = 0.0;
    Flag traverseFlag = Mesh::CALL_LEAF_EL | Mesh::FILL_COORDS | Mesh::FILL_DET;      
    TraverseStack stack;    
    ElInfo *elInfo = stack.traverseFirst(feSpace->getMesh(), -1, traverseFlag);
    while (elInfo) {
      double tmp = 0.0;
      for (int iq = 0; iq < fastQuad->getNumPoints(); iq++) {
	elInfo->coordToWorld(fastQuad->getLambda(iq), coords);
 	tmp += fastQuad->getWeight(iq) * (*fct)(coords);
      }

      value += tmp * elInfo->getDet();
      
      elInfo = stack.traverseNext(elInfo);
    }

#ifdef HAVE_PARALLEL_DOMAIN_AMDIS
    double localValue = value;
    MPI::COMM_WORLD.Allreduce(&localValue, &value, 1, MPI_DOUBLE, MPI_SUM);
#endif

    return value;
  }
}