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/******************************************************************************
 *
 * AMDiS - Adaptive multidimensional simulations
 *
 * Copyright (C) 2013 Dresden University of Technology. All Rights Reserved.
 * Web: https://fusionforge.zih.tu-dresden.de/projects/amdis
 *
 * Authors: 
 * Simon Vey, Thomas Witkowski, Andreas Naumann, Simon Praetorius, et al.
 *
 * This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
 * WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
 *
 *
 * This file is part of AMDiS
 *
 * See also license.opensource.txt in the distribution.
 * 
 ******************************************************************************/
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#include <algorithm>
#include <set>
#include <map>

#include "time.h"

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#include "io/ArhReader.h"
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#include "io/MacroReader.h"
#include "io/MacroInfo.h"
#include "io/MacroWriter.h"

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#include "AdaptStationary.h"
#include "AdaptInstationary.h"
#include "FiniteElemSpace.h"
#include "ElementData.h"
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#include "ElementDofIterator.h"
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#include "MacroElement.h"
#include "Mesh.h"
#include "Traverse.h"
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#include "Initfile.h"
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#include "FixVec.h"
#include "DOFVector.h"
#include "CoarseningManager.h"
#include "DOFIterator.h"
#include "VertexVector.h"
#include "Projection.h"
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#include "ElInfoStack.h"
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#include "Serializer.h"
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#include "Lagrange.h"
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namespace AMDiS {

#define TIME_USED(f,s) ((double)((s)-(f))/(double)CLOCKS_PER_SEC)

  //**************************************************************************
  //  flags, which information should be present in the elInfo structure     
  //**************************************************************************

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  const Flag Mesh::FILL_NOTHING    = 0X00L;
  const Flag Mesh::FILL_COORDS     = 0X01L;
  const Flag Mesh::FILL_BOUND      = 0X02L;
  const Flag Mesh::FILL_NEIGH      = 0X04L;
  const Flag Mesh::FILL_OPP_COORDS = 0X08L;
  const Flag Mesh::FILL_ORIENTATION= 0X10L;
  const Flag Mesh::FILL_DET        = 0X20L;
  const Flag Mesh::FILL_GRD_LAMBDA = 0X40L;
  const Flag Mesh::FILL_ADD_ALL    = 0X80L;


  const Flag Mesh::FILL_ANY_1D = (0X01L|0X02L|0X04L|0X08L|0x20L|0X40L|0X80L);
  const Flag Mesh::FILL_ANY_2D = (0X01L|0X02L|0X04L|0X08L|0x20L|0X40L|0X80L);
  const Flag Mesh::FILL_ANY_3D = (0X01L|0X02L|0X04L|0X08L|0X10L|0x20L|0X40L|0X80L);
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  //**************************************************************************
  //  flags for Mesh traversal                                                
  //**************************************************************************

  const Flag Mesh::CALL_EVERY_EL_PREORDER  = 0X0100L;
  const Flag Mesh::CALL_EVERY_EL_INORDER   = 0X0200L;
  const Flag Mesh::CALL_EVERY_EL_POSTORDER = 0X0400L;
  const Flag Mesh::CALL_LEAF_EL            = 0X0800L;
  const Flag Mesh::CALL_LEAF_EL_LEVEL      = 0X1000L;
  const Flag Mesh::CALL_EL_LEVEL           = 0X2000L;
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  const Flag Mesh::CALL_MG_LEVEL           = 0X4000L;  
  const Flag Mesh::CALL_REVERSE_MODE       = 0X8000L;
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  vector<DegreeOfFreedom> Mesh::dof_used;
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  const int Mesh::MAX_DOF = 100;
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  map<pair<DegreeOfFreedom, int>, DegreeOfFreedom*> Mesh::serializedDOFs;
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  Mesh::Mesh(string aName, int dimension) 
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    : name(aName), 
      dim(dimension), 
      nVertices(0),
      nEdges(0),
      nLeaves(0), 
      nElements(0),
      parametric(NULL), 
      preserveCoarseDOFs(false),
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      nDofEl(0),
      nDof(dimension, DEFAULT_VALUE, 0),
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      nNodeEl(0),
      node(dimension, DEFAULT_VALUE, 0),
      elementPrototype(NULL),
      elementDataPrototype(NULL),
      elementIndex(-1),
      initialized(false),
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      macroFileInfo(NULL),
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      changeIndex(0),
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      final_lambda(dimension, DEFAULT_VALUE, 0.0)
  {
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    FUNCNAME("Mesh::Mesh()");
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#ifdef HAVE_PARALLEL_DOMAIN_AMDIS
    nParallelPreRefinements = 0;
#endif

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    // set default element prototype
    switch(dim) {
    case 1:
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      elementPrototype = new Line(this);
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      break;
    case 2:
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      elementPrototype = new Triangle(this);
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      break;
    case 3:
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      elementPrototype = new Tetrahedron(this);
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      break;
    default:
      ERROR_EXIT("invalid dimension\n");
    }

    elementPrototype->setIndex(-1);

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    elementIndex = 0;
  }
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  Mesh::~Mesh()
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  {
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    deleteMeshStructure();
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    if (macroFileInfo != NULL)
      delete macroFileInfo;    
    if (elementPrototype)
      delete elementPrototype;    
    if (elementDataPrototype)
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      delete elementDataPrototype;        
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  }
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  Mesh& Mesh::operator=(const Mesh& m)
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  {
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    FUNCNAME("Mesh::operator=()");

    if (this == &m)
      return *this;

    TEST_EXIT(dim == m.dim)("operator= works only on meshes with equal dim!\n");

    name = m.name;
    nVertices = m.nVertices;
    nEdges = m.nEdges;
    nLeaves = m.nLeaves;
    nElements = m.nElements;
    nFaces = m.nFaces;
    maxEdgeNeigh = m.maxEdgeNeigh;
    diam = m.diam;
    parametric = NULL;

    preserveCoarseDOFs = m.preserveCoarseDOFs;
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    nDofEl = m.nDofEl;
    nDof = m.nDof;
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    nNodeEl = m.nNodeEl;
    node = m.node;
    elementIndex = m.elementIndex;
    initialized = m.initialized;
    final_lambda = m.final_lambda;
    
    /* ====================== Create new DOFAdmins ================== */
    admin.resize(m.admin.size());
    for (int i = 0; i < static_cast<int>(admin.size()); i++) {
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      admin[i] = new DOFAdmin(this);
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      *(admin[i]) = *(m.admin[i]);
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      admin[i]->setMesh(this);
    }
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    /* ====================== Copy macro elements =================== */
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    // mapIndex[i] is the index of the MacroElement element in the vector
    // macroElements, for which holds: element->getIndex() = i    
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    map<int, int> mapIndex;
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    // We use this map for coping the DOFs of the Elements within the
    // MacroElements objects.
    Mesh::serializedDOFs.clear();

    int insertCounter = 0;
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    macroElements.clear();

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    // Go through all MacroElements of mesh m, and create for every a new
    // MacroElement in this mesh.
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    for (deque<MacroElement*>::const_iterator it = m.macroElements.begin();
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	 it != m.macroElements.end(); ++it, insertCounter++) {
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      // Create new MacroElement.
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      MacroElement *el = new MacroElement(dim);
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      // Use copy operator to copy all the data to the new MacroElement.
      *el = **it;

      // Make a copy of the Element data, together with all DOFs
      el->setElement((*it)->getElement()->cloneWithDOFs());

      // Insert the new MacroElement in the vector of all MacroElements.
      macroElements.push_back(el);

      // Update the index map.
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      mapIndex.insert(pair<int, int>(el->getIndex(), insertCounter));
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    }

    // Now we have to go through all the new MacroElements, and update the neighbour
    // connections.
    insertCounter = 0;
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    for (deque<MacroElement*>::const_iterator it = m.macroElements.begin();
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	 it != m.macroElements.end();
	 ++it, insertCounter++) {
      // Go through all neighbours.
      for (int i = 0; i < dim; i++) {
	// 1. Get index of the old MacroElement for its i-th neighbour.
	// 2. Because the index in the new MacroElement is the same, search
	//    for the vector index the corresponding element is stored in.
	// 3. Get this element from macroElements, and set it as the i-th
	//    neighbour for the current element.
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	if((*it)->getNeighbour(i)!=NULL) {
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	macroElements[insertCounter]->
	  setNeighbour(i, macroElements[mapIndex[(*it)->getNeighbour(i)->getIndex()]]);
      }
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      }
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    }

    // Cleanup
    Mesh::serializedDOFs.clear();

    /* ================== Things will be done when required ============ */
      
    TEST_EXIT(elementDataPrototype == NULL)("TODO\n");
    TEST_EXIT(m.parametric == NULL)("TODO\n");
    TEST_EXIT(periodicAssociations.size() == 0)("TODO\n");

    return *this;
  }

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  void Mesh::updateNumberOfLeaves()
  {
    nLeaves = 0;

    TraverseStack stack;
    ElInfo *elInfo = stack.traverseFirst(this, -1, Mesh::CALL_LEAF_EL);
    while (elInfo) {
      nLeaves++;
      elInfo = stack.traverseNext(elInfo);
    }
  }

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  void Mesh::addMacroElement(MacroElement* me) 
  {
    macroElements.push_back(me); 
    me->setIndex(macroElements.size());
  }

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  void Mesh::removeMacroElements(std::set<MacroElement*>& delMacros,
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				 vector<const FiniteElemSpace*>& feSpaces) 
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  {
    FUNCNAME("Mesh::removeMacroElement()");

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    typedef map<const DegreeOfFreedom*, std::set<MacroElement*> > DofElMap;
    typedef map<const DegreeOfFreedom*, GeoIndex> DofPosMap;
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    TEST_EXIT(feSpaces.size() > 0)("Should not happen!\n");
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    // Search for the FE space with the highest degree of polynomials. Using this
    // FE space ensures that deleting DOFs defined on it, also DOFs of lower
    // order FE spaces will be deleted correctly.
    const FiniteElemSpace *feSpace = FiniteElemSpace::getHighest(feSpaces);
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    // === Determine to all DOFs in mesh the macro elements where the DOF  ===
    // === is part of.                                                     ===
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    // Map that stores for each DOF pointer (which may have a list of DOFs)
    // all macro element indices that own this DOF.
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    DofElMap dofsOwner;
    DofPosMap dofsPosIndex;
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    ElementDofIterator elDofIter(feSpace);
    TraverseStack stack;
    ElInfo *elInfo = stack.traverseFirst(this, -1, Mesh::CALL_LEAF_EL);
    while (elInfo) {
      elDofIter.reset(elInfo->getElement());
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      do {
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	dofsOwner[elDofIter.getBaseDof()].insert(elInfo->getMacroElement());
	dofsPosIndex[elDofIter.getBaseDof()] = elDofIter.getPosIndex();
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      } while (elDofIter.nextStrict());
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      elInfo = stack.traverseNext(elInfo);
    }		   

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    // === Remove macro elements from mesh macro element list. ===

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    // Removing arbitrary elements from an deque is very slow. Therefore, we
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    // create a new deque with all macro elements that should not be deleted. The
    // macro element deque is than replaced by the new created one.

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    deque<MacroElement*> newMacroElements;
    for (deque<MacroElement*>::iterator elIter = macroElements.begin();
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	 elIter != macroElements.end(); ++elIter) {
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      // If the current mesh macro element should not be deleted, i.e., it is not
      // a member of the list of macro elements to be deleted, is is inserted to
      // the new macro element list.
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      if (delMacros.find(*elIter) == delMacros.end())
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	newMacroElements.push_back(*elIter);     
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    }
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    // And replace the macro element list with the new one.
    macroElements.clear();
    macroElements = newMacroElements;

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    // === For all macro elements to be deleted, delete them also to be       ===
    // === neighbours of some other macro elements. Furtheremore, delete the  ===
    // === whole element hierarchie structure of the macro element.           ===
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    for (std::set<MacroElement*>::iterator macroIt = delMacros.begin();
	 macroIt != delMacros.end(); ++macroIt) {
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      // Go through all neighbours of the macro element and remove this macro
      // element to be neighbour of some other macro element.
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      for (int i = 0; i < getGeo(NEIGH); i++)
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	if ((*macroIt)->getNeighbour(i))
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	  for (int j = 0; j < getGeo(NEIGH); j++)
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	    if ((*macroIt)->getNeighbour(i)->getNeighbour(j) == *macroIt)
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	      (*macroIt)->getNeighbour(i)->setNeighbour(j, NULL);

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      Element *mel = (*macroIt)->getElement();
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      // Delete element hierarchie
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      if (!(mel->isLeaf())) {
	delete mel->getChild(0);
	delete mel->getChild(1);
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	mel->child[0] = NULL;
	mel->child[1] = NULL;
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	mel->setElementData(elementDataPrototype->clone()); 
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      }
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      mel->delDofPtr();
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    }     
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    // === Check now all the DOFs that have no owner anymore and therefore  ===
    // === have to be removed.                                              ===
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    for (DofElMap::iterator dofsIt = dofsOwner.begin(); 
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	 dofsIt != dofsOwner.end(); ++dofsIt) {
      
      bool deleteDof = true;

      for (std::set<MacroElement*>::iterator elIter = dofsIt->second.begin();
	   elIter != dofsIt->second.end(); ++elIter) {
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	std::set<MacroElement*>::iterator mIt = delMacros.find(*elIter);
	if (mIt == delMacros.end()) {
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	  deleteDof = false;
	  break;
	}
      }

      if (deleteDof)
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	freeDof(const_cast<DegreeOfFreedom*>(dofsIt->first), 
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		dofsPosIndex[dofsIt->first]);      
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    }

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    // === Update number of elements, vertices, etc. ===
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    nLeaves = 0;
    nElements = 0;

    std::set<const DegreeOfFreedom*> allVertices;

    elInfo = stack.traverseFirst(this, -1, Mesh::CALL_EVERY_EL_PREORDER);
    while (elInfo) {
      nElements++;
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      if (elInfo->getElement()->isLeaf()) {
	nLeaves++;

	for (int i = 0; i < getGeo(VERTEX); i++)
	  allVertices.insert(elInfo->getElement()->getDof(i));
      }

      elInfo = stack.traverseNext(elInfo);
    }

    nVertices = allVertices.size();

    // === Note: Although the macro elements are removed from the mesh,   ===
    // === they are not deleted from memory. The macro elements are still ===
    // === stored in macroInfo structure. They are needed, if the mesh is ===
    // === redistributed between the ranks.                               ===
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  }
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  void Mesh::addDOFAdmin(DOFAdmin *localAdmin)
  {    
    FUNCNAME("Mesh::addDOFAdmin()");

    localAdmin->setMesh(this);

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    TEST_EXIT(find(admin.begin(), admin.end(), localAdmin) == admin.end())
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      ("admin %s is already associated to mesh %s\n",
       localAdmin->getName().c_str(), this->getName().c_str());
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    admin.push_back(localAdmin);

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    nDofEl = 0;
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    localAdmin->setNumberOfPreDofs(VERTEX, nDof[VERTEX]);
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    nDof[VERTEX] += localAdmin->getNumberOfDofs(VERTEX);
    nDofEl += getGeo(VERTEX) * nDof[VERTEX];
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    if (dim > 1) {
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      localAdmin->setNumberOfPreDofs(EDGE, nDof[EDGE]);
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      nDof[EDGE] += localAdmin->getNumberOfDofs(EDGE);
      nDofEl += getGeo(EDGE) * nDof[EDGE];
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    }

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    localAdmin->setNumberOfPreDofs(CENTER, nDof[CENTER]);
    nDof[CENTER] += localAdmin->getNumberOfDofs(CENTER);
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    nDofEl += nDof[CENTER];
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    TEST_EXIT_DBG(nDof[VERTEX] > 0)("no vertex dofs\n");
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    node[VERTEX] = 0;
    nNodeEl = getGeo(VERTEX);
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    if (dim > 1) {
      node[EDGE] = nNodeEl;
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      if (nDof[EDGE] > 0) 
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	nNodeEl += getGeo(EDGE);
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    }

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    if (dim == 3) {
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      localAdmin->setNumberOfPreDofs(FACE, nDof[FACE]);
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      nDof[FACE] += localAdmin->getNumberOfDofs(FACE);
      nDofEl += getGeo(FACE) * nDof[FACE];
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      node[FACE] = nNodeEl;
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      if (nDof[FACE] > 0) 
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	nNodeEl += getGeo(FACE);
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    }

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    node[CENTER] = nNodeEl;
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    if (nDof[CENTER] > 0)
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      nNodeEl += 1;
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  }

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  void Mesh::dofCompress()
  {
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    FUNCNAME_DBG("Mesh::dofCompress()");
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    for (unsigned int iadmin = 0; iadmin < admin.size(); iadmin++) {
      DOFAdmin* compressAdmin = admin[iadmin];
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      TEST_EXIT_DBG(compressAdmin)("no admin[%d] in mesh\n", iadmin);
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      int size = compressAdmin->getSize();
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      if (size < 1 || 
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	  compressAdmin->getUsedDofs() < 1 || 
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	  compressAdmin->getHoleCount() < 1)    
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	continue;
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      vector<int> newDofIndex(size);     
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      compressAdmin->compress(newDofIndex);
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      Flag fill_flag = (preserveCoarseDOFs ?  
			Mesh::CALL_EVERY_EL_PREORDER | Mesh::FILL_NOTHING :
			Mesh::CALL_LEAF_EL | Mesh::FILL_NOTHING);          
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      TraverseStack stack;
      ElInfo *elInfo = stack.traverseFirst(this, -1, fill_flag);
      while (elInfo) {
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	elInfo->getElement()->newDofFct1(compressAdmin, newDofIndex);
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	elInfo = stack.traverseNext(elInfo);
      }

      elInfo = stack.traverseFirst(this, -1, fill_flag);
      while (elInfo) {
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	elInfo->getElement()->newDofFct2(compressAdmin);
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	elInfo = stack.traverseNext(elInfo);
      }
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    }       
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  }


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  DegreeOfFreedom *Mesh::getDof(GeoIndex position)
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  {
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    FUNCNAME_DBG("Mesh::getDof()");
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    TEST_EXIT_DBG(position >= CENTER && position <= FACE)
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      ("unknown position %d\n", position);
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    int ndof = getNumberOfDofs(position);
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    if (ndof <= 0) 
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      return NULL;
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    DegreeOfFreedom *dof = new DegreeOfFreedom[ndof];
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    for (int i = 0; i < getNumberOfDOFAdmin(); i++) {
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      const DOFAdmin *localAdmin = &getDofAdmin(i);
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      TEST_EXIT_DBG(localAdmin)("no admin[%d]\n", i);
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      int n  = localAdmin->getNumberOfDofs(position);
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      int n0 = localAdmin->getNumberOfPreDofs(position);
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      TEST_EXIT_DBG(n + n0 <= ndof)
	("n = %d, n0 = %d too large: ndof = %d\n", n, n0, ndof);
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      for (int j = 0; j < n; j++)
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	dof[n0 + j] = const_cast<DOFAdmin*>(localAdmin)->getDOFIndex();
    }
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    return dof;
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  }


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  DegreeOfFreedom **Mesh::createDofPtrs()
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  {
    if (nNodeEl <= 0)
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      return NULL;
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    DegreeOfFreedom **ptrs = new DegreeOfFreedom*[nNodeEl];
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    for (int i = 0; i < nNodeEl; i++)
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      ptrs[i] = NULL;

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    return ptrs;
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  }

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  void Mesh::freeDofPtrs(DegreeOfFreedom **ptrs)
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  {
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    FUNCNAME_DBG("Mesh::freeDofPtrs()");
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    TEST_EXIT_DBG(ptrs)("ptrs is NULL!\n");
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    if (nNodeEl <= 0)
      return;
  
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    delete [] ptrs;
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  }


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  const DOFAdmin *Mesh::createDOFAdmin(string lname, DimVec<int> lnDof)
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  {    
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    DOFAdmin *localAdmin = new DOFAdmin(this, lname);
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    for (int i = 0; i < dim + 1; i++)
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      localAdmin->setNumberOfDofs(i, lnDof[i]);
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    addDOFAdmin(localAdmin);

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    return localAdmin;
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  }


  const DOFAdmin* Mesh::getVertexAdmin() const
  {
    const DOFAdmin *localAdmin = NULL;

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    for (unsigned int i = 0; i < admin.size(); i++) {
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      if (admin[i]->getNumberOfDofs(VERTEX)) {
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	if (!localAdmin)  
	  localAdmin = admin[i];
	else if (admin[i]->getSize() < localAdmin->getSize())
	  localAdmin = admin[i];
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      }
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    }

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    return localAdmin;
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  }

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  void Mesh::freeDof(DegreeOfFreedom* dof, GeoIndex position)
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  {
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    FUNCNAME_DBG("Mesh::freeDof()");
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    TEST_EXIT_DBG(position >= CENTER && position <= FACE)
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      ("unknown position %d\n", position);
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    if (nDof[position]) {
      TEST_EXIT_DBG(dof != NULL)("dof = NULL, but ndof = %d\n", nDof[position]);
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    } else  {
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      TEST_EXIT_DBG(dof == NULL)("dof != NULL, but ndof = 0\n");
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    }
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    TEST_EXIT_DBG(nDof[position] <= MAX_DOF)
      ("ndof too big: ndof = %d, MAX_DOF = %d\n", nDof[position], MAX_DOF);
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    for (unsigned int i = 0; i < admin.size(); i++) {
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      int n = admin[i]->getNumberOfDofs(position);
      int n0 = admin[i]->getNumberOfPreDofs(position);
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      TEST_EXIT_DBG(n + n0 <= nDof[position])
	("n = %d, n0 = %d too large: ndof = %d\n", n, n0, nDof[position]);
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      for (int j = 0; j < n; j++)
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	admin[i]->freeDofIndex(dof[n0 + j]);      
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    }
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    delete [] dof;
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  }

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  void Mesh::freeElement(Element* el)
  {
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    freeDofPtrs(const_cast<DegreeOfFreedom**>(el->getDof()));
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    delete el;
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  }


  Element* Mesh::createNewElement(Element *parent)
  {
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    FUNCNAME_DBG("Mesh::createNewElement()");
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    TEST_EXIT_DBG(elementPrototype)("no element prototype\n");
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    Element *el = parent ? parent->clone() : elementPrototype->clone();
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    if (!parent && elementDataPrototype)
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      el->setElementData(elementDataPrototype->clone()); 
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    else
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      el->setElementData(NULL); // must be done in ElementData::refineElementData()
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    return el;
  }

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  ElInfo* Mesh::createNewElInfo()
  {
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    FUNCNAME("Mesh::createNewElInfo()");

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    switch (dim) {
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    case 1:
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      return new ElInfo1d(this);
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      break;
    case 2:
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      return new ElInfo2d(this);
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      break;
    case 3:
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      return new ElInfo3d(this);
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      break;
    default:
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      ERROR_EXIT("invalid dim [%d]\n",dim);
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      return NULL;
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    }
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  }

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  bool Mesh::findElInfoAtPoint(const WorldVector<double>& xy,
			       ElInfo *el_info,
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			       DimVec<double>& bary,
			       const MacroElement *start_mel,
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			       const WorldVector<double> *xy0,
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			       double *sp)
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  {
    static const MacroElement *mel = NULL;
    DimVec<double> lambda(dim, NO_INIT);
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    ElInfo *mel_info = createNewElInfo();
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    if (start_mel != NULL)
      mel = start_mel;
    else
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      if (mel == NULL || mel->getElement()->getMesh() != this)
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	mel = *(macroElements.begin());

    mel_info->setFillFlag(Mesh::FILL_COORDS);
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    g_xy = &xy;
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    g_xy0 = xy0;
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    g_sp = sp;
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    mel_info->fillMacroInfo(mel);

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    // We have the care about not to visite a macro element twice. In this case the
    // function would end up in an infinite loop. If a macro element is visited a 
    // second time, what can happen with periodic boundary conditions, the point is
    // not within the mesh!
    std::set<int> macrosVisited;
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    std::stack<MacroElement*> active;
    
//     macrosVisited.insert(mel->getIndex());
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    int k;
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    while ((k = mel_info->worldToCoord(xy, &lambda)) >= 0) {
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      macrosVisited.insert(mel->getIndex());
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      if (mel->getNeighbour(k) && !macrosVisited.count(mel->getNeighbour(k)->getIndex())) {
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	mel = mel->getNeighbour(k);
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// 	if (macrosVisited.count(mel->getIndex())) // Nur für periodische RB interessant, muss noch implementiert werden
// 	  return false;
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	mel_info->fillMacroInfo(mel);
	continue;
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      } else {
	for (int i = 0; i < dim + 1; ++i) {
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	  if (i !=  k && mel->getNeighbour(i) && !macrosVisited.count(mel->getNeighbour(i)->getIndex()))
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	    active.push(mel->getNeighbour(i));    
	}
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	if (active.empty()) {
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	  if (macrosVisited.size() == getNumberOfMacros()) {
	    delete mel_info;
	    return false;
	  } else {
	    deque<MacroElement*>::iterator it;
	    bool found = false;
	    for (it = firstMacroElement(); it != endOfMacroElements(); it++) {
	      if (!macrosVisited.count(it->getIndex())) {
		active.push(*it);
		found = true;
	      }
	    }
	    TEST_EXIT(found)("No macro-element found that was not visited yet!\n");
	  }
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	}
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	mel = active.top();
	active.pop();
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	mel_info->fillMacroInfo(mel);
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      }
    }

    /* now, descend in tree to find leaf element at point */
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    bool inside = findElementAtPointRecursive(mel_info, lambda, k, el_info);
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    for (int i = 0; i <= dim; i++)
      bary[i] = final_lambda[i];   
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    delete mel_info;
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    return inside;
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  }

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  bool Mesh::findElementAtPoint(const WorldVector<double>&  xy,
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				Element **elp, 
				DimVec<double>& bary,
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				const MacroElement *start_mel,
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				const WorldVector<double> *xy0,
				double *sp)
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  {
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    ElInfo *el_info = createNewElInfo();
    int val = findElInfoAtPoint(xy, el_info, bary, start_mel, xy0, sp);
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    *elp = el_info->getElement();

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    delete el_info;
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    return val;
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  }

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  bool Mesh::findElementAtPointRecursive(ElInfo *el_info,
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					 const DimVec<double>& lambda,
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					 int outside,
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					 ElInfo* final_el_info)
  {
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    FUNCNAME("Mesh::findElementAtPointRecursive()");
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    Element *el = el_info->getElement();
    DimVec<double> c_lambda(dim, NO_INIT);
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    int inside;
    int ichild, c_outside;
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    if (el->isLeaf()) {
      *final_el_info = *el_info;
      if (outside < 0) {
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	for (int i = 0; i <= dim; i++)
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	  final_lambda[i] = lambda[i];
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	return true;
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      }  else {  /* outside */
	if (g_xy0) { /* find boundary point of [xy0, xy] */
	  el_info->worldToCoord(*(g_xy0), &c_lambda);
	  double s = lambda[outside] / (lambda[outside] - c_lambda[outside]);
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	  for (int i = 0; i <= dim; i++) 
	    final_lambda[i] = s * c_lambda[i] + (1.0 - s) * lambda[i];
	  
	  if (g_sp)
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	    *(g_sp) = s;
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	  if (dim == 3) 
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	    MSG("Outside finest level on el %d: s = %.3e\n", el->getIndex(), s);
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	  return false;  /* ??? */
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	} else {
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	  return false;
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	}
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      }
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    }

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    ElInfo *c_el_info = createNewElInfo();
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    if (dim == 1) {
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      if (lambda[0] >= lambda[1]) {
	c_el_info->fillElInfo(0, el_info);
	if (outside >= 0) {
	  outside = el_info->worldToCoord(*(g_xy), &c_lambda);
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	  TEST_EXIT(outside == 0)("point outside domain\n");
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	} else {
	  c_lambda[0] = lambda[0] - lambda[1];
	  c_lambda[1] = 2.0 * lambda[1];
	}
      } else {
	c_el_info->fillElInfo(1, el_info);
	if (outside >= 0)  {
	  outside = el_info->worldToCoord(*(g_xy), &c_lambda);
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	  TEST_EXIT(outside == 0)("point outside domain\n");
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	} else {
	  c_lambda[1] = lambda[1] - lambda[0];
	  c_lambda[0] = 2.0 * lambda[0];
	}
      }
    } /* DIM == 1 */

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    if (dim == 2) {
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      if (lambda[0] >= lambda[1]) {
	c_el_info->fillElInfo(0, el_info);
	if (el->isNewCoordSet()) {
	  outside = c_el_info->worldToCoord(*(g_xy), &c_lambda);
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	  TEST_EXIT(outside == 0)("outside curved boundary child 0\n");	  
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	} else {
	  c_lambda[0] = lambda[2];
	  c_lambda[1] = lambda[0] - lambda[1];
	  c_lambda[2] = 2.0 * lambda[1];
	}
      } else {
	c_el_info->fillElInfo(1, el_info);
	if (el->isNewCoordSet()) {
	  outside = c_el_info->worldToCoord(*(g_xy), &c_lambda);
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	  TEST_EXIT(outside == 0)("outside curved boundary child 1\n");	  
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