Mesh.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 <algorithm>
#include <set>
#include <map>

#include "time.h"

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

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

namespace AMDiS {

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

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

  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);

  //**************************************************************************
  //  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;
  const Flag Mesh::CALL_MG_LEVEL           = 0X4000L;  
  const Flag Mesh::CALL_REVERSE_MODE       = 0X8000L;


  vector<DegreeOfFreedom> Mesh::dof_used;
  const int Mesh::MAX_DOF = 100;
  map<pair<DegreeOfFreedom, int>, DegreeOfFreedom*> Mesh::serializedDOFs;

  Mesh::Mesh(string aName, int dimension) 
    : name(aName), 
      dim(dimension), 
      nVertices(0),
      nEdges(0),
      nLeaves(0), 
      nElements(0),
      parametric(NULL), 
      preserveCoarseDOFs(false),
      nDofEl(0),
      nDof(dimension, DEFAULT_VALUE, 0),
      nNodeEl(0),
      node(dimension, DEFAULT_VALUE, 0),
      elementPrototype(NULL),
      elementDataPrototype(NULL),
      elementIndex(-1),
      initialized(false),
      macroFileInfo(NULL),
      changeIndex(0),
      final_lambda(dimension, DEFAULT_VALUE, 0.0)
  {
    FUNCNAME("Mesh::Mesh()");

#ifdef HAVE_PARALLEL_DOMAIN_AMDIS
    nParallelPreRefinements = 0;
#endif

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

    elementPrototype->setIndex(-1);

    elementIndex = 0;
  }


  Mesh::~Mesh()
  {
    deleteMeshStructure();

    if (macroFileInfo != NULL)
      delete macroFileInfo;    
    if (elementPrototype)
      delete elementPrototype;    
    if (elementDataPrototype)
      delete elementDataPrototype;    
    
    for (unsigned int i = 0; i < admin.size(); i++)
      delete admin[i];    
  }


  Mesh& Mesh::operator=(const Mesh& m)
  {
    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;
    nDofEl = m.nDofEl;
    nDof = m.nDof;
    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++) {
      admin[i] = new DOFAdmin(this);
      *(admin[i]) = *(m.admin[i]);
      admin[i]->setMesh(this);
    }


    /* ====================== Copy macro elements =================== */
  
    // mapIndex[i] is the index of the MacroElement element in the vector
    // macroElements, for which holds: element->getIndex() = i    
    map<int, int> mapIndex;

    // We use this map for coping the DOFs of the Elements within the
    // MacroElements objects.
    Mesh::serializedDOFs.clear();

    int insertCounter = 0;

    macroElements.clear();

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

      // Create new MacroElement.
      MacroElement *el = new MacroElement(dim);

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

    // Now we have to go through all the new MacroElements, and update the neighbour
    // connections.
    insertCounter = 0;
    for (deque<MacroElement*>::const_iterator it = m.macroElements.begin();
	 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.
	if((*it)->getNeighbour(i)!=NULL) {
	macroElements[insertCounter]->
	  setNeighbour(i, macroElements[mapIndex[(*it)->getNeighbour(i)->getIndex()]]);
      }
      }
    }

    // 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;
  }


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

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


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


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

    typedef map<const DegreeOfFreedom*, std::set<MacroElement*> > DofElMap;
    typedef map<const DegreeOfFreedom*, GeoIndex> DofPosMap;

    TEST_EXIT(feSpaces.size() > 0)("Should not happen!\n");

    // 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);

    
    // === Determine to all DOFs in mesh the macro elements where the DOF  ===
    // === is part of.                                                     ===

    // Map that stores for each DOF pointer (which may have a list of DOFs)
    // all macro element indices that own this DOF.
    DofElMap dofsOwner;
    DofPosMap dofsPosIndex;

    ElementDofIterator elDofIter(feSpace);
    TraverseStack stack;
    ElInfo *elInfo = stack.traverseFirst(this, -1, Mesh::CALL_LEAF_EL);
    while (elInfo) {
      elDofIter.reset(elInfo->getElement());
      do {
	dofsOwner[elDofIter.getBaseDof()].insert(elInfo->getMacroElement());
	dofsPosIndex[elDofIter.getBaseDof()] = elDofIter.getPosIndex();
      } while (elDofIter.nextStrict());

      elInfo = stack.traverseNext(elInfo);
    }		   


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

    // Removing arbitrary elements from an deque is very slow. Therefore, we
    // 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.

    deque<MacroElement*> newMacroElements;
    for (deque<MacroElement*>::iterator elIter = macroElements.begin();
	 elIter != macroElements.end(); ++elIter) {
      // 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.
      if (delMacros.find(*elIter) == delMacros.end())
	newMacroElements.push_back(*elIter);     
    }

    // And replace the macro element list with the new one.
    macroElements.clear();
    macroElements = newMacroElements;


    // === 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.           ===
    
    for (std::set<MacroElement*>::iterator macroIt = delMacros.begin();
	 macroIt != delMacros.end(); ++macroIt) {

      // Go through all neighbours of the macro element and remove this macro
      // element to be neighbour of some other macro element.
      for (int i = 0; i < getGeo(NEIGH); i++)
	if ((*macroIt)->getNeighbour(i))
	  for (int j = 0; j < getGeo(NEIGH); j++)
	    if ((*macroIt)->getNeighbour(i)->getNeighbour(j) == *macroIt)
	      (*macroIt)->getNeighbour(i)->setNeighbour(j, NULL);

      Element *mel = (*macroIt)->getElement();
      // Delete element hierarchie
      if (!(mel->isLeaf())) {
	delete mel->getChild(0);
	delete mel->getChild(1);

	mel->child[0] = NULL;
	mel->child[1] = NULL;

	mel->setElementData(elementDataPrototype->clone()); 
      }

      mel->delDofPtr();
    }     


    // === Check now all the DOFs that have no owner anymore and therefore  ===
    // === have to be removed.                                              ===

    for (DofElMap::iterator dofsIt = dofsOwner.begin(); 
	 dofsIt != dofsOwner.end(); ++dofsIt) {
      
      bool deleteDof = true;

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

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


    // === Update number of elements, vertices, etc. ===

    nLeaves = 0;
    nElements = 0;

    std::set<const DegreeOfFreedom*> allVertices;

    elInfo = stack.traverseFirst(this, -1, Mesh::CALL_EVERY_EL_PREORDER);
    while (elInfo) {
      nElements++;

      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.                               ===
  }


  void Mesh::addDOFAdmin(DOFAdmin *localAdmin)
  {    
    FUNCNAME("Mesh::addDOFAdmin()");

    localAdmin->setMesh(this);

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

    admin.push_back(localAdmin);

    nDofEl = 0;

    localAdmin->setNumberOfPreDofs(VERTEX, nDof[VERTEX]);
    nDof[VERTEX] += localAdmin->getNumberOfDofs(VERTEX);
    nDofEl += getGeo(VERTEX) * nDof[VERTEX];

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

    localAdmin->setNumberOfPreDofs(CENTER, nDof[CENTER]);
    nDof[CENTER] += localAdmin->getNumberOfDofs(CENTER);
    nDofEl += nDof[CENTER];

    TEST_EXIT_DBG(nDof[VERTEX] > 0)("no vertex dofs\n");

    node[VERTEX] = 0;
    nNodeEl = getGeo(VERTEX);

    if (dim > 1) {
      node[EDGE] = nNodeEl;
      if (nDof[EDGE] > 0) 
	nNodeEl += getGeo(EDGE);
    }

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

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


  void Mesh::dofCompress()
  {
    FUNCNAME("Mesh::dofCompress()");

    for (unsigned int iadmin = 0; iadmin < admin.size(); iadmin++) {
      DOFAdmin* compressAdmin = admin[iadmin];

      TEST_EXIT_DBG(compressAdmin)("no admin[%d] in mesh\n", iadmin);
      
      int size = compressAdmin->getSize();
      if (size < 1 || 
	  compressAdmin->getUsedDofs() < 1 || 
	  compressAdmin->getHoleCount() < 1)    
	continue;

      vector<int> newDofIndex(size);     
      compressAdmin->compress(newDofIndex);

      Flag fill_flag = (preserveCoarseDOFs ?  
			Mesh::CALL_EVERY_EL_PREORDER | Mesh::FILL_NOTHING :
			Mesh::CALL_LEAF_EL | Mesh::FILL_NOTHING);          
      TraverseStack stack;
      ElInfo *elInfo = stack.traverseFirst(this, -1, fill_flag);
      while (elInfo) {
	elInfo->getElement()->newDofFct1(compressAdmin, newDofIndex);
	elInfo = stack.traverseNext(elInfo);
      }

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


  DegreeOfFreedom *Mesh::getDof(GeoIndex position)
  {
    FUNCNAME("Mesh::getDof()");

    TEST_EXIT_DBG(position >= CENTER && position <= FACE)
      ("unknown position %d\n", position);

    int ndof = getNumberOfDofs(position);
    if (ndof <= 0) 
      return NULL;

    DegreeOfFreedom *dof = new DegreeOfFreedom[ndof];

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


  DegreeOfFreedom **Mesh::createDofPtrs()
  {
    FUNCNAME("Mesh::createDofPtrs()");

    if (nNodeEl <= 0)
      return NULL;

    DegreeOfFreedom **ptrs = new DegreeOfFreedom*[nNodeEl];
    for (int i = 0; i < nNodeEl; i++)
      ptrs[i] = NULL;

    return ptrs;
  }


  void Mesh::freeDofPtrs(DegreeOfFreedom **ptrs)
  {
    FUNCNAME("Mesh::freeDofPtrs()");

    TEST_EXIT_DBG(ptrs)("ptrs is NULL!\n");

    if (nNodeEl <= 0)
      return;
  
    delete [] ptrs;
  }


  const DOFAdmin *Mesh::createDOFAdmin(string lname, DimVec<int> lnDof)
  {
    FUNCNAME("Mesh::createDOFAdmin()");
    
    DOFAdmin *localAdmin = new DOFAdmin(this, lname);

    for (int i = 0; i < dim + 1; i++)
      localAdmin->setNumberOfDofs(i, lnDof[i]);

    addDOFAdmin(localAdmin);

    return localAdmin;
  }


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

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

    return localAdmin;
  }


  void Mesh::freeDof(DegreeOfFreedom* dof, GeoIndex position)
  {
    FUNCNAME("Mesh::freeDof()");

    TEST_EXIT_DBG(position >= CENTER && position <= FACE)
      ("unknown position %d\n", position);

    int ndof = nDof[position];
    if (ndof) {
      if (!dof) {
	MSG("dof = NULL, but ndof = %d\n", ndof);
	return;
      }
    } else  {
      if (dof)
	MSG("dof != NULL, but ndof = 0\n");

      return;
    }

    TEST_EXIT_DBG(ndof <= MAX_DOF)
      ("ndof too big: ndof = %d, MAX_DOF = %d\n", ndof, MAX_DOF);

    for (unsigned int i = 0; i < admin.size(); i++) {
      int n = admin[i]->getNumberOfDofs(position);
      int n0 = admin[i]->getNumberOfPreDofs(position);
      
      TEST_EXIT_DBG(n + n0 <= ndof)
	("n = %d, n0 = %d too large: ndof = %d\n", n, n0, ndof);
      
      for (int j = 0; j < n; j++)
	admin[i]->freeDofIndex(dof[n0 + j]);      
    }

    delete [] dof;
  }


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


  Element* Mesh::createNewElement(Element *parent)
  {
    FUNCNAME("Mesh::createNewElement()");

    TEST_EXIT_DBG(elementPrototype)("no element prototype\n");

    Element *el = parent ? parent->clone() : elementPrototype->clone();

    if (!parent && elementDataPrototype)
      el->setElementData(elementDataPrototype->clone()); 
    else
      el->setElementData(NULL); // must be done in ElementData::refineElementData()

    return el;
  }


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

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


  bool Mesh::findElInfoAtPoint(const WorldVector<double>& xy,
			       ElInfo *el_info,
			       DimVec<double>& bary,
			       const MacroElement *start_mel,
			       const WorldVector<double> *xy0,
			       double *sp)
  {
    static const MacroElement *mel = NULL;
    DimVec<double> lambda(dim, NO_INIT);
    ElInfo *mel_info = createNewElInfo();

    if (start_mel != NULL)
      mel = start_mel;
    else
      if (mel == NULL || mel->getElement()->getMesh() != this)
	mel = *(macroElements.begin());

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

    mel_info->fillMacroInfo(mel);

    // 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;
    std::stack<MacroElement*> active;
    
//     macrosVisited.insert(mel->getIndex());

    int k;
    while ((k = mel_info->worldToCoord(xy, &lambda)) >= 0) {
      macrosVisited.insert(mel->getIndex());
      if (mel->getNeighbour(k) && !macrosVisited.count(mel->getNeighbour(k)->getIndex())) {
	mel = mel->getNeighbour(k);
// 	if (macrosVisited.count(mel->getIndex())) // Nur für periodische RB interessant, muss noch implementiert werden
// 	  return false;

	mel_info->fillMacroInfo(mel);
	continue;
      } else {
	for (int i = 0; i < dim + 1; ++i) {
	  if (i !=  k && mel->getNeighbour(i) && !macrosVisited.count(mel->getNeighbour(i)->getIndex()))
	    active.push(mel->getNeighbour(i));    
	}
	if (active.empty())
	  return false;
	mel = active.top();
	active.pop();

	mel_info->fillMacroInfo(mel);
      }
    }

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

    return inside;
  }


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

    *elp = el_info->getElement();

    delete el_info;

    return val;
  }


  bool Mesh::findElementAtPointRecursive(ElInfo *el_info,
					 const DimVec<double>& lambda,
					 int outside,
					 ElInfo* final_el_info)
  {
    FUNCNAME("Mesh::findElementAtPointRecursive()");

    Element *el = el_info->getElement();
    DimVec<double> c_lambda(dim, NO_INIT);
    int inside;
    int ichild, c_outside;

    if (el->isLeaf()) {
      *final_el_info = *el_info;
      if (outside < 0) {
	for (int i = 0; i <= dim; i++)
	  final_lambda[i] = lambda[i];
	
	return true;
      }  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]);
	  for (int i = 0; i <= dim; i++) 
	    final_lambda[i] = s * c_lambda[i] + (1.0 - s) * lambda[i];
	  
	  if (g_sp)
	    *(g_sp) = s;
	  
	  if (dim == 3) 
	    MSG("Outside finest level on el %d: s = %.3e\n", el->getIndex(), s);

	  return false;  /* ??? */
	} else {
	  return false;
	}
      }
    }

    ElInfo *c_el_info = createNewElInfo();

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

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