serendipitylocalcoefficients.hh

// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
// vi: set et ts=4 sw=2 sts=2:
 
#ifndef DUNE_LOCALFUNCTIONS_SERENDIPITY_LOCALCOEFFICIENTS_HH
#define DUNE_LOCALFUNCTIONS_SERENDIPITY_LOCALCOEFFICIENTS_HH
 
#include <array>
#include <cassert>
#include <vector>
 
#include <dune/common/exceptions.hh>
#include <dune/common/power.hh>
 
#include <dune/localfunctions/common/localkey.hh>
 
namespace Dune
{
  template<int k, int d>
  class SerendipityLocalCoefficients {
 
    typedef typename Dune::FieldVector<int,d> DuneVector;
 
    static void multiindex (DuneVector& alpha)
    {
            int i = 0;
            for (int j=0; j<d; j++){
                    i+=alpha[j]*pow(k+1,j);
            }
            i++;
            for (int j=0; j<d; j++)
            {
                    alpha[j] = i % (k+1);
                    i = i/(k+1);
            }
            unsigned int sum = 0;
            for (unsigned int j=0; j<d; j++){
          if(alpha[j] > 0 && alpha[j] < k){ sum++; }
            }
            if(sum > 1){
          multiindex(alpha);
            }
    }
 
    void setup1d(std::vector<unsigned int>& subEntity)
    {
      // Special-handling for piecewise constant elements
      if (k==0)
      {
        subEntity[0] = 0;
        return;
      }
 
      unsigned lastIndex=0;
 
      /* edge and vertex numbering
         0----0----1
       */
 
      // lower edge (2)
      subEntity[lastIndex++] = 0;                 // corner 0
      for (unsigned i = 0; i < k - 1; ++i)
        subEntity[lastIndex++] = 0;               // inner dofs of element (0)
 
      subEntity[lastIndex++] = 1;                 // corner 1
 
      assert((size()==lastIndex));
    }
 
    void setup2d(std::vector<unsigned int>& subEntity)
    {
      // Special-handling for piecewise constant elements
      if (k==0)
      {
        subEntity[0] = 0;
        return;
      }
 
      unsigned lastIndex=0;
 
      // LocalKey: entity number , entity codim, dof indices within each entity
      /* edge and vertex numbering
       2----3----3
       |         |
       |         |
       0         1
       |         |
       |         |
       0----2----1
       */
 
      // lower edge (2)
      subEntity[lastIndex++] = 0;                 // corner 0
      for (unsigned i = 0; i < k - 1; ++i)
        subEntity[lastIndex++] = 2;           // inner dofs of lower edge (2)
      subEntity[lastIndex++] = 1;                 // corner 1
 
      // iterate from bottom to top over inner edge dofs
      for (unsigned e = 0; e < k - 1; ++e) {
        subEntity[lastIndex++] = 0;                   // left edge (0)
        subEntity[lastIndex++] = 1;                   // right edge (1)
      }
 
      // upper edge (3)
      subEntity[lastIndex++] = 2;                 // corner 2
      for (unsigned i = 0; i < k - 1; ++i)
        subEntity[lastIndex++] = 3;                   // inner dofs of upper edge (3)
      subEntity[lastIndex++] = 3;                 // corner 3
 
      assert((size()==lastIndex));
    }
 
 
 
    void setup3d(std::vector<unsigned int>& subEntity)
    {
      // Special-handling for piecewise constant elements
      if (k==0)
      {
        subEntity[0] = 0;
        return;
      }
 
#ifndef NDEBUG
      const unsigned numIndices = size();
#endif
      const unsigned numInnerEdgeDofs = k-1;
 
      // LocalKey: entity number , entity codim, dof indices within each entity
      /* edge and vertex numbering
 
              6---(11)--7              6---------7
             /|        /|             /|  (5)   /|
           (8)|      (9)|            / | top   / |
           / (2)     / (3)          /  |(3)bac/k |
          4---(10)--5   |          4---------5   |
          |   |     |   |      left|(0)|     |(1)|right
          |   2--(7)|---3          |   2-----|---3
         (0) /     (1) /           |(2)front |  /
          |(4)      |(5)           | /  (4)  | /
          |/        |/             |/ bottom |/
          0---(6)---1              0---------1
       */
 
      //============================== bottom face (4) =================================
      unsigned lastIndex=0;
      // lower edge (6)
      subEntity[lastIndex++] = 0;              // corner 0
      for (unsigned i = 0; i < numInnerEdgeDofs; ++i)
        subEntity[lastIndex++] = 6;                // inner dofs of lower edge (6)
      subEntity[lastIndex++] = 1;              // corner 1
 
      // iterate from bottom to top over inner edge dofs
      for (unsigned e = 0; e < numInnerEdgeDofs; ++e) {
        subEntity[lastIndex++] = 4;                // left edge (4)
        subEntity[lastIndex++] = 5;                 // right edge (5)
      }
 
      // upper edge (7)
      subEntity[lastIndex++] = 2;              // corner 2
      for (unsigned i = 0; i < numInnerEdgeDofs; ++i)
        subEntity[lastIndex++] = 7;                // inner dofs of upper edge (7)
      subEntity[lastIndex++] = 3;                // corner 3
 
      //=============================== end bottom face (4) ============================
 
      //=============================== inner faces ====================================
      for(unsigned f = 0; f < numInnerEdgeDofs; ++f) {
        // lower edge (connecting  edges 0 and 1)
        subEntity[lastIndex++] = 0;                // dof on edge 0
        subEntity[lastIndex++] = 1;                // dof on edge 1
 
        // upper edge (connecting  edges 0 and 1)
        subEntity[lastIndex++] = 2;                // dof on edge 2
        subEntity[lastIndex++] = 3;                // dof on edge 3
      }
      //============================= end inner faces =================================
 
      //============================= top face (5) ====================================
      // lower edge (10)
      subEntity[lastIndex++] = 4;              // corner 4
      for (unsigned i = 0; i < numInnerEdgeDofs; ++i)
        subEntity[lastIndex++] = 10;                // inner dofs on lower edge (10)
      subEntity[lastIndex++] = 5;              // corner 5
 
      // iterate from bottom to top over inner edge dofs
      for (unsigned e = 0; e < numInnerEdgeDofs; ++e) {
        subEntity[lastIndex++] = 8;                // left edge (8)
        subEntity[lastIndex++] = 9;                // right edge (9)
      }
 
      // upper edge (11)
      subEntity[lastIndex++] = 6;              // corner 6
      for (unsigned i = 0; i < numInnerEdgeDofs; ++i)
        subEntity[lastIndex++] = 11;                // inner dofs of upper edge (11)
      subEntity[lastIndex++] = 7;              // corner 7
      //============================ end top face ====================================
 
      assert(numIndices==lastIndex);
    }
 
  public:
    SerendipityLocalCoefficients () : li(size())
    {
      // Set up array of codimension-per-dof-number
      std::vector<unsigned int> codim(li.size());
      DuneVector mIdx(0);
      for (std::size_t i=0; i < size(); i++) {
        codim[i] = 0;
        if (k==0)
          continue;
        // Codimension gets increased by 1 for each coordinate direction
        // where dof is on boundary
        if(i>0){ multiindex(mIdx); }
        for (int j=0; j<d; j++)
          if (mIdx[j]==0 or mIdx[j]==k)
            codim[i]++;
      }
 
      // Set up index vector (the index of the dof in the set of dofs of a given subentity)
      // Algorithm: the 'index' has the same ordering as the dof number 'i'.
      // To make it consecutive we interpret 'i' in the (k+1)-adic system, omit all digits
      // that correspond to axes where the dof is on the element boundary, and transform the
      // rest to the (k-1)-adic system.
      std::vector<unsigned int> index(size());
      mIdx = 0;
      for (std::size_t i=0; i<size(); i++) {
        index[i] = 0;
        if(i>0){ multiindex(mIdx); }
 
        for (int j=d-1; j>=0; j--)
          if (mIdx[j]>0 and mIdx[j]<k)
            index[i] = (k-1)*index[i] + (mIdx[j]-1);
      }
 
      // Set up entity and dof numbers for each (supported) dimension separately
      std::vector<unsigned int> subEntity(li.size());
 
      if (k==1) {  // We can handle the first-order case in any dimension
        for (std::size_t i=0; i<size(); i++)
          subEntity[i] = i;
      }
      else if (d==1) {
        setup1d(subEntity);
      }
      else if (d==2) {
        setup2d(subEntity);
      }
      else if (d==3) {
        setup3d(subEntity);
      }
      else
        DUNE_THROW(Dune::NotImplemented, "SerendipityLocalCoefficients for k==" << k << " and d==" << d);
 
      for (size_t i=0; i<li.size(); i++){
        li[i] = LocalKey(subEntity[i], codim[i], index[i]);
      }
    }
 
    std::size_t size () const
    {
      if(d == 1){
        return k+1;
      }
      if(d == 2){
        return 2*(k+1)+2*(k-1);
      }
      if(d == 3){
        return 4*(k+1)+8*(k-1);
      }
    }
 
    const LocalKey& localKey (std::size_t i) const
    {
      return li[i];
    }
 
  private:
    std::vector<LocalKey> li;
  };
 
}
 
#endif