qklocalcoefficients.hh

// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
// vi: set et ts=4 sw=2 sts=2:
 
#ifndef DUNE_LOCALFUNCTIONS_QK_LOCALCOEFFICIENTS_HH
#define DUNE_LOCALFUNCTIONS_QK_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 QkLocalCoefficients {
 
    static const unsigned unsignedK = k;
 
    // Return i as a d-digit number in the (k+1)-nary system
    static std::array<unsigned int,d> multiindex (unsigned int i)
    {
      std::array<unsigned int,d> alpha;
      for (int j=0; j<d; j++)
      {
        alpha[j] = i % (k+1);
        i = i/(k+1);
      }
      return 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
       */
 
      // edge (0)
      subEntity[lastIndex++] = 0;                 // corner 0
      for (unsigned i = 0; i < unsignedK - 1; ++i)
        subEntity[lastIndex++] = 0;               // inner dofs of element (0)
 
      subEntity[lastIndex++] = 1;                 // corner 1
 
      assert((StaticPower<k+1,d>::power==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 < unsignedK - 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 < unsignedK - 1; ++e) {
        subEntity[lastIndex++] = 0;                   // left edge (0)
        for (unsigned i = 0; i < unsignedK - 1; ++i)
          subEntity[lastIndex++] = 0;                     // face dofs
        subEntity[lastIndex++] = 1;                   // right edge (1)
      }
 
      // upper edge (3)
      subEntity[lastIndex++] = 2;                 // corner 2
      for (unsigned i = 0; i < unsignedK - 1; ++i)
        subEntity[lastIndex++] = 3;                   // inner dofs of upper edge (3)
 
      subEntity[lastIndex++] = 3;                 // corner 3
 
      assert((StaticPower<k+1,d>::power==lastIndex));
    }
 
 
 
    void setup3d(std::vector<unsigned int>& subEntity)
    {
      // Special-handling for piecewise constant elements
      if (k==0)
      {
        subEntity[0] = 0;
        return;
      }
 
      unsigned lastIndex=0;
#ifndef NDEBUG
      const unsigned numIndices = StaticPower<k+1,d>::power;
      const unsigned numFaceIndices = StaticPower<k+1,d-1>::power;
#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)
      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)
        for (unsigned i = 0; i < numInnerEdgeDofs; ++i)
          subEntity[lastIndex++] = 4;                       // inner face dofs
        subEntity[lastIndex++] = 5;                 // right edge (5)
      }
 
      // upper edge (7)
      subEntity[lastIndex++] = 2;              // corner 2
      for (unsigned i = 0; i < unsignedK - 1; ++i)
        subEntity[lastIndex++] = 7;                // inner dofs of upper edge (7)
      subEntity[lastIndex++] = 3;                // corner 3
 
      assert(numFaceIndices==lastIndex);       // added 1 face so far
 
      for(unsigned f = 0; f < numInnerEdgeDofs; ++f) {
 
        // lower edge (connecting  edges 0 and 1)
        subEntity[lastIndex++] = 0;                // dof on edge 0
        for (unsigned i = 0; i < numInnerEdgeDofs; ++i)
          subEntity[lastIndex++] = 2;                            // dof in front face
        subEntity[lastIndex++] = 1;                // dof on edge 1
 
        // iterate from bottom to top over inner edge dofs
        for (unsigned e = 0; e < numInnerEdgeDofs; ++e) {
          subEntity[lastIndex++] = 0;                  // on left face (0)
          for (unsigned i = 0; i < numInnerEdgeDofs; ++i)
            subEntity[lastIndex++] = 0;                    // volume dofs
          subEntity[lastIndex++] = 1;                  // right face (1)
        }
 
        // upper edge (connecting  edges 0 and 1)
        subEntity[lastIndex++] = 2;                // dof on edge 2
        for (unsigned i = 0; i < numInnerEdgeDofs; ++i)
          subEntity[lastIndex++] = 3;                  // dof on rear face (3)
        subEntity[lastIndex++] = 3;                // dof on edge 3
 
        assert(lastIndex==(f+1+1)*numFaceIndices);
      }
 
      // lower edge (10)
      subEntity[lastIndex++] = 4;              // corner 4
      for (unsigned i = 0; i < unsignedK - 1; ++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 < unsignedK - 1; ++e) {
        subEntity[lastIndex++] = 8;                // left edge (8)
        for (unsigned i = 0; i < unsignedK - 1; ++i)
          subEntity[lastIndex++] = 5;                  // face dofs
        subEntity[lastIndex++] = 9;                // right edge (9)
      }
 
      // upper edge (11)
      subEntity[lastIndex++] = 6;              // corner 6
      for (unsigned i = 0; i < unsignedK - 1; ++i)
        subEntity[lastIndex++] = 11;                // inner dofs of upper edge (11)
      subEntity[lastIndex++] = 7;              // corner 7
 
      assert(numIndices==lastIndex);
    }
 
  public:
    QkLocalCoefficients () : li(StaticPower<k+1,d>::power)
    {
      // Set up array of codimension-per-dof-number
      std::vector<unsigned int> codim(li.size());
 
      for (std::size_t i=0; i<codim.size(); i++) {
        codim[i] = 0;
        if (k==0)
          continue;
        // Codimension gets increased by 1 for each coordinate direction
        // where dof is on boundary
        std::array<unsigned int,d> mIdx = multiindex(i);
        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());
 
      for (std::size_t i=0; i<size(); i++) {
 
        index[i] = 0;
 
        std::array<unsigned int,d> mIdx = multiindex(i);
 
        for (int j=d-1; j>=0; j--)
          if (mIdx[j]>0 and mIdx[j]<unsignedK)
            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, "QkLocalCoefficients 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
    {
      return StaticPower<k+1,d>::power;
    }
 
    const LocalKey& localKey (std::size_t i) const
    {
      return li[i];
    }
 
  private:
    std::vector<LocalKey> li;
  };
 
}
 
#endif