checkgeometry.hh

// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
// vi: set et ts=4 sw=2 sts=2:
 
#ifndef DUNE_CHECK_GEOMETRY_HH
#define DUNE_CHECK_GEOMETRY_HH
 
#include <limits>
 
#include <dune/common/typetraits.hh>
#include <dune/common/fvector.hh>
#include <dune/common/fmatrix.hh>
 
#include <dune/geometry/referenceelements.hh>
#include <dune/geometry/quadraturerules.hh>
#include <dune/geometry/referenceelements.hh>
 
namespace Dune
{
 
  template <class TestGeometry>
  bool checkGeometry ( const TestGeometry& geometry )
  {
    bool pass = true;
 
    // Extract all static information
 
    // dimension of the corresponding reference element
    static const int mydim = TestGeometry::mydimension;
 
    // dimension of the world space
    static const int coorddim = TestGeometry::coorddimension;
 
    // type used for coordinate coefficients
    typedef typename TestGeometry::ctype ctype;
 
    // vector type used for points in the domain
    typedef typename TestGeometry::LocalCoordinate LocalCoordinate DUNE_UNUSED;
 
    // vector type used for image points
    typedef typename TestGeometry::GlobalCoordinate GlobalCoordinate DUNE_UNUSED;
 
    // Matrix-like type for the return value of the jacobianTransposed method
    typedef typename TestGeometry::JacobianTransposed JacobianTransposed;
 
    // Matrix-like type for the return value of the jacobianInverseTransposed method
    typedef typename TestGeometry::JacobianInverseTransposed JacobianInverseTransposed;
 
    const ctype tolerance = std::sqrt( std::numeric_limits< ctype >::epsilon() );
 
 
    const int corners = geometry.corners();
    if( corners == 0 )
      DUNE_THROW( Exception, "A geometry must have at least one corner." );
 
    GlobalCoordinate cornerAvg ( 0 );
    for( int i = 0; i < corners; ++i )
      cornerAvg += geometry.corner( i );
    cornerAvg /= ctype( corners );
 
    const GlobalCoordinate center = geometry.center();
 
    if( corners > 1 )
    {
      // if we have more than one corner, no corner may coincide with their average or the center
      for( int i = 0; i < corners; ++i )
      {
        const GlobalCoordinate corner = geometry.corner( i );
        if( (corner - center).two_norm() <= tolerance )
        {
          std::cerr << "Error: Geometry has multiple corners, but one corner coincides with the center." << std::endl;
          pass = false;
        }
 
        if( (corner - cornerAvg).two_norm() <= tolerance )
        {
          std::cerr << "Error: Geometry has multiple corners, but one corner coincides with their average." << std::endl;
          pass = false;
        }
      }
    }
    else
    {
      // the single corner must coincide with the center
      if( (center - cornerAvg).two_norm() > tolerance )
      {
        std::cerr << "Error: Geometry has a single corner (" << cornerAvg << "), but it does not coincide with the center (" << center << ")." << std::endl;
        pass = false;
      }
    }
 
    const ctype volume = geometry.volume();
    if( volume < tolerance )
    {
      std::cerr << "Error: Geometry has nearly vanishing volume (" << volume << ")" << std::endl;
      pass = false;
    }
 
 
    const GeometryType type = geometry.type();
    if( type.isNone() )
      return pass;
 
    const ReferenceElement< ctype, mydim > &refElement = ReferenceElements< ctype, mydim >::general(type);
 
    // Test whether the return value of the method 'center' corresponds to the center of the
    // reference element.  That is the current definition of the method.
    if( (center - geometry.global( refElement.position( 0, 0 ) )).two_norm() > tolerance )
      DUNE_THROW( Exception, "center() is not consistent with global(refElem.position(0,0))." );
 
    // Test whether the number and placement of the corners is consistent
    // with the corners of the corresponding reference element.
 
    if( refElement.size( mydim ) == corners )
    {
      for( int i = 0; i < geometry.corners(); ++i )
      {
        if( (geometry.corner( i ) - geometry.global( refElement.position( i, mydim ) )).two_norm() > tolerance )
        {
          std::cerr << "Error: Methods corner and global are inconsistent." << std::endl;
          pass = false;
        }
      }
    }
    else
    {
      std::cerr << "Error: Incorrect number of corners (" << geometry.corners() << ", should be " << refElement.size( mydim ) << ")." << std::endl;
      pass = false;
    }
 
    // Use a quadrature rule as a set of test points and loop over them
    const Dune::QuadratureRule<ctype, mydim> & quadrature = Dune::QuadratureRules<ctype, mydim>::rule(geometry.type(), 2);
    for (const auto& ip : quadrature)
    {
      const typename TestGeometry::LocalCoordinate &x = ip.position();
 
      // Test whether the methods 'local' and 'global' are inverse to each other
      if ( (x - geometry.local( geometry.global( x ) )).two_norm() > 1e-8 ) {
        std::cerr << "Error: global and local are not inverse to each other." << std::endl;
        pass = false;
      }
 
      // Test whether the methods 'jacobianTransposed' and 'jacobianInverseTransposed'
      // return matrices that are inverse to each other.
      const JacobianTransposed &jt = geometry.jacobianTransposed( x );
      const JacobianInverseTransposed &jit = geometry.jacobianInverseTransposed( x );
 
      // Transform to FieldMatrix, so we can have coefficent access and other goodies
      // We need some black magic for the transformation, because there is no
      // official easy way yet.
      // The following code does the transformation by multiplying jt and jit from
      // the right by identity matrices.  That way, only the mv method is used.
      FieldMatrix< ctype, mydim, coorddim > jtAsFieldMatrix;
      for (int j=0; j<coorddim; j++) {
 
        FieldVector<ctype,coorddim> idColumn(0);
        idColumn[j] = 1;
 
        FieldVector<ctype,mydim> column;
        jt.mv(idColumn,column);
 
        for (int k=0; k<mydim; k++)
          jtAsFieldMatrix[k][j] = column[k];
 
      }
 
      FieldMatrix< ctype, coorddim, mydim > jitAsFieldMatrix;
      for (int j=0; j<mydim; j++) {
 
        FieldVector<ctype,mydim> idColumn(0);
        idColumn[j] = 1;
 
        FieldVector<ctype,coorddim> column;
        jit.mv(idColumn,column);
 
        for (int k=0; k<coorddim; k++)
          jitAsFieldMatrix[k][j] = column[k];
 
      }
 
 
      FieldMatrix< ctype, mydim, mydim > id;
      FMatrixHelp::multMatrix( jtAsFieldMatrix, jitAsFieldMatrix, id );
      bool isId = true;
      for( int j = 0; j < mydim; ++j )
        for( int k = 0; k < mydim; ++k )
          isId &= (std::abs( id[ j ][ k ] - (j == k ? 1 : 0) ) < 1e-8);
      if( !isId)
      {
        std::cerr << "Error: jacobianTransposed and jacobianInverseTransposed are not inverse to each other." << std::endl;
        std::cout << "       id != [ ";
        for( int j = 0; j < mydim; ++j )
          std::cout << (j > 0 ? " | " : "") << id[ j ];
        std::cout << " ]" << std::endl;
        pass = false;
      }
 
      // Test whether integrationElement returns something nonnegative
      if( geometry.integrationElement( x ) < 0 ) {
        std::cerr << "Error: Negative integrationElement found." << std::endl;
        pass = false;
      }
 
      FieldMatrix< ctype, mydim, mydim > jtj( 0 );
      for( int i = 0; i < mydim; ++i )
        for( int j = 0; j < mydim; ++j )
          for( int k = 0; k < coorddim; ++k )
            jtj[ i ][ j ] += jtAsFieldMatrix[ i ][ k ] * jtAsFieldMatrix[ j ][ k ];
 
      if( std::abs( std::sqrt( jtj.determinant() ) - geometry.integrationElement( x ) ) > 1e-8 ) {
        std::cerr << "Error: integrationElement is not consistent with jacobianTransposed." << std::endl;
        pass = false;
      }
      if (geometry.affine())
        if( std::abs( geometry.volume() - refElement.volume()*geometry.integrationElement( x ) ) > 1e-8 ) {
          std::cerr << "Error: volume is not consistent with jacobianTransposed." << std::endl;
          pass = false;
        }
    }
 
    return pass;
  }
 
}
 
#endif // #ifndef DUNE_CHECK_GEOMETRY_HH