/usr/include/dune/localfunctions/refined/common/refinedsimplexlocalbasis.hh is in libdune-localfunctions-dev 2.3.1-1.
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// vi: set et ts=4 sw=2 sts=2:
#ifndef DUNE_REFINED_SIMPLEX_LOCALBASIS_HH
#define DUNE_REFINED_SIMPLEX_LOCALBASIS_HH
/** \file
\brief Contains a base class for LocalBasis classes based on uniform refinement
*/
#include <dune/common/fvector.hh>
#include <dune/common/exceptions.hh>
#include <dune/localfunctions/common/localbasis.hh>
namespace Dune
{
template<class D, int dim>
class RefinedSimplexLocalBasis
{
protected:
RefinedSimplexLocalBasis()
{
DUNE_THROW(Dune::NotImplemented,"RefinedSimplexLocalBasis not implemented for dim > 3.");
}
};
/**@ingroup LocalBasisImplementation
\brief Base class for LocalBasis classes based on uniform refinement in 1D; provides numbering and local coordinates of subelements
\tparam D Type to represent the field in the domain.
\nosubgrouping
*/
template<class D>
class RefinedSimplexLocalBasis<D,1>
{
protected:
/** \brief Protected default constructor so this class can only be instantiated as a base class. */
RefinedSimplexLocalBasis() {}
/** \brief Get the number of the subelement containing a given point.
*
* The subelements are ordered according to
*
* 0 1
* |-------:-------|
*
* \param[in] global Coordinates in the reference element
* \returns Number of the subtriangle containing <tt>global</tt>
*/
static int getSubElement(const FieldVector<D,1>& global)
{
if (global[0] <= 0.5)
return 0;
else if (global[0] <= 1.0)
return 1;
DUNE_THROW(InvalidStateException, "no subelement defined");
}
/** \brief Get local coordinates in the subelement
\param[in] global Coordinates in the reference element
\param[out] subElement Number of the subelement containing <tt>global</tt>
\param[out] local The local coordinates in the subelement
*/
static void getSubElement(const FieldVector<D,1>& global,
int& subElement,
FieldVector<D,1>& local)
{
if (global[0] <= 0.5) {
subElement = 0;
local[0] = 2.0 * global[0];
return;
}
subElement = 1;
local[0] = 2.0 * global[0] - 1.0;
}
};
/**@ingroup LocalBasisImplementation
\brief Base class for LocalBasis classes based on uniform refinement in 2D; provides numbering and local coordinates of subelements
Shape functions like these are necessary for hierarchical error estimators
for certain nonlinear problems.
\tparam D Type to represent the field in the domain.
\nosubgrouping
*/
template<class D>
class RefinedSimplexLocalBasis<D,2>
{
protected:
/** \brief Protected default constructor so this class can only be instantiated as a base class. */
RefinedSimplexLocalBasis() {}
/** \brief Get the number of the subtriangle containing a given point.
*
* The triangles are ordered according to
* \verbatim
|\
|\|2\
|\|--\
|\|\3|\
|\|0\|1\
------ \endverbatim
*
* \param[in] global Coordinates in the reference triangle
* \returns Number of the subtriangle containing <tt>global</tt>
*/
static int getSubElement(const FieldVector<D,2>& global)
{
if (global[0] + global[1] <= 0.5)
return 0;
else if (global[0] >= 0.5)
return 1;
else if (global[1] >= 0.5)
return 2;
return 3;
}
/** \brief Get local coordinates in the subtriangle
\param[in] global Coordinates in the reference triangle
\param[out] subElement Number of the subtriangle containing <tt>global</tt>
\param[out] local The local coordinates in the subtriangle
*/
static void getSubElement(const FieldVector<D,2>& global,
int& subElement,
FieldVector<D,2>& local)
{
if (global[0] + global[1] <= 0.5) {
subElement = 0;
local[0] = 2*global[0];
local[1] = 2*global[1];
return;
} else if (global[0] >= 0.5) {
subElement = 1;
local[0] = 2*global[0]-1;
local[1] = 2*global[1];
return;
} else if (global[1] >= 0.5) {
subElement = 2;
local[0] = 2*global[0];
local[1] = 2*global[1]-1;
return;
}
subElement = 3;
local[0] = -2 * global[0] + 1;
local[1] = -2 * global[1] + 1;
}
};
/**@ingroup LocalBasisImplementation
\brief Base class for LocalBasis classes based on uniform refinement in 3D; provides numbering and local coordinates of subelements
Shape functions like these are necessary for hierarchical error estimators
for certain nonlinear problems.
\tparam D Type to represent the field in the domain.
\nosubgrouping
*/
template<class D>
class RefinedSimplexLocalBasis<D,3>
{
protected:
/** \brief Protected default constructor so this class can only be instantiated as a base class. */
RefinedSimplexLocalBasis() {}
/** \brief Get the number of the subsimplex containing a given point in the reference element
*
* Defining the following points in the reference simplex
*
* 0: (0.0, 0.0, 0.0)
* 1: (1.0, 0.0, 0.0)
* 2: (0.0, 1.0, 0.0)
* 3: (0.0, 0.0, 1.0)
* 4: (0.5, 0.0, 0.0)
* 5: (0.5, 0.5, 0.0)
* 6: (0.0, 0.5, 0.0)
* 7: (0.0, 0.0, 0.5)
* 8: (0.5, 0.0, 0.5)
* 9: (0.0, 0.5, 0.5)
*
* The subsimplices are numbered according to
*
* 0: 0467 -
* 1: 4158 |_ "cut off" vertices
* 2: 6529 |
* 3: 7893 -
*
* 4: 6487 -
* 5: 4568 |_ octahedron partition
* 6: 6897 |
* 7: 6895 -
*
* \param[in] global Coordinates in the reference simplex
* \returns Number of the subsimplex containing <tt>global</tt>
*/
static int getSubElement(const FieldVector<D,3>& global)
{
if (global[0] + global[1] + global[2] <= 0.5)
return 0;
else if (global[0] >= 0.5)
return 1;
else if (global[1] >= 0.5)
return 2;
else if (global[2] >= 0.5)
return 3;
else if ((global[0] + global[1] <= 0.5)and (global[1] + global[2] <= 0.5))
return 4;
else if ((global[0] + global[1] >= 0.5)and (global[1] + global[2] <= 0.5))
return 5;
else if ((global[0] + global[1] <= 0.5)and (global[1] + global[2] >= 0.5))
return 6;
else if ((global[0] + global[1] >= 0.5)and (global[1] + global[2] >= 0.5))
return 7;
DUNE_THROW(InvalidStateException, "no subelement defined");
}
/** \brief Get local coordinates in the subsimplex
\param[in] global Coordinates in the reference simplex
\param[out] subElement Number of the subsimplex containing <tt>global</tt>
\param[out] local The local coordinates in the subsimplex
*/
static void getSubElement(const FieldVector<D,3>& global,
int& subElement,
FieldVector<D,3>& local)
{
if (global[0] + global[1] + global[2] <= 0.5) {
subElement = 0;
local = global;
local *= 2.0;
return;
} else if (global[0] >= 0.5) {
subElement = 1;
local = global;
local[0] -= 0.5;
local *= 2.0;
return;
} else if (global[1] >= 0.5) {
subElement = 2;
local = global;
local[1] -= 0.5;
local *= 2.0;
return;
} else if (global[2] >= 0.5) {
subElement = 3;
local = global;
local[2] -= 0.5;
local *= 2.0;
return;
} else if ((global[0] + global[1] <= 0.5)and (global[1] + global[2] <= 0.5)) {
subElement = 4;
local[0] = 2.0 * global[1];
local[1] = 2.0 * (0.5 - global[0] - global[1]);
local[2] = 2.0 * (-0.5 + global[0] + global[1] + global[2]);
// Dune::FieldMatrix<double,3,3> A(0.0);
// A[0][1] = 2.0;
// A[1][0] = -2.0;
// A[1][1] = -2.0;
// A[2][0] = 2.0;
// A[2][1] = 2.0;
// A[2][2] = 2.0;
// A.mv(global,local);
// local[1] += 1.0;
// local[2] -= 1.0;
return;
} else if ((global[0] + global[1] >= 0.5)and (global[1] + global[2] <= 0.5)) {
subElement = 5;
local[0] = 2.0 * (0.5 - global[0]);
local[1] = 2.0 * (0.5 - global[1] - global[2]);
local[2] = 2.0 * global[2];
// Dune::FieldMatrix<double,3,3> A(0.0);
// A[0][0] = -2.0;
// A[1][1] = -2.0;
// A[1][2] = -2.0;
// A[2][2] = 2.0;
// A.mv(global,local);
// local[0] += 1.0;
// local[1] += 1.0;
return;
} else if ((global[0] + global[1] <= 0.5)and (global[1] + global[2] >= 0.5)) {
subElement = 6;
local[0] = 2.0 * (0.5 - global[0] - global[1]);
local[1] = 2.0 * global[0];
local[2] = 2.0 * (-0.5 + global[1] + global[2]);
// Dune::FieldMatrix<double,3,3> A(0.0);
// A[0][0] = -2.0;
// A[0][1] = -2.0;
// A[1][0] = 2.0;
// A[2][1] = 2.0;
// A[2][2] = 2.0;
// A.mv(global,local);
// local[0] += 1.0;
// local[2] -= 1.0;
return;
} else if ((global[0] + global[1] >= 0.5)and (global[1] + global[2] >= 0.5)) {
subElement = 7;
local[0] = 2.0 * (-0.5 + global[1] + global[2]);
local[1] = 2.0 * (0.5 - global[1]);
local[2] = 2.0 * (-0.5 + global[0] + global[1]);
// Dune::FieldMatrix<double,3,3> A(0.0);
// A[0][1] = 2.0;
// A[0][2] = 2.0;
// A[1][1] = -2.0;
// A[2][0] = 2.0;
// A[2][1] = 2.0;
// A.mv(global,local);
// local[0] -= 1.0;
// local[1] += 1.0;
// local[2] -= 1.0;
return;
}
DUNE_THROW(InvalidStateException, "no subelement defined");
}
};
}
#endif
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