/usr/include/dune/localfunctions/brezzidouglasmarini/brezzidouglasmarini2simplex2d/brezzidouglasmarini2simplex2dlocalbasis.hh is in libdune-localfunctions-dev 2.5.0-2.
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// vi: set et ts=4 sw=2 sts=2:
#ifndef DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_SIMPLEX2D_LOCALBASIS_HH
#define DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_SIMPLEX2D_LOCALBASIS_HH
#include <array>
#include <bitset>
#include <numeric>
#include <vector>
#include <dune/common/fmatrix.hh>
#include "../../common/localbasis.hh"
namespace Dune
{
/**
* \ingroup LocalBasisImplementation
* \brief First order Brezzi-Douglas-Marini shape functions on quadrilaterals.
*
* \tparam D Type to represent the field in the domain.
* \tparam R Type to represent the field in the range.
*
* \nosubgrouping
*/
template<class D, class R>
class BDM2Simplex2DLocalBasis
{
public:
typedef LocalBasisTraits<D,2,Dune::FieldVector<D,2>,
R,2,Dune::FieldVector<R,2>,
Dune::FieldMatrix<R,2,2> > Traits;
//! \brief Standard constructor
BDM2Simplex2DLocalBasis()
{
for (size_t i=0; i<3; i++)
sign_[i] = 1.0;
}
/**
* \brief Make set number s, where 0 <= s < 8
*
* \param s Edge orientation indicator
*/
BDM2Simplex2DLocalBasis(std::bitset<3> s)
{
for (size_t i=0; i<3; i++)
sign_[i] = s[i] ? -1.0 : 1.0;
}
//! \brief number of shape functions
unsigned int size() const
{
return 12;
}
/**
* \brief Evaluate all shape functions
*
* \param in Position
* \param out return value
*/
inline void evaluateFunction(const typename Traits::DomainType& in,
std::vector<typename Traits::RangeType>& out) const
{
out.resize(size());
out[0][0] = sign_[0]*(-2*in[0]*in[1] + in[0]*in[0]);
out[0][1] = sign_[0]*(-1 + 6*in[1] -2*in[0]*in[1] - 5*in[1]*in[1]);
out[1][0] = 1.5*in[0] + 3*in[0]*in[1] - 4.5*in[0]*in[0];
out[1][1] = -3 + 6*in[0] + 10.5*in[1] - 15*in[0]*in[1] - 7.5*in[1]*in[1];
out[2][0] = sign_[0]*(-7.5*in[0] + 5*in[0]*in[1] + 12.5*in[0]*in[0]);
out[2][1] = sign_[0]*(-5 + 30*in[0] + 7.5*in[1] - 25*in[0]*in[1] - 30*in[0]*in[0] - 2.5*in[1]*in[1]);
out[3][0] = sign_[1]*(-1 + 6*in[0] - 2*in[0]*in[1] - 5*in[0]*in[0]);
out[3][1] = sign_[1]*(-2*in[0]*in[1] + in[1]*in[1]);
out[4][0] = 3 - 10.5*in[0] - 6*in[1] + 15*in[0]*in[1] + 7.5*in[0]*in[0];
out[4][1] = -1.5*in[1] - 3*in[0]*in[1] + 4.5*in[1]*in[1];
out[5][0] = sign_[1]*(-5 + 7.5*in[0] + 30*in[1] - 25*in[0]*in[1] - 2.5*in[0]*in[0] - 30*in[1]*in[1]);
out[5][1] = sign_[1]*(-7.5*in[1] + 5*in[0]*in[1] + 12.5*in[1]*in[1]);
out[6][0] = sign_[2]*(-3*in[0] + 4*in[0]*in[1] + 4*in[0]*in[0]);
out[6][1] = sign_[2]*(-3*in[1] + 4*in[0]*in[1] + 4*in[1]*in[1]);
out[7][0] = -3*in[0] + 6*in[0]*in[0];
out[7][1] = 3*in[1] - 6*in[1]*in[1];
out[8][0] = sign_[2]*(-10*in[0]*in[1] + 5*in[0]*in[0]);
out[8][1] = sign_[2]*(-10*in[0]*in[1] + 5*in[1]*in[1]);
out[9][0] = 18*in[0] - 12*in[0]*in[1] - 18*in[0]*in[0];
out[9][1] = 6*in[1] - 12*in[0]*in[1] - 6*in[1]*in[1];
out[10][0] = 6*in[0] - 12*in[0]*in[1] - 6*in[0]*in[0];
out[10][1] = 18*in[1] - 12*in[0]*in[1] - 18*in[1]*in[1];
out[11][0] = 90*in[0] - 180*in[0]*in[1] - 90*in[0]*in[0];
out[11][1] = -90*in[1] + 180*in[0]*in[1] + 90*in[1]*in[1];
}
/**
* \brief Evaluate Jacobian of all shape functions
*
* \param in Position
* \param out return value
*/
inline void evaluateJacobian(const typename Traits::DomainType& in,
std::vector<typename Traits::JacobianType>& out) const
{
out.resize(size());
out[0][0][0] = sign_[0]*(-2*in[1] + 2*in[0]);
out[0][0][1] = sign_[0]*(-2*in[0]);
out[0][1][0] = sign_[0]*(-2*in[1]);
out[0][1][1] = sign_[0]*(6 -2*in[0] - 10*in[1]);
out[1][0][0] = 1.5 + 3*in[1] - 9*in[0];
out[1][0][1] = 3*in[0];
out[1][1][0] = 6 - 15*in[1];
out[1][1][1] = 10.5 - 15*in[0] - 15*in[1];
out[2][0][0] = sign_[0]*(-7.5 + 5*in[1] + 25*in[0]);
out[2][0][1] = sign_[0]*(5*in[0]);
out[2][1][0] = sign_[0]*(30 - 25*in[1] - 60*in[0]);
out[2][1][1] = sign_[0]*(7.5 - 25*in[0] - 5*in[1]);
out[3][0][0] = sign_[1]*(6 - 2*in[1] - 10*in[0]);
out[3][0][1] = sign_[1]*(-2*in[0]);
out[3][1][0] = sign_[1]*(-2*in[1]);
out[3][1][1] = sign_[1]*(-2*in[0] + 2*in[1]);
out[4][0][0] = -10.5 + 15*in[1] + 15*in[0];
out[4][0][1] = -6 + 15*in[0];
out[4][1][0] = -3*in[1];
out[4][1][1] = -1.5 - 3*in[0] + 9*in[1];
out[5][0][0] = sign_[1]*(7.5 - 25*in[1] - 5*in[0]);
out[5][0][1] = sign_[1]*(30 - 25*in[0] - 60*in[1]);
out[5][1][0] = sign_[1]*(5*in[1]);
out[5][1][1] = sign_[1]*(-7.5 + 5*in[0] + 25*in[1]);
out[6][0][0] = sign_[2]*(-3 + 4*in[1] + 8*in[0]);
out[6][0][1] = sign_[2]*(4*in[0]);
out[6][1][0] = sign_[2]*(4*in[1]);
out[6][1][1] = sign_[2]*(-3 + 4*in[0] + 8*in[1]);
out[7][0][0] = -3 + 12*in[0];
out[7][0][1] = 0;
out[7][1][0] = 0;
out[7][1][1] = 3 - 12*in[1];
out[8][0][0] = sign_[2]*(-10*in[1] + 10*in[0]);
out[8][0][1] = sign_[2]*(-10*in[0]);
out[8][1][0] = sign_[2]*(-10*in[1]);
out[8][1][1] = sign_[2]*(-10*in[0] + 10*in[1]);
out[9][0][0] = 18 - 12*in[1] - 36*in[0];
out[9][0][1] = -12*in[0];
out[9][1][0] = -12*in[1];
out[9][1][1] = 6 - 12*in[0] - 12*in[1];
out[10][0][0] = 6 - 12*in[1] - 12*in[0];
out[10][0][1] = -12*in[0];
out[10][1][0] = -12*in[1];
out[10][1][1] = 18 - 12*in[0] - 36*in[1];
out[11][0][0] = 90 - 180*in[1] - 180*in[0];
out[11][0][1] = -180*in[0];
out[11][1][0] = 180*in[1];
out[11][1][1] = -90 + 180*in[0] + 180*in[1];
}
//! \brief Evaluate partial derivatives of all shape functions
void partial (const std::array<unsigned int, 2>& order,
const typename Traits::DomainType& in, // position
std::vector<typename Traits::RangeType>& out) const // return value
{
auto totalOrder = std::accumulate(order.begin(), order.end(), 0);
if (totalOrder == 0) {
evaluateFunction(in, out);
} else if (totalOrder == 1) {
out.resize(size());
auto const direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 1));
switch (direction) {
case 0:
out[0][0] = sign_[0]*(-2*in[1] + 2*in[0]);
out[0][1] = sign_[0]*(-2*in[1]);
out[1][0] = 1.5 + 3*in[1] - 9*in[0];
out[1][1] = 6 - 15*in[1];
out[2][0] = sign_[0]*(-7.5 + 5*in[1] + 25*in[0]);
out[2][1] = sign_[0]*(30 - 25*in[1] - 60*in[0]);
out[3][0] = sign_[1]*(6 - 2*in[1] - 10*in[0]);
out[3][1] = sign_[1]*(-2*in[1]);
out[4][0] = -10.5 + 15*in[1] + 15*in[0];
out[4][1] = -3*in[1];
out[5][0] = sign_[1]*(7.5 - 25*in[1] - 5*in[0]);
out[5][1] = sign_[1]*(5*in[1]);
out[6][0] = sign_[2]*(-3 + 4*in[1] + 8*in[0]);
out[6][1] = sign_[2]*(4*in[1]);
out[7][0] = -3 + 12*in[0];
out[7][1] = 0;
out[8][0] = sign_[2]*(-10*in[1] + 10*in[0]);
out[8][1] = sign_[2]*(-10*in[1]);
out[9][0] = 18 - 12*in[1] - 36*in[0];
out[9][1] = -12*in[1];
out[10][0] = 6 - 12*in[1] - 12*in[0];
out[10][1] = -12*in[1];
out[11][0] = 90 - 180*in[1] - 180*in[0];
out[11][1] = 180*in[1];
break;
case 1:
out[0][0] = sign_[0]*(-2*in[0]);
out[0][1] = sign_[0]*(6 -2*in[0] - 10*in[1]);
out[1][0] = 3*in[0];
out[1][1] = 10.5 - 15*in[0] - 15*in[1];
out[2][0] = sign_[0]*(5*in[0]);
out[2][1] = sign_[0]*(7.5 - 25*in[0] - 5*in[1]);
out[3][0] = sign_[1]*(-2*in[0]);
out[3][1] = sign_[1]*(-2*in[0] + 2*in[1]);
out[4][0] = -6 + 15*in[0];
out[4][1] = -1.5 - 3*in[0] + 9*in[1];
out[5][0] = sign_[1]*(30 - 25*in[0] - 60*in[1]);
out[5][1] = sign_[1]*(-7.5 + 5*in[0] + 25*in[1]);
out[6][0] = sign_[2]*(4*in[0]);
out[6][1] = sign_[2]*(-3 + 4*in[0] + 8*in[1]);
out[7][0] = 0;
out[7][1] = 3 - 12*in[1];
out[8][0] = sign_[2]*(-10*in[0]);
out[8][1] = sign_[2]*(-10*in[0] + 10*in[1]);
out[9][0] = -12*in[0];
out[9][1] = 6 - 12*in[0] - 12*in[1];
out[10][0] = -12*in[0];
out[10][1] = 18 - 12*in[0] - 36*in[1];
out[11][0] = -180*in[0];
out[11][1] = -90 + 180*in[0] + 180*in[1];
break;
default:
DUNE_THROW(RangeError, "Component out of range.");
}
} else {
DUNE_THROW(NotImplemented, "Desired derivative order is not implemented");
}
}
//! \brief Polynomial order of the shape functions
unsigned int order() const
{
return 2; // TODO: check whether this is not order 3
}
private:
std::array<R,3> sign_;
};
} // end namespace Dune
#endif // DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_SIMPLEX2D_LOCALBASIS_HH
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