/usr/include/dune/localfunctions/brezzidouglasmarini/brezzidouglasmarini1q2d/brezzidouglasmarini1q2dlocalbasis.hh is in libdune-localfunctions-dev 2.2.1-2.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 | #ifndef DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI1Q2DLOCALBASIS_HH
#define DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI1Q2DLOCALBASIS_HH
#include <vector>
#include <dune/common/fmatrix.hh>
#include "../../common/localbasis.hh"
namespace Dune
{
/**
* @ingroup LocalBasisImplementation
* \brief First order Brezzi-Douglas-Marini shape functions on the reference quadrilateral.
*
* \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 BDM1Q2DLocalBasis
{
public:
typedef LocalBasisTraits<D,2,Dune::FieldVector<D,2>,R,2,Dune::FieldVector<R,2>,
Dune::FieldMatrix<R,2,2> > Traits;
//! \brief Standard constructor
BDM1Q2DLocalBasis ()
{
sign0 = sign1 = sign2 = sign3 = 1.0;
}
/**
* \brief Make set number s, where 0 <= s < 16
*
* \param s Edge orientation indicator
*/
BDM1Q2DLocalBasis (unsigned int s)
{
sign0 = sign1 = sign2 = sign3 = 1.0;
if (s & 1)
{
sign0 = -1.0;
}
if (s & 2)
{
sign1 = -1.0;
}
if (s & 4)
{
sign2 = -1.0;
}
if (s & 8)
{
sign3 = -1.0;
}
}
//! \brief number of shape functions
unsigned int size () const
{
return 8;
}
/**
* \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(8);
out[0][0] = sign0*(in[0] - 1.0);
out[0][1] = 0.0;
out[1][0] = 6.0*in[0]*in[1] - 3.0*in[0]-6*in[1] + 3.0;
out[1][1] = -3.0*in[1]*in[1] + 3.0*in[1];
out[2][0] = sign1*(in[0]);
out[2][1] = 0.0;
out[3][0] = -6.0*in[0]*in[1] + 3.0*in[0];
out[3][1] = 3.0*in[1]*in[1] - 3.0*in[1];
out[4][0] = 0.0;
out[4][1] = sign2*(in[1] - 1.0);
out[5][0] = 3.0*in[0]*in[0] - 3.0*in[0];
out[5][1] = -6.0*in[0]*in[1] + 6.0*in[0] + 3.0*in[1] - 3.0;
out[6][0] = 0.0;
out[6][1] = sign3*(in[1]);
out[7][0] = -3.0*in[0]*in[0] + 3.0*in[0];
out[7][1] = 6.0*in[0]*in[1] - 3.0*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(8);
out[0][0][0] = sign0;
out[0][0][1] = 0.0;
out[0][1][0] = 0.0;
out[0][1][1] = 0.0;
out[1][0][0] = 6.0*in[1] - 3.0;
out[1][0][1] = 6.0*in[0] - 6.0;
out[1][1][0] = 0.0;
out[1][1][1] = -6.0*in[1] + 3.0;
out[2][0][0] = sign1;
out[2][0][1] = 0.0;
out[2][1][0] = 0.0;
out[2][1][1] = 0.0;
out[3][0][0] = -6.0*in[1] + 3.0;
out[3][0][1] = -6.0*in[0];
out[3][1][0] = 0.0;
out[3][1][1] = 6.0*in[1] - 3.0;
out[4][0][0] = 0.0;
out[4][0][1] = 0.0;
out[4][1][0] = 0.0;
out[4][1][1] = sign2;
out[5][0][0] = 6.0*in[0] - 3.0;
out[5][0][1] = 0.0;
out[5][1][0] = -6.0*in[1] + 6.0;
out[5][1][1] = -6.0*in[0] + 3.0;
out[6][0][0] = 0.0;
out[6][0][1] = 0.0;
out[6][1][0] = 0.0;
out[6][1][1] = sign3;
out[7][0][0] = -6.0*in[0] + 3.0;
out[7][0][1] = 0.0;
out[7][1][0] = 6.0*in[1];
out[7][1][1] = 6.0*in[0] - 3.0;
}
//! \brief Polynomial order of the shape functions
unsigned int order () const
{
return 2;
}
private:
R sign0, sign1, sign2, sign3;
};
}
#endif // DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI1Q2DLOCALBASIS_HH
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