raviartthomas0q2dall.hh
Go to the documentation of this file.00001 #ifndef DUNE_RT0Q2DALL_HH
00002 #define DUNE_RT0Q2DALL_HH
00003
00004 #include <cstddef>
00005 #include <vector>
00006
00007 #include <dune/common/fmatrix.hh>
00008
00009 #include <dune/localfunctions/common/localbasis.hh>
00010 #include <dune/localfunctions/common/localkey.hh>
00011
00012 namespace Dune
00013 {
00022 template<class D, class R>
00023 class RT0Q2DLocalBasis
00024 {
00025 public:
00026 typedef LocalBasisTraits<D,2,Dune::FieldVector<D,2>,R,2,Dune::FieldVector<R,2>,
00027 Dune::FieldMatrix<R,2,2> > Traits;
00028
00030 RT0Q2DLocalBasis ()
00031 {
00032 sign0 = sign1 = sign2 = sign3 = 1.0;
00033 }
00034
00036 RT0Q2DLocalBasis (unsigned int s)
00037 {
00038 sign0 = sign1 = sign2 = sign3 = 1.0;
00039 if (s&1) sign0 = -1.0;
00040 if (s&2) sign1 = -1.0;
00041 if (s&4) sign2 = -1.0;
00042 if (s&8) sign3 = -1.0;
00043 }
00044
00046 unsigned int size () const
00047 {
00048 return 4;
00049 }
00050
00052 inline void evaluateFunction (const typename Traits::DomainType& in,
00053 std::vector<typename Traits::RangeType>& out) const
00054 {
00055 out.resize(4);
00056 out[0][0] = sign0*(in[0]-1.0); out[0][1]=0.0;
00057 out[1][0] = sign1*(in[0]); out[1][1]=0.0;
00058 out[2][0] = 0.0; out[2][1]=sign2*(in[1]-1.0);
00059 out[3][0] = 0.0; out[3][1]=sign3*(in[1]);
00060 }
00061
00063 inline void
00064 evaluateJacobian (const typename Traits::DomainType& in,
00065 std::vector<typename Traits::JacobianType>& out) const
00066 {
00067 out.resize(4);
00068 out[0][0][0] = sign0; out[0][0][1] = 0;
00069 out[0][1][0] = 0; out[0][1][1] = 0;
00070
00071 out[1][0][0] = sign1; out[1][0][1] = 0;
00072 out[1][1][0] = 0; out[1][1][1] = 0;
00073
00074 out[2][0][0] = 0; out[2][0][1] = 0;
00075 out[2][1][0] = 0; out[2][1][1] = sign2;
00076
00077 out[3][0][0] = 0; out[3][0][1] = 0;
00078 out[3][1][0] = 0; out[3][1][1] = sign3;
00079 }
00080
00082 unsigned int order () const
00083 {
00084 return 1;
00085 }
00086
00087 private:
00088 R sign0, sign1, sign2, sign3;
00089 };
00090
00091
00099 template<class LB>
00100 class RT0Q2DLocalInterpolation
00101 {
00102 public:
00103
00105 RT0Q2DLocalInterpolation ()
00106 {
00107 }
00108
00110 RT0Q2DLocalInterpolation (unsigned int s)
00111 {
00112 sign0 = sign1 = sign2 = sign3 = 1.0;
00113 if (s&1) sign0 *= -1.0;
00114 if (s&2) sign1 *= -1.0;
00115 if (s&4) sign2 *= -1.0;
00116 if (s&8) sign3 *= -1.0;
00117
00118 m0[0] = 0.0; m0[1] = 0.5;
00119 m1[0] = 1.0; m1[1] = 0.5;
00120 m2[0] = 0.5; m2[1] = 0.0;
00121 m3[0] = 0.5; m3[1] = 1.0;
00122
00123 n0[0] = -1.0; n0[1] = 0.0;
00124 n1[0] = 1.0; n1[1] = 0.0;
00125 n2[0] = 0.0; n2[1] = -1.0;
00126 n3[0] = 0.0; n3[1] = 1.0;
00127 }
00128
00129 template<typename F, typename C>
00130 void interpolate (const F& f, std::vector<C>& out) const
00131 {
00132
00133 typename F::Traits::RangeType y;
00134
00135 out.resize(4);
00136
00137 f.evaluate(m0,y); out[0] = (y[0]*n0[0]+y[1]*n0[1])*sign0;
00138 f.evaluate(m1,y); out[1] = (y[0]*n1[0]+y[1]*n1[1])*sign1;
00139 f.evaluate(m2,y); out[2] = (y[0]*n2[0]+y[1]*n2[1])*sign2;
00140 f.evaluate(m3,y); out[3] = (y[0]*n3[0]+y[1]*n3[1])*sign3;
00141 }
00142
00143 private:
00144 typename LB::Traits::RangeFieldType sign0,sign1,sign2,sign3;
00145 typename LB::Traits::DomainType m0,m1,m2,m3;
00146 typename LB::Traits::DomainType n0,n1,n2,n3;
00147 };
00148
00155 class RT0Q2DLocalCoefficients
00156 {
00157 public:
00159 RT0Q2DLocalCoefficients () : li(4)
00160 {
00161 for (std::size_t i=0; i<4; i++)
00162 li[i] = LocalKey(i,1,0);
00163 }
00164
00166 std::size_t size () const
00167 {
00168 return 4;
00169 }
00170
00172 const LocalKey& localKey (std::size_t i) const
00173 {
00174 return li[i];
00175 }
00176
00177 private:
00178 std::vector<LocalKey> li;
00179 };
00180
00181 }
00182 #endif