raviartthomas0q2dall.hh

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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,         // position
00065                                           std::vector<typename Traits::JacobianType>& out) const      // return value
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           // f gives v*outer normal at a point on the edge!
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

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