dune-localfunctions  2.2.0
brezzidouglasmarini1q2dlocalbasis.hh
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00001 #ifndef DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI1Q2DLOCALBASIS_HH
00002 #define DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI1Q2DLOCALBASIS_HH
00003 
00004 #include <vector>
00005 
00006 #include <dune/common/fmatrix.hh>
00007 
00008 #include "../../common/localbasis.hh"
00009 
00010 namespace Dune 
00011 {
00021   template<class D, class R>
00022   class BDM1Q2DLocalBasis
00023   {
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     BDM1Q2DLocalBasis ()
00031     {
00032       sign0 = sign1 = sign2 = sign3 = 1.0;
00033     }
00034 
00040     BDM1Q2DLocalBasis (unsigned int s)
00041     {
00042       sign0 = sign1 = sign2 = sign3 = 1.0;
00043       if (s & 1)
00044       {
00045         sign0 = -1.0;
00046       }
00047       if (s & 2)
00048       {
00049         sign1 = -1.0;
00050       }
00051       if (s & 4)
00052       {
00053         sign2 = -1.0;
00054       }
00055       if (s & 8)
00056       {
00057         sign3 = -1.0;
00058       }
00059     }
00060 
00062     unsigned int size () const
00063     {
00064       return 8;
00065     }
00066 
00073     inline void evaluateFunction (const typename Traits::DomainType& in,
00074                                   std::vector<typename Traits::RangeType>& out) const
00075     {     
00076       out.resize(8);
00077 
00078       out[0][0] = sign0*(in[0] - 1.0);
00079       out[0][1] = 0.0;
00080       out[1][0] = 6.0*in[0]*in[1] - 3.0*in[0]-6*in[1] + 3.0;
00081       out[1][1] = -3.0*in[1]*in[1] + 3.0*in[1];
00082       out[2][0] = sign1*(in[0]);
00083       out[2][1] = 0.0;
00084       out[3][0] = -6.0*in[0]*in[1] + 3.0*in[0];
00085       out[3][1] = 3.0*in[1]*in[1] - 3.0*in[1];
00086       out[4][0] = 0.0;
00087       out[4][1] = sign2*(in[1] - 1.0);
00088       out[5][0] = 3.0*in[0]*in[0] - 3.0*in[0];
00089       out[5][1] = -6.0*in[0]*in[1] + 6.0*in[0] + 3.0*in[1] - 3.0;
00090       out[6][0] = 0.0;
00091       out[6][1] = sign3*(in[1]);
00092       out[7][0] = -3.0*in[0]*in[0] + 3.0*in[0];
00093       out[7][1] = 6.0*in[0]*in[1] - 3.0*in[1];
00094     }
00095 
00102     inline void evaluateJacobian (const typename Traits::DomainType& in,
00103                                   std::vector<typename Traits::JacobianType>& out) const
00104     {  
00105       out.resize(8);
00106 
00107       out[0][0][0] = sign0;
00108       out[0][0][1] = 0.0;
00109       out[0][1][0] = 0.0;
00110       out[0][1][1] = 0.0;
00111 
00112       out[1][0][0] = 6.0*in[1] - 3.0;
00113       out[1][0][1] = 6.0*in[0] - 6.0;
00114       out[1][1][0] = 0.0;
00115       out[1][1][1] = -6.0*in[1] + 3.0;
00116 
00117       out[2][0][0] = sign1;
00118       out[2][0][1] = 0.0;
00119       out[2][1][0] = 0.0;
00120       out[2][1][1] = 0.0;
00121 
00122       out[3][0][0] = -6.0*in[1] + 3.0;
00123       out[3][0][1] = -6.0*in[0];
00124       out[3][1][0] = 0.0;
00125       out[3][1][1] = 6.0*in[1] - 3.0;
00126 
00127       out[4][0][0] = 0.0;
00128       out[4][0][1] = 0.0;
00129       out[4][1][0] = 0.0;
00130       out[4][1][1] = sign2;
00131 
00132       out[5][0][0] = 6.0*in[0] - 3.0;
00133       out[5][0][1] = 0.0;
00134       out[5][1][0] = -6.0*in[1] + 6.0;
00135       out[5][1][1] = -6.0*in[0] + 3.0;
00136  
00137       out[6][0][0] = 0.0;
00138       out[6][0][1] = 0.0;
00139       out[6][1][0] = 0.0;
00140       out[6][1][1] = sign3;
00141 
00142       out[7][0][0] = -6.0*in[0] + 3.0;
00143       out[7][0][1] = 0.0;
00144       out[7][1][0] = 6.0*in[1];
00145       out[7][1][1] = 6.0*in[0] - 3.0;
00146     }
00147 
00149     unsigned int order () const
00150     {
00151       return 2;
00152     }
00153 
00154 private:
00155     R sign0, sign1, sign2, sign3;
00156   };
00157 }
00158 #endif // DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI1Q2DLOCALBASIS_HH