1 // -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*- 2 // vi: set et ts=4 sw=2 sts=2: 3 #ifndef DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI1_SIMPLEX2D_LOCALINTERPOLATION_HH 4 #define DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI1_SIMPLEX2D_LOCALINTERPOLATION_HH 5 6 #include <vector> 7 8 #include <dune/geometry/quadraturerules.hh> 9 #include <dune/localfunctions/common/localinterpolation.hh> 10 11 namespace Dune 12 { 13 /** 14 * \ingroup LocalInterpolationImplementation 15 * \brief First order Brezzi-Douglas-Marini shape functions on the reference triangle. 16 * 17 * \tparam LB corresponding LocalBasis giving traits 18 * 19 * \nosubgrouping 20 */ 21 template<class LB> 22 class BDM1Simplex2DLocalInterpolation 23 { 24 25 public: 26 //! \brief Standard constructor BDM1Simplex2DLocalInterpolation()27 BDM1Simplex2DLocalInterpolation () 28 { 29 sign0 = sign1 = sign2 = 1.0; 30 } 31 32 /** 33 * \brief Make set number s, where 0 <= s < 8 34 * 35 * \param s Edge orientation indicator 36 */ BDM1Simplex2DLocalInterpolation(unsigned int s)37 BDM1Simplex2DLocalInterpolation (unsigned int s) 38 { 39 using std::sqrt; 40 sign0 = sign1 = sign2 = 1.0; 41 if (s & 1) 42 { 43 sign0 = -1.0; 44 } 45 if (s & 2) 46 { 47 sign1 = -1.0; 48 } 49 if (s & 4) 50 { 51 sign2 = -1.0; 52 } 53 54 n0[0] = 0.0; 55 n0[1] = -1.0; 56 n1[0] = -1.0; 57 n1[1] = 0.0; 58 n2[0] = 1.0/sqrt(2.0); 59 n2[1] = 1.0/sqrt(2.0); 60 c0 = 0.5*n0[0] - 1.0*n0[1]; 61 c1 = -1.0*n1[0] + 0.5*n1[1]; 62 c2 = 0.5*n2[0] + 0.5*n2[1]; 63 } 64 65 /** 66 * \brief Interpolate a given function with shape functions 67 * 68 * \tparam F Function type for function which should be interpolated 69 * \tparam C Coefficient type 70 * \param ff function which should be interpolated 71 * \param out return value, vector of coefficients 72 */ 73 template<typename F, typename C> interpolate(const F & ff,std::vector<C> & out) const74 void interpolate (const F& ff, std::vector<C>& out) const 75 { 76 // f gives v*outer normal at a point on the edge! 77 typedef typename LB::Traits::RangeFieldType Scalar; 78 79 auto&& f = Impl::makeFunctionWithCallOperator<typename LB::Traits::DomainType>(ff); 80 81 out.resize(6); 82 fill(out.begin(), out.end(), 0.0); 83 84 const int qOrder = 4; 85 const Dune::QuadratureRule<Scalar,1>& rule = Dune::QuadratureRules<Scalar,1>::rule(Dune::GeometryTypes::simplex(1), qOrder); 86 87 for (typename Dune::QuadratureRule<Scalar,1>::const_iterator it=rule.begin(); it!=rule.end(); ++it) 88 { 89 Scalar qPos = it->position(); 90 typename LB::Traits::DomainType localPos; 91 92 localPos[0] = qPos; 93 localPos[1] = 0.0; 94 auto y = f(localPos); 95 out[0] += (y[0]*n0[0] + y[1]*n0[1])*it->weight()*sign0/c0; 96 out[3] += (y[0]*n0[0] + y[1]*n0[1])*(2.0*qPos - 1.0)*it->weight()/c0; 97 98 localPos[0] = 0.0; 99 localPos[1] = qPos; 100 y = f(localPos); 101 out[1] += (y[0]*n1[0] + y[1]*n1[1])*it->weight()*sign1/c1; 102 out[4] += (y[0]*n1[0] + y[1]*n1[1])*(1.0 - 2.0*qPos)*it->weight()/c1; 103 104 localPos[0] = 1.0 - qPos; 105 localPos[1] = qPos; 106 y = f(localPos); 107 out[2] += (y[0]*n2[0] + y[1]*n2[1])*it->weight()*sign2/c2; 108 out[5] += (y[0]*n2[0] + y[1]*n2[1])*(2.0*qPos - 1.0)*it->weight()/c2; 109 } 110 } 111 112 private: 113 typename LB::Traits::RangeFieldType sign0,sign1,sign2; 114 typename LB::Traits::DomainType n0,n1,n2; 115 typename LB::Traits::RangeFieldType c0,c1,c2; 116 }; 117 } 118 119 #endif // DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI1_SIMPLEX2D_LOCALINTERPOLATION_HH 120