5#ifndef DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS3_CUBE2D_LOCALINTERPOLATION_HH
6#define DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS3_CUBE2D_LOCALINTERPOLATION_HH
36 for (
size_t i=0; i<4; i++)
37 sign_[i] = (s[i]) ? -1.0 : 1.0;
53 template<
typename F,
typename C>
57 typedef typename LB::Traits::RangeFieldType
Scalar;
58 typedef typename LB::Traits::DomainFieldType Vector;
61 fill(out.begin(), out.end(), 0.0);
66 for (
auto&& qp : rule1)
68 Scalar qPos = qp.position();
69 typename LB::Traits::DomainType localPos;
71 localPos = {0.0, qPos};
73 out[0] += (y[0]*n_[0][0] + y[1]*n_[0][1])*qp.weight()*sign_[0];
74 out[1] += (y[0]*n_[0][0] + y[1]*n_[0][1])*(2.0*qPos - 1.0)*qp.weight();
75 out[2] += (y[0]*n_[0][0] + y[1]*n_[0][1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*qp.weight()*sign_[0];
76 out[3] += (y[0]*n_[0][0] + y[1]*n_[0][1])*(20.0*qPos*qPos*qPos - 30.0*qPos*qPos + 12.0*qPos - 1.0)*qp.weight();
78 localPos = {1.0, qPos};
80 out[4] += (y[0]*n_[1][0] + y[1]*n_[1][1])*qp.weight()*sign_[1];
81 out[5] += (y[0]*n_[1][0] + y[1]*n_[1][1])*(1.0 - 2.0*qPos)*qp.weight();
82 out[6] += (y[0]*n_[1][0] + y[1]*n_[1][1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*qp.weight()*sign_[1];
83 out[7] += (y[0]*n_[1][0] + y[1]*n_[1][1])*(-20.0*qPos*qPos*qPos + 30.0*qPos*qPos - 12.0*qPos + 1.0)*qp.weight();
85 localPos = {qPos, 0.0};
87 out[8] += (y[0]*n_[2][0] + y[1]*n_[2][1])*qp.weight()*sign_[2];
88 out[9] += (y[0]*n_[2][0] + y[1]*n_[2][1])*(1.0 - 2.0*qPos)*qp.weight();
89 out[10] += (y[0]*n_[2][0] + y[1]*n_[2][1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*qp.weight()*sign_[2];
90 out[11] += (y[0]*n_[2][0] + y[1]*n_[2][1])*(-20.0*qPos*qPos*qPos + 30.0*qPos*qPos - 12.0*qPos + 1.0)*qp.weight();
92 localPos = {qPos, 1.0};
94 out[12] += (y[0]*n_[3][0] + y[1]*n_[3][1])*qp.weight()*sign_[3];
95 out[13] += (y[0]*n_[3][0] + y[1]*n_[3][1])*(2.0*qPos - 1.0)*qp.weight();
96 out[14] += (y[0]*n_[3][0] + y[1]*n_[3][1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*qp.weight()*sign_[3];
97 out[15] += (y[0]*n_[3][0] + y[1]*n_[3][1])*(20.0*qPos*qPos*qPos - 30.0*qPos*qPos + 12.0*qPos - 1.0)*qp.weight();
102 for (
auto&& qp : rule2)
104 auto qPos = qp.position();
108 double l1_x=2.0*qPos[0]-1.0;
109 double l2_x=6.0*qPos[0]*qPos[0]-6.0*qPos[0]+1.0;
110 double l3_x=20.0*qPos[0]*qPos[0]*qPos[0] - 30.0*qPos[0]*qPos[0] + 12.0*qPos[0] - 1.0;
112 double l1_y=2.0*qPos[1]-1.0;
113 double l2_y=6.0*qPos[1]*qPos[1]-6.0*qPos[1]+1.0;
114 double l3_y=20.0*qPos[1]*qPos[1]*qPos[1] - 30.0*qPos[1]*qPos[1] + 12.0*qPos[1] - 1.0;
116 out[16] += y[0]*l0_x*l0_y*qp.weight();
117 out[17] += y[0]*l0_x*l1_y*qp.weight();
118 out[18] += y[0]*l0_x*l2_y*qp.weight();
119 out[19] += y[0]*l0_x*l3_y*qp.weight();
120 out[20] += y[0]*l1_x*l0_y*qp.weight();
121 out[21] += y[0]*l1_x*l1_y*qp.weight();
122 out[22] += y[0]*l1_x*l2_y*qp.weight();
123 out[23] += y[0]*l1_x*l3_y*qp.weight();
124 out[24] += y[0]*l2_x*l0_y*qp.weight();
125 out[25] += y[0]*l2_x*l1_y*qp.weight();
126 out[26] += y[0]*l2_x*l2_y*qp.weight();
127 out[27] += y[0]*l2_x*l3_y*qp.weight();
129 out[28] += y[1]*l0_x*l0_y*qp.weight();
130 out[29] += y[1]*l0_x*l1_y*qp.weight();
131 out[30] += y[1]*l0_x*l2_y*qp.weight();
132 out[31] += y[1]*l1_x*l0_y*qp.weight();
133 out[32] += y[1]*l1_x*l1_y*qp.weight();
134 out[33] += y[1]*l1_x*l2_y*qp.weight();
135 out[34] += y[1]*l2_x*l0_y*qp.weight();
136 out[35] += y[1]*l2_x*l1_y*qp.weight();
137 out[36] += y[1]*l2_x*l2_y*qp.weight();
138 out[37] += y[1]*l3_x*l0_y*qp.weight();
139 out[38] += y[1]*l3_x*l1_y*qp.weight();
140 out[39] += y[1]*l3_x*l2_y*qp.weight();
146 std::array<typename LB::Traits::RangeFieldType, 4> sign_;
149 std::array<typename LB::Traits::DomainType, 4> n_;
static const QuadratureRule & rule(const GeometryType &t, int p, QuadratureType::Enum qt=QuadratureType::GaussLegendre)
select the appropriate QuadratureRule for GeometryType t and order p
Definition: quadraturerules.hh:326
Second order Raviart-Thomas shape functions on the reference quadrilateral.
Definition: raviartthomas3cube2dlocalinterpolation.hh:25
RT3Cube2DLocalInterpolation(std::bitset< 4 > s=0)
Make set number s, where 0 <= s < 16.
Definition: raviartthomas3cube2dlocalinterpolation.hh:34
void interpolate(const F &f, std::vector< C > &out) const
Interpolate a given function with shape functions.
Definition: raviartthomas3cube2dlocalinterpolation.hh:54
constexpr GeometryType cube(unsigned int dim)
Returns a GeometryType representing a hypercube of dimension dim.
Definition: type.hh:462
typename Overloads::ScalarType< std::decay_t< V > >::type Scalar
Element type of some SIMD type.
Definition: interface.hh:235
Dune namespace.
Definition: alignedallocator.hh:13