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130 lines
4.6 KiB
130 lines
4.6 KiB
#include "drake/multibody/fem/simplex_gaussian_quadrature.h"
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namespace drake {
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namespace multibody {
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namespace fem {
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namespace internal {
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using std::make_pair;
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using std::move;
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/* Linear triangle quadrature. */
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template <>
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std::pair<SimplexGaussianQuadrature<2, 1>::LocationsType,
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SimplexGaussianQuadrature<2, 1>::WeightsType>
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SimplexGaussianQuadrature<2, 1>::ComputePointsAndWeights() {
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/* quadrature point location, weight/area
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(1/3, 1/3) 1.0 */
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LocationsType points = {{{1.0 / 3.0, 1.0 / 3.0}}};
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/* For a unit triangle, area = 0.5. */
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WeightsType weights = {{0.5}};
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return make_pair(move(points), move(weights));
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}
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/* Quadratic triangle quadrature. */
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template <>
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std::pair<SimplexGaussianQuadrature<2, 2>::LocationsType,
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SimplexGaussianQuadrature<2, 2>::WeightsType>
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SimplexGaussianQuadrature<2, 2>::ComputePointsAndWeights() {
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/* quadrature point location, weight/area
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(1/6, 1/6) 1/3
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(2/3, 1/6) 1/3
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(1/6, 2/3) 1/3
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Note: Here we choose r=1/2 in section 3 of [Hammer, 1956]. They also
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mentioned the other choice with r=-1/2. We do not use r=-1/2 as it
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lies out side of the element. */
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LocationsType points;
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points[0] = {1.0 / 6.0, 1.0 / 6.0};
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points[1] = {2.0 / 3.0, 1.0 / 6.0};
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points[2] = {1.0 / 6.0, 2.0 / 3.0};
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/* For a unit triangle, area = 0.5. */
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WeightsType weights = {{1.0 / 6.0, 1.0 / 6.0, 1.0 / 6.0}};
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return make_pair(move(points), move(weights));
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}
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/* Cubic triangle quadrature. */
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template <>
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std::pair<SimplexGaussianQuadrature<2, 3>::LocationsType,
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SimplexGaussianQuadrature<2, 3>::WeightsType>
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SimplexGaussianQuadrature<2, 3>::ComputePointsAndWeights() {
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/* quadrature point location, weight/area
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(1/3, 1/3) -9/16
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(3/5, 1/5) 25/48
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(1/5, 3/5) 25/48
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(1/5, 1/5) 25/48 */
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LocationsType points;
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points[0] = {1.0 / 3.0, 1.0 / 3.0};
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points[1] = {0.6, 0.2};
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points[2] = {0.2, 0.6};
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points[3] = {0.2, 0.2};
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/* For a unit triangle, area = 0.5. */
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WeightsType weights = {{-9.0 / 32.0, 25.0 / 96.0, 25.0 / 96.0, 25.0 / 96.0}};
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return make_pair(move(points), move(weights));
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}
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/* Linear tetrahedral quadrature. */
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template <>
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std::pair<SimplexGaussianQuadrature<3, 1>::LocationsType,
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SimplexGaussianQuadrature<3, 1>::WeightsType>
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SimplexGaussianQuadrature<3, 1>::ComputePointsAndWeights() {
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/* quadrature point location, weight/area
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(1/4, 1/4, 1/4) 1.0 */
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LocationsType points = {{{0.25, 0.25, 0.25}}};
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/* For a unit tetrahedron, area = 1/6. */
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WeightsType weights = {{1.0 / 6.0}};
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return make_pair(move(points), move(weights));
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}
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/* Quadratic tetrahedral quadrature. */
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template <>
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std::pair<SimplexGaussianQuadrature<3, 2>::LocationsType,
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SimplexGaussianQuadrature<3, 2>::WeightsType>
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SimplexGaussianQuadrature<3, 2>::ComputePointsAndWeights() {
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/* quadrature point location, weight/area
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(a, b, b) 1/4
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(b, a, b) 1/4
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(b, b, a) 1/4
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(b, b, b) 1/4
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where a = (1+3*sqrt(1/5))/4, b = (1-1/sqrt(1/5))/4. */
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LocationsType points;
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double a = (1.0 + 3.0 * sqrt(0.2)) / 4.0;
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double b = (1.0 - sqrt(0.2)) / 4.0;
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points[0] = {a, b, b};
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points[1] = {b, a, b};
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points[2] = {b, b, a};
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points[3] = {b, b, b};
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/* For a unit tetrahedron, area = 1/6. */
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WeightsType weights = {{1.0 / 24.0, 1.0 / 24.0, 1.0 / 24.0, 1.0 / 24.0}};
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return make_pair(move(points), move(weights));
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}
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/* Cubic tetrahedral quadrature. */
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template <>
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std::pair<SimplexGaussianQuadrature<3, 3>::LocationsType,
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SimplexGaussianQuadrature<3, 3>::WeightsType>
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SimplexGaussianQuadrature<3, 3>::ComputePointsAndWeights() {
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/* quadrature point location, weight/area
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(1/4, 1/4, 1/4) -4/5
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(a, b, b) 9/20
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(b, a, b) 9/20
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(b, b, a) 9/20
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(b, b, b) 9/20
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where a = 1/2, b = 1/6. */
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LocationsType points;
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double a = 0.5;
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double b = 1.0 / 6.0;
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points[0] = {0.25, 0.25, 0.25};
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points[1] = {a, b, b};
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points[2] = {b, a, b};
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points[3] = {b, b, a};
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points[4] = {b, b, b};
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/* For a unit tetrahedron, area = 1/6. */
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WeightsType weights = {
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{-2.0 / 15.0, 3.0 / 40.0, 3.0 / 40.0, 3.0 / 40.0, 3.0 / 40.0}};
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return make_pair(move(points), move(weights));
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}
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} // namespace internal
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} // namespace fem
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} // namespace multibody
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} // namespace drake
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