From 19ca4f31d73feef4571ce7ea37f359fd6d64e3f1 Mon Sep 17 00:00:00 2001 From: Peter Munch Date: Sun, 19 Jul 2020 17:43:58 +0200 Subject: [PATCH] Extend QProjector for simplex --- source/base/qprojector.cc | 229 ++++++++++++- tests/simplex/q_projection_01.cc | 163 +++++++++ tests/simplex/q_projection_01.output | 481 +++++++++++++++++++++++++++ 3 files changed, 870 insertions(+), 3 deletions(-) create mode 100644 tests/simplex/q_projection_01.cc create mode 100644 tests/simplex/q_projection_01.output diff --git a/source/base/qprojector.cc b/source/base/qprojector.cc index 275a9356be..ccd41a6745 100644 --- a/source/base/qprojector.cc +++ b/source/base/qprojector.cc @@ -13,9 +13,12 @@ // // --------------------------------------------------------------------- +#include #include #include +#include + DEAL_II_NAMESPACE_OPEN @@ -519,8 +522,70 @@ QProjector<2>::project_to_all_faces( const ReferenceCell::Type reference_cell_type, const SubQuadrature & quadrature) { + if (reference_cell_type == ReferenceCell::Type::Tri) + { + // the quadrature rule to be projected ... + const auto &sub_quadrature_points = quadrature.get_points(); + const auto &sub_quadrature_weights = quadrature.get_weights(); + + // ... on to the faces (defined by its support points and arc length) + const std::array, 2>, double>, 3> faces = { + {{{Point<2>(0.0, 0.0), Point<2>(1.0, 0.0)}, 1.0}, + {{Point<2>(1.0, 0.0), Point<2>(0.0, 1.0)}, std::sqrt(2.0)}, + {{Point<2>(0.0, 1.0), Point<2>(0.0, 0.0)}, 1.0}}}; + + // linear polynomial to map the reference quadrature points correctly + // on faces + const Simplex::ScalarPolynomial<1> poly(1); + + // new (projected) quadrature points and weights + std::vector> points; + std::vector weights; + + // loop over all faces (lines) ... + for (const auto &face : faces) + // ... and over all possible orientations + for (unsigned int orientation = 0; orientation < 2; ++orientation) + { + std::array, 2> support_points; + + // determine support point of the current line with the correct + // orientation + switch (orientation) + { + case 0: + support_points = {face.first[1], face.first[0]}; + break; + case 1: + support_points = {face.first[0], face.first[1]}; + break; + default: + Assert(false, ExcNotImplemented()); + } + + // loop over all quadrature points + for (unsigned int j = 0; j < sub_quadrature_points.size(); ++j) + { + Point<2> mapped_point; + + // map reference quadrature point + for (unsigned int i = 0; i < 2; ++i) + mapped_point += + support_points[i] * + poly.compute_value(i, sub_quadrature_points[j]); + + points.emplace_back(mapped_point); + + // scale weight by arc length + weights.emplace_back(sub_quadrature_weights[j] * face.second); + } + } + + // construct new quadrature rule + return {points, weights}; + } + Assert(reference_cell_type == ReferenceCell::Type::Quad, ExcNotImplemented()); - (void)reference_cell_type; const unsigned int dim = 2; @@ -571,8 +636,154 @@ QProjector<3>::project_to_all_faces( const ReferenceCell::Type reference_cell_type, const SubQuadrature & quadrature) { + if (reference_cell_type == ReferenceCell::Type::Tet) + { + // the quadrature rule to be projected ... + const auto &sub_quadrature_points = quadrature.get_points(); + const auto &sub_quadrature_weights = quadrature.get_weights(); + + // ... on to the faces (defined by its support points and its area) + // note: the area is later not used as a scaling factor but recomputed + const std::array, 3>, double>, 4> faces = { + {{{Point<3>(0.0, 0.0, 0.0), + Point<3>(1.0, 0.0, 0.0), + Point<3>(0.0, 1.0, 0.0)}, + 0.5}, + {{Point<3>(1.0, 0.0, 0.0), + Point<3>(0.0, 0.0, 0.0), + Point<3>(0.0, 0.0, 1.0)}, + 0.5}, + {{Point<3>(0.0, 0.0, 0.0), + Point<3>(0.0, 1.0, 0.0), + Point<3>(0.0, 0.0, 1.0)}, + 0.5}, + {{Point<3>(0.0, 1.0, 0.0), + Point<3>(1.0, 0.0, 0.0), + Point<3>(0.0, 0.0, 1.0)}, + 0.5 * sqrt(3.0) /*equilateral triangle*/}}}; + + // linear polynomial to map the reference quadrature points correctly + // on faces + const Simplex::ScalarPolynomial<2> poly(1); + + // new (projected) quadrature points and weights + std::vector> points; + std::vector weights; + + // loop over all faces (triangles) ... + for (const auto &face : faces) + // ... and over all possible orientations + for (unsigned int orientation = 0; orientation < 6; ++orientation) + { + std::array, 3> support_points; + + // determine support point of the current line with the correct + // orientation + switch (orientation) + { + case 1: + support_points = {face.first[0], + face.first[1], + face.first[2]}; + break; + case 3: + support_points = {face.first[1], + face.first[0], + face.first[2]}; + break; + case 5: + support_points = {face.first[2], + face.first[0], + face.first[1]}; + break; + case 0: + support_points = {face.first[0], + face.first[2], + face.first[1]}; + break; + case 2: + support_points = {face.first[1], + face.first[2], + face.first[0]}; + break; + case 4: + support_points = {face.first[2], + face.first[1], + face.first[0]}; + break; + default: + Assert(false, ExcNotImplemented()); + } + + // loop over all quadrature points + for (unsigned int j = 0; j < sub_quadrature_points.size(); ++j) + { + Point<3> mapped_point; + + // map reference quadrature point + for (unsigned int i = 0; i < 3; ++i) + mapped_point += + support_points[i] * + poly.compute_value(i, sub_quadrature_points[j]); + + points.push_back(mapped_point); + + // scale quadrature weight + const double scaling = [&]() { + const auto &supp_pts = support_points; + + const unsigned int n_shape_functions = 3; + const unsigned int dim_ = 2; + const unsigned int spacedim = 3; + + double result[spacedim][dim_]; + + std::vector> shape_derivatives( + n_shape_functions); + + for (unsigned int i = 0; i < 3; ++i) + shape_derivatives[i] = + poly.compute_1st_derivative(i, sub_quadrature_points[j]); + + for (unsigned int i = 0; i < spacedim; ++i) + for (unsigned int j = 0; j < dim_; ++j) + result[i][j] = shape_derivatives[0][j] * supp_pts[0][i]; + for (unsigned int k = 1; k < n_shape_functions; ++k) + for (unsigned int i = 0; i < spacedim; ++i) + for (unsigned int j = 0; j < dim_; ++j) + result[i][j] += + shape_derivatives[k][j] * supp_pts[k][i]; + + DerivativeForm<1, dim_, spacedim> contravariant; + + for (unsigned int i = 0; i < spacedim; ++i) + for (unsigned int j = 0; j < dim_; ++j) + contravariant[i][j] = result[i][j]; + + + Tensor<1, spacedim> DX_t[dim_]; + for (unsigned int i = 0; i < spacedim; ++i) + for (unsigned int j = 0; j < dim_; ++j) + DX_t[j][i] = contravariant[i][j]; + + Tensor<2, dim_> G; + for (unsigned int i = 0; i < dim_; ++i) + for (unsigned int j = 0; j < dim_; ++j) + G[i][j] = DX_t[i] * DX_t[j]; + + return std::sqrt(determinant(G)); + }(); + + weights.push_back(sub_quadrature_weights[j] * scaling); + } + } + + // construct new quadrature rule + return {points, weights}; + } + + Assert(reference_cell_type == ReferenceCell::Type::Hex, ExcNotImplemented()); - (void)reference_cell_type; const unsigned int dim = 3; @@ -996,9 +1207,21 @@ QProjector::DataSetDescriptor::face( const bool face_rotation, const unsigned int n_quadrature_points) { + if (reference_cell_type == ReferenceCell::Type::Tri || + reference_cell_type == ReferenceCell::Type::Tet) + { + if (dim == 2) + return {(2 * face_no + face_orientation) * n_quadrature_points}; + else if (dim == 3) + { + const unsigned int orientation = + (face_flip * 2 + face_rotation) * 2 + face_orientation; + return {(6 * face_no + orientation) * n_quadrature_points}; + } + } + Assert(reference_cell_type == ReferenceCell::get_hypercube(dim), ExcNotImplemented()); - (void)reference_cell_type; Assert(face_no < GeometryInfo::faces_per_cell, ExcInternalError()); diff --git a/tests/simplex/q_projection_01.cc b/tests/simplex/q_projection_01.cc new file mode 100644 index 0000000000..919c388394 --- /dev/null +++ b/tests/simplex/q_projection_01.cc @@ -0,0 +1,163 @@ +// --------------------------------------------------------------------- +// +// Copyright (C) 2020 by the deal.II authors +// +// This file is part of the deal.II library. +// +// The deal.II library is free software; you can use it, redistribute +// it, and/or modify it under the terms of the GNU Lesser General +// Public License as published by the Free Software Foundation; either +// version 2.1 of the License, or (at your option) any later version. +// The full text of the license can be found in the file LICENSE.md at +// the top level directory of deal.II. +// +// --------------------------------------------------------------------- + + +// Test QProjection for Simplex::PGauss. + + +#include + +#include + +#include "../tests.h" + +using namespace dealii; + +template +void +test(const unsigned int) +{ + AssertThrow(false, ExcNotImplemented()) +} + +template <> +void +test<2>(const unsigned int n_points) +{ + const int dim = 2; + + Simplex::PGauss quad_ref(n_points); + + const auto quad = + QProjector::project_to_all_faces(ReferenceCell::Type::Tri, quad_ref); + + const auto print = [&](const unsigned int face_no, + const bool face_orientation) { + deallog << "face_no=" << face_no + << " face_orientation=" << (face_orientation ? "true" : "false") + << ":" << std::endl; + for (unsigned int + q = 0, + i = + QProjector::DataSetDescriptor::face(ReferenceCell::Type::Tri, + face_no, + face_orientation, + false, + false, + n_points); + q < n_points; + ++q, ++i) + { + deallog << quad.point(i) << " "; + deallog << quad.weight(i) << " "; + deallog << std::endl; + } + deallog << std::endl; + }; + + for (unsigned int i = 0; i < 3; ++i) + { + print(i, true); // 1 + print(i, false); // 0 + } +} + +template <> +void +test<3>(const unsigned int n_points) +{ + const int dim = 3; + + Simplex::PGauss quad_ref(n_points); + + const auto quad = + QProjector::project_to_all_faces(ReferenceCell::Type::Tet, quad_ref); + + const auto print = [&](const unsigned int face_no, + const bool face_orientation, + const bool face_flip, + const bool face_rotation) { + deallog << "face_no=" << face_no + << " face_orientation=" << (face_orientation ? "true" : "false") + << " face_flip=" << (face_flip ? "true" : "false") + << " face_rotation=" << (face_rotation ? "true" : "false") << ":" + << std::endl; + for (unsigned int + q = 0, + i = + QProjector::DataSetDescriptor::face(ReferenceCell::Type::Tet, + face_no, + face_orientation, + face_flip, + face_rotation, + n_points); + q < n_points; + ++q, ++i) + { + deallog << quad.point(i) << " "; + deallog << quad.weight(i) << " "; + deallog << std::endl; + } + deallog << std::endl; + }; + + for (unsigned int i = 0; i < 4; ++i) + { + print(i, true, false, false); // 1 + print(i, true, true, false); // 3 + print(i, true, false, true); // 5 + print(i, false, false, false); // 0 + print(i, false, true, false); // 2 + print(i, false, false, true); // 4 + } +} + +int +main() +{ + initlog(); + + { + deallog.push("2d-1"); + test<2>(1); + deallog.pop(); + } + { + deallog.push("2d-2"); + test<2>(2); + deallog.pop(); + } + { + deallog.push("2d-3"); + test<2>(3); + deallog.pop(); + } + + { + deallog.push("3d-1"); + test<3>(1); + deallog.pop(); + } + { + deallog.push("3d-4"); + test<3>(3); + deallog.pop(); + } + { + deallog.push("3d-10"); + test<3>(7); + deallog.pop(); + } +} diff --git a/tests/simplex/q_projection_01.output b/tests/simplex/q_projection_01.output new file mode 100644 index 0000000000..862e421643 --- /dev/null +++ b/tests/simplex/q_projection_01.output @@ -0,0 +1,481 @@ + +DEAL:2d-1::face_no=0 face_orientation=true: +DEAL:2d-1::0.500000 0.00000 1.00000 +DEAL:2d-1:: +DEAL:2d-1::face_no=0 face_orientation=false: +DEAL:2d-1::0.500000 0.00000 1.00000 +DEAL:2d-1:: +DEAL:2d-1::face_no=1 face_orientation=true: +DEAL:2d-1::0.500000 0.500000 1.41421 +DEAL:2d-1:: +DEAL:2d-1::face_no=1 face_orientation=false: +DEAL:2d-1::0.500000 0.500000 1.41421 +DEAL:2d-1:: +DEAL:2d-1::face_no=2 face_orientation=true: +DEAL:2d-1::0.00000 0.500000 1.00000 +DEAL:2d-1:: +DEAL:2d-1::face_no=2 face_orientation=false: +DEAL:2d-1::0.00000 0.500000 1.00000 +DEAL:2d-1:: +DEAL:2d-2::face_no=0 face_orientation=true: +DEAL:2d-2::0.211325 0.00000 0.500000 +DEAL:2d-2::0.788675 0.00000 0.500000 +DEAL:2d-2:: +DEAL:2d-2::face_no=0 face_orientation=false: +DEAL:2d-2::0.788675 0.00000 0.500000 +DEAL:2d-2::0.211325 0.00000 0.500000 +DEAL:2d-2:: +DEAL:2d-2::face_no=1 face_orientation=true: +DEAL:2d-2::0.788675 0.211325 0.707107 +DEAL:2d-2::0.211325 0.788675 0.707107 +DEAL:2d-2:: +DEAL:2d-2::face_no=1 face_orientation=false: +DEAL:2d-2::0.211325 0.788675 0.707107 +DEAL:2d-2::0.788675 0.211325 0.707107 +DEAL:2d-2:: +DEAL:2d-2::face_no=2 face_orientation=true: +DEAL:2d-2::0.00000 0.788675 0.500000 +DEAL:2d-2::0.00000 0.211325 0.500000 +DEAL:2d-2:: +DEAL:2d-2::face_no=2 face_orientation=false: +DEAL:2d-2::0.00000 0.211325 0.500000 +DEAL:2d-2::0.00000 0.788675 0.500000 +DEAL:2d-2:: +DEAL:2d-3::face_no=0 face_orientation=true: +DEAL:2d-3::0.112702 0.00000 0.277778 +DEAL:2d-3::0.500000 0.00000 0.444444 +DEAL:2d-3::0.887298 0.00000 0.277778 +DEAL:2d-3:: +DEAL:2d-3::face_no=0 face_orientation=false: +DEAL:2d-3::0.887298 0.00000 0.277778 +DEAL:2d-3::0.500000 0.00000 0.444444 +DEAL:2d-3::0.112702 0.00000 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+DEAL:3d-1::face_no=0 face_orientation=true face_flip=false face_rotation=true: +DEAL:3d-1::0.333333 0.333333 0.00000 1.00000 +DEAL:3d-1:: +DEAL:3d-1::face_no=0 face_orientation=false face_flip=false face_rotation=false: +DEAL:3d-1::0.333333 0.333333 0.00000 1.00000 +DEAL:3d-1:: +DEAL:3d-1::face_no=0 face_orientation=false face_flip=true face_rotation=false: +DEAL:3d-1::0.333333 0.333333 0.00000 1.00000 +DEAL:3d-1:: +DEAL:3d-1::face_no=0 face_orientation=false face_flip=false face_rotation=true: +DEAL:3d-1::0.333333 0.333333 0.00000 1.00000 +DEAL:3d-1:: +DEAL:3d-1::face_no=1 face_orientation=true face_flip=false face_rotation=false: +DEAL:3d-1::0.333333 0.00000 0.333333 1.00000 +DEAL:3d-1:: +DEAL:3d-1::face_no=1 face_orientation=true face_flip=true face_rotation=false: +DEAL:3d-1::0.333333 0.00000 0.333333 1.00000 +DEAL:3d-1:: +DEAL:3d-1::face_no=1 face_orientation=true face_flip=false face_rotation=true: +DEAL:3d-1::0.333333 0.00000 0.333333 1.00000 +DEAL:3d-1:: +DEAL:3d-1::face_no=1 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