From 23dbf1cddba3391ecd941cf66022b377a62b7fd6 Mon Sep 17 00:00:00 2001 From: Peter Munch Date: Sat, 16 Oct 2021 16:37:56 +0200 Subject: [PATCH] QIterated: varying subdivisions --- include/deal.II/base/quadrature.h | 12 + source/base/quadrature.cc | 152 ++++++--- tests/base/quadrature_qiterated_01.cc | 71 ++++ tests/base/quadrature_qiterated_01.output | 399 ++++++++++++++++++++++ 4 files changed, 591 insertions(+), 43 deletions(-) create mode 100644 tests/base/quadrature_qiterated_01.cc create mode 100644 tests/base/quadrature_qiterated_01.output diff --git a/include/deal.II/base/quadrature.h b/include/deal.II/base/quadrature.h index 6ef0acbdfb..22261e79e6 100644 --- a/include/deal.II/base/quadrature.h +++ b/include/deal.II/base/quadrature.h @@ -373,6 +373,18 @@ public: */ QIterated(const Quadrature<1> &base_quadrature, const unsigned int n_copies); + /** + * Constructor. Iterate the given quadrature formula on the given subintervals + * defined by adjacent points in @p intervals in each direction. The resulting + * quadrature rule will have `base_quadrature.size() * (intervals.size() - 1)` + * quadrature points if no quadrature point of `base_quadrature` is positioned + * on the boundaries. + * + * @note We require that `intervals.front() == 0` and `interval.back() == 1`. + */ + QIterated(const Quadrature<1> & base_quadrature, + const std::vector> &intervals); + /** * Exception */ diff --git a/source/base/quadrature.cc b/source/base/quadrature.cc index 2631376590..15888fb538 100644 --- a/source/base/quadrature.cc +++ b/source/base/quadrature.cc @@ -449,12 +449,35 @@ namespace internal [](const Point<1> &p) { return p == Point<1>{1.}; }); return (at_left && at_right); } + + std::vector> + create_interval_points(const unsigned int n_copies) + { + std::vector> support_points(n_copies + 1); + + for (unsigned int copy = 0; copy < n_copies; ++copy) + support_points[copy][0] = + static_cast(copy) / static_cast(n_copies); + + support_points[n_copies][0] = 1.0; + + return support_points; + } } // namespace } // namespace QIteratedImplementation } // namespace internal +template <> +QIterated<0>::QIterated(const Quadrature<1> &, const std::vector> &) + : Quadrature<0>() +{ + Assert(false, ExcNotImplemented()); +} + + + template <> QIterated<0>::QIterated(const Quadrature<1> &, const unsigned int) : Quadrature<0>() @@ -465,15 +488,17 @@ QIterated<0>::QIterated(const Quadrature<1> &, const unsigned int) template <> -QIterated<1>::QIterated(const Quadrature<1> &base_quadrature, - const unsigned int n_copies) +QIterated<1>::QIterated(const Quadrature<1> & base_quadrature, + const std::vector> &intervals) : Quadrature<1>( internal::QIteratedImplementation::uses_both_endpoints(base_quadrature) ? - (base_quadrature.size() - 1) * n_copies + 1 : - base_quadrature.size() * n_copies) + (base_quadrature.size() - 1) * (intervals.size() - 1) + 1 : + base_quadrature.size() * (intervals.size() - 1)) { Assert(base_quadrature.size() > 0, ExcNotInitialized()); - Assert(n_copies > 0, ExcZero()); + Assert(intervals.size() > 1, ExcZero()); + + const unsigned int n_copies = intervals.size() - 1; if (!internal::QIteratedImplementation::uses_both_endpoints(base_quadrature)) // we don't have to skip some points in order to get a reasonable quadrature @@ -485,10 +510,12 @@ QIterated<1>::QIterated(const Quadrature<1> &base_quadrature, ++q_point) { this->quadrature_points[next_point] = - Point<1>(base_quadrature.point(q_point)(0) / n_copies + - (1.0 * copy) / n_copies); + Point<1>(base_quadrature.point(q_point)(0) * + (intervals[copy + 1][0] - intervals[copy][0]) + + intervals[copy][0]); this->weights[next_point] = - base_quadrature.weight(q_point) / n_copies; + base_quadrature.weight(q_point) * + (intervals[copy + 1][0] - intervals[copy][0]); ++next_point; } @@ -496,54 +523,71 @@ QIterated<1>::QIterated(const Quadrature<1> &base_quadrature, else // skip doubly available points { - unsigned int next_point = 0; - - // first find out the weights of the left and the right boundary points. - // note that these usually are but need not necessarily be the same - double double_point_weight = 0; - unsigned int n_end_points = 0; - for (unsigned int i = 0; i < base_quadrature.size(); ++i) - // add up the weight if this is an endpoint - if ((base_quadrature.point(i) == Point<1>(0.0)) || - (base_quadrature.point(i) == Point<1>(1.0))) - { - double_point_weight += base_quadrature.weight(i); - ++n_end_points; - } - // scale the weight correctly - double_point_weight /= n_copies; - - // make sure the base quadrature formula has only one quadrature point per - // end point - Assert(n_end_points == 2, ExcInvalidQuadratureFormula()); - - - for (unsigned int copy = 0; copy < n_copies; ++copy) + const unsigned int left_index = + std::distance(base_quadrature.get_points().begin(), + std::find_if(base_quadrature.get_points().cbegin(), + base_quadrature.get_points().cend(), + [](const Point<1> &p) { + return p == Point<1>{0.}; + })); + + const unsigned int right_index = + std::distance(base_quadrature.get_points().begin(), + std::find_if(base_quadrature.get_points().cbegin(), + base_quadrature.get_points().cend(), + [](const Point<1> &p) { + return p == Point<1>{1.}; + })); + + const unsigned double_point_offset = + left_index + (base_quadrature.size() - right_index); + + for (unsigned int copy = 0, next_point = 0; copy < n_copies; ++copy) for (unsigned int q_point = 0; q_point < base_quadrature.size(); ++q_point) { // skip the left point of this copy since we have already entered it // the last time if ((copy > 0) && (base_quadrature.point(q_point) == Point<1>(0.0))) - continue; + { + Assert(this->quadrature_points[next_point - double_point_offset] + .distance(Point<1>( + base_quadrature.point(q_point)(0) * + (intervals[copy + 1][0] - intervals[copy][0]) + + intervals[copy][0])) < 1e-10 /*tolerance*/, + ExcInternalError()); + + this->weights[next_point - double_point_offset] += + base_quadrature.weight(q_point) * + (intervals[copy + 1][0] - intervals[copy][0]); + + continue; + } this->quadrature_points[next_point] = - Point<1>(base_quadrature.point(q_point)(0) / n_copies + - (1.0 * copy) / n_copies); + Point<1>(base_quadrature.point(q_point)(0) * + (intervals[copy + 1][0] - intervals[copy][0]) + + intervals[copy][0]); // if this is the rightmost point of one of the non-last copies: // give it the double weight - if ((copy != n_copies - 1) && - (base_quadrature.point(q_point) == Point<1>(1.0))) - this->weights[next_point] = double_point_weight; - else - this->weights[next_point] = - base_quadrature.weight(q_point) / n_copies; + this->weights[next_point] = + base_quadrature.weight(q_point) * + (intervals[copy + 1][0] - intervals[copy][0]); ++next_point; } } + // make sure that there is no rounding error for 0.0 and 1.0, since there + // are multiple asserts in the library checking for equality without + // tolorances + for (auto &i : this->quadrature_points) + if (std::abs(i[0] - 0.0) < 1e-12) + i[0] = 0.0; + else if (std::abs(i[0] - 1.0) < 1e-12) + i[0] = 1.0; + #if DEBUG double sum_of_weights = 0; for (unsigned int i = 0; i < this->size(); ++i) @@ -554,13 +598,35 @@ QIterated<1>::QIterated(const Quadrature<1> &base_quadrature, +template <> +QIterated<1>::QIterated(const Quadrature<1> &base_quadrature, + const unsigned int n_copies) + : QIterated<1>(base_quadrature, + internal::QIteratedImplementation::create_interval_points( + n_copies)) +{ + Assert(base_quadrature.size() > 0, ExcNotInitialized()); + Assert(n_copies > 0, ExcZero()); +} + + + // construct higher dimensional quadrature formula by tensor product // of lower dimensional iterated quadrature formulae +template +QIterated::QIterated(const Quadrature<1> & base_quadrature, + const std::vector> &intervals) + : Quadrature(QIterated(base_quadrature, intervals), + QIterated<1>(base_quadrature, intervals)) +{} + + + template QIterated::QIterated(const Quadrature<1> &base_quadrature, - const unsigned int N) - : Quadrature(QIterated(base_quadrature, N), - QIterated<1>(base_quadrature, N)) + const unsigned int n_copies) + : Quadrature(QIterated(base_quadrature, n_copies), + QIterated<1>(base_quadrature, n_copies)) {} diff --git a/tests/base/quadrature_qiterated_01.cc b/tests/base/quadrature_qiterated_01.cc new file mode 100644 index 0000000000..6711fe1dfe --- /dev/null +++ b/tests/base/quadrature_qiterated_01.cc @@ -0,0 +1,71 @@ +// --------------------------------------------------------------------- +// +// Copyright (C) 2020 - 2021 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 QIterated for varying subdivisions. + + +#include + +#include "../tests.h" + +using namespace dealii; + +template +void +test(const Quadrature<1> &q_outer, const Quadrature<1> &q_inner) +{ + QIterated quad(q_inner, q_outer.get_points()); + + for (unsigned int q = 0; q < quad.size(); ++q) + { + deallog << quad.point(q) << " "; + deallog << quad.weight(q) << " "; + deallog << std::endl; + } + deallog << std::endl; +} + +template +void +test() +{ + for (unsigned int i = 2; i <= 4; ++i) + for (unsigned int j = 1; j <= 3; ++j) + { + deallog.push("QGaussLobatto<1>(" + std::to_string(i) + + ") + QGauss<1>(" + std::to_string(j) + ")"); + test(QGaussLobatto<1>(i), QGauss<1>(j)); + deallog.pop(); + } + + for (unsigned int i = 2; i <= 4; ++i) + for (unsigned int j = 2; j <= 3; ++j) + { + deallog.push("QGaussLobatto<1>(" + std::to_string(i) + + ") + QGaussLobatto<1>(" + std::to_string(j) + ")"); + test(QGaussLobatto<1>(i), QGaussLobatto<1>(j)); + deallog.pop(); + } +} + +int +main() +{ + initlog(); + + test<1>(); + test<2>(); +} diff --git a/tests/base/quadrature_qiterated_01.output b/tests/base/quadrature_qiterated_01.output new file mode 100644 index 0000000000..623936dfce --- /dev/null +++ b/tests/base/quadrature_qiterated_01.output @@ -0,0 +1,399 @@ + +DEAL:QGaussLobatto<1>(2) + QGauss<1>(1)::0.500000 1.00000 +DEAL:QGaussLobatto<1>(2) + QGauss<1>(1):: +DEAL:QGaussLobatto<1>(2) + QGauss<1>(2)::0.211325 0.500000 +DEAL:QGaussLobatto<1>(2) + QGauss<1>(2)::0.788675 0.500000 +DEAL:QGaussLobatto<1>(2) + QGauss<1>(2):: +DEAL:QGaussLobatto<1>(2) + QGauss<1>(3)::0.112702 0.277778 +DEAL:QGaussLobatto<1>(2) + QGauss<1>(3)::0.500000 0.444444 +DEAL:QGaussLobatto<1>(2) + QGauss<1>(3)::0.887298 0.277778 +DEAL:QGaussLobatto<1>(2) + QGauss<1>(3):: +DEAL:QGaussLobatto<1>(3) + QGauss<1>(1)::0.250000 0.500000 +DEAL:QGaussLobatto<1>(3) + QGauss<1>(1)::0.750000 0.500000 +DEAL:QGaussLobatto<1>(3) + QGauss<1>(1):: +DEAL:QGaussLobatto<1>(3) + QGauss<1>(2)::0.105662 0.250000 +DEAL:QGaussLobatto<1>(3) + QGauss<1>(2)::0.394338 0.250000 +DEAL:QGaussLobatto<1>(3) + QGauss<1>(2)::0.605662 0.250000 +DEAL:QGaussLobatto<1>(3) + QGauss<1>(2)::0.894338 0.250000 +DEAL:QGaussLobatto<1>(3) + QGauss<1>(2):: +DEAL:QGaussLobatto<1>(3) + QGauss<1>(3)::0.0563508 0.138889 +DEAL:QGaussLobatto<1>(3) + QGauss<1>(3)::0.250000 0.222222 +DEAL:QGaussLobatto<1>(3) + QGauss<1>(3)::0.443649 0.138889 +DEAL:QGaussLobatto<1>(3) + QGauss<1>(3)::0.556351 0.138889 +DEAL:QGaussLobatto<1>(3) + QGauss<1>(3)::0.750000 0.222222 +DEAL:QGaussLobatto<1>(3) + QGauss<1>(3)::0.943649 0.138889 +DEAL:QGaussLobatto<1>(3) + QGauss<1>(3):: +DEAL:QGaussLobatto<1>(4) + QGauss<1>(1)::0.138197 0.276393 +DEAL:QGaussLobatto<1>(4) + QGauss<1>(1)::0.500000 0.447214 +DEAL:QGaussLobatto<1>(4) + QGauss<1>(1)::0.861803 0.276393 +DEAL:QGaussLobatto<1>(4) + QGauss<1>(1):: +DEAL:QGaussLobatto<1>(4) + QGauss<1>(2)::0.0584088 0.138197 +DEAL:QGaussLobatto<1>(4) + QGauss<1>(2)::0.217984 0.138197 +DEAL:QGaussLobatto<1>(4) + QGauss<1>(2)::0.370901 0.223607 +DEAL:QGaussLobatto<1>(4) + QGauss<1>(2)::0.629099 0.223607 +DEAL:QGaussLobatto<1>(4) + QGauss<1>(2)::0.782016 0.138197 +DEAL:QGaussLobatto<1>(4) + QGauss<1>(2)::0.941591 0.138197 +DEAL:QGaussLobatto<1>(4) + QGauss<1>(2):: +DEAL:QGaussLobatto<1>(4) + QGauss<1>(3)::0.0311500 0.0767759 +DEAL:QGaussLobatto<1>(4) + QGauss<1>(3)::0.138197 0.122841 +DEAL:QGaussLobatto<1>(4) + QGauss<1>(3)::0.245243 0.0767759 +DEAL:QGaussLobatto<1>(4) + QGauss<1>(3)::0.326795 0.124226 +DEAL:QGaussLobatto<1>(4) + QGauss<1>(3)::0.500000 0.198762 +DEAL:QGaussLobatto<1>(4) + QGauss<1>(3)::0.673205 0.124226 +DEAL:QGaussLobatto<1>(4) + QGauss<1>(3)::0.754757 0.0767759 +DEAL:QGaussLobatto<1>(4) + QGauss<1>(3)::0.861803 0.122841 +DEAL:QGaussLobatto<1>(4) + QGauss<1>(3)::0.968850 0.0767759 +DEAL:QGaussLobatto<1>(4) + QGauss<1>(3):: +DEAL:QGaussLobatto<1>(2) + QGaussLobatto<1>(2)::0.00000 0.500000 +DEAL:QGaussLobatto<1>(2) + QGaussLobatto<1>(2)::1.00000 0.500000 +DEAL:QGaussLobatto<1>(2) + QGaussLobatto<1>(2):: +DEAL:QGaussLobatto<1>(2) + QGaussLobatto<1>(3)::0.00000 0.166667 +DEAL:QGaussLobatto<1>(2) + QGaussLobatto<1>(3)::0.500000 0.666667 +DEAL:QGaussLobatto<1>(2) + QGaussLobatto<1>(3)::1.00000 0.166667 +DEAL:QGaussLobatto<1>(2) + QGaussLobatto<1>(3):: +DEAL:QGaussLobatto<1>(3) + QGaussLobatto<1>(2)::0.00000 0.250000 +DEAL:QGaussLobatto<1>(3) + QGaussLobatto<1>(2)::0.500000 0.500000 +DEAL:QGaussLobatto<1>(3) + QGaussLobatto<1>(2)::1.00000 0.250000 +DEAL:QGaussLobatto<1>(3) + QGaussLobatto<1>(2):: +DEAL:QGaussLobatto<1>(3) + QGaussLobatto<1>(3)::0.00000 0.0833333 +DEAL:QGaussLobatto<1>(3) + QGaussLobatto<1>(3)::0.250000 0.333333 +DEAL:QGaussLobatto<1>(3) + QGaussLobatto<1>(3)::0.500000 0.166667 +DEAL:QGaussLobatto<1>(3) + QGaussLobatto<1>(3)::0.750000 0.333333 +DEAL:QGaussLobatto<1>(3) + QGaussLobatto<1>(3)::1.00000 0.0833333 +DEAL:QGaussLobatto<1>(3) + QGaussLobatto<1>(3):: 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