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| 1 | // -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- | ||
| 2 | // vi: set et ts=4 sw=4 sts=4: | ||
| 3 | // | ||
| 4 | // SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder | ||
| 5 | // SPDX-License-Identifier: GPL-3.0-or-later | ||
| 6 | // | ||
| 7 | /*! | ||
| 8 | * \file | ||
| 9 | * \ingroup Core | ||
| 10 | * \brief Define helper functions for integration | ||
| 11 | */ | ||
| 12 | #ifndef DUMUX_COMMON_INTEGRATE_HH | ||
| 13 | #define DUMUX_COMMON_INTEGRATE_HH | ||
| 14 | |||
| 15 | #include <cmath> | ||
| 16 | #include <type_traits> | ||
| 17 | |||
| 18 | #include <dune/common/typetraits.hh> | ||
| 19 | #include <dune/geometry/quadraturerules.hh> | ||
| 20 | #include <dune/common/concept.hh> | ||
| 21 | |||
| 22 | #if HAVE_DUNE_FUNCTIONS | ||
| 23 | #include <dune/functions/gridfunctions/gridfunction.hh> | ||
| 24 | #endif | ||
| 25 | |||
| 26 | #include <dumux/common/doubleexpintegrator.hh> | ||
| 27 | #include <dumux/discretization/evalsolution.hh> | ||
| 28 | #include <dumux/discretization/elementsolution.hh> | ||
| 29 | |||
| 30 | namespace Dumux { | ||
| 31 | |||
| 32 | // implementation details of the integrate functions | ||
| 33 | #ifndef DOXYGEN | ||
| 34 | namespace Detail { | ||
| 35 | |||
| 36 | struct HasLocalFunction | ||
| 37 | { | ||
| 38 | template<class F> | ||
| 39 | auto require(F&& f) -> decltype( | ||
| 40 | localFunction(f), | ||
| 41 | localFunction(f).unbind() | ||
| 42 | ); | ||
| 43 | }; | ||
| 44 | |||
| 45 | template<class F> | ||
| 46 | static constexpr bool hasLocalFunction() | ||
| 47 | { return Dune::models<HasLocalFunction, F>(); } | ||
| 48 | |||
| 49 | template<class Error, | ||
| 50 | typename std::enable_if_t<Dune::IsIndexable<Error>::value, int> = 0> | ||
| 51 | Error sqrtNorm(const Error& error) | ||
| 52 | { | ||
| 53 | using std::sqrt; | ||
| 54 | auto e = error; | ||
| 55 | for (int i = 0; i < error.size(); ++i) | ||
| 56 | e[i] = sqrt(error[i]); | ||
| 57 | return e; | ||
| 58 | } | ||
| 59 | |||
| 60 | template<class Error, | ||
| 61 | typename std::enable_if_t<!Dune::IsIndexable<Error>::value, int> = 0> | ||
| 62 | Error sqrtNorm(const Error& error) | ||
| 63 | { | ||
| 64 | using std::sqrt; | ||
| 65 | return sqrt(error); | ||
| 66 | } | ||
| 67 | |||
| 68 | template<class T, typename = int> | ||
| 69 | struct FieldTypeImpl | ||
| 70 | { | ||
| 71 | using type = T; | ||
| 72 | }; | ||
| 73 | |||
| 74 | template<class T> | ||
| 75 | struct FieldTypeImpl<T, typename std::enable_if<(sizeof(std::declval<T>()[0]) > 0), int>::type> | ||
| 76 | { | ||
| 77 | using type = typename FieldTypeImpl<std::decay_t<decltype(std::declval<T>()[0])>>::type; | ||
| 78 | }; | ||
| 79 | |||
| 80 | template<class T> | ||
| 81 | using FieldType = typename FieldTypeImpl<T>::type; | ||
| 82 | |||
| 83 | } // end namespace Detail | ||
| 84 | #endif | ||
| 85 | |||
| 86 | /*! | ||
| 87 | * \brief Integrate a grid function over a grid view | ||
| 88 | * \param gg the grid geometry | ||
| 89 | * \param sol the solution vector | ||
| 90 | * \param order the order of the quadrature rule | ||
| 91 | */ | ||
| 92 | template<class GridGeometry, class SolutionVector, | ||
| 93 | typename std::enable_if_t<!Detail::hasLocalFunction<SolutionVector>(), int> = 0> | ||
| 94 | auto integrateGridFunction(const GridGeometry& gg, | ||
| 95 | const SolutionVector& sol, | ||
| 96 | std::size_t order) | ||
| 97 | { | ||
| 98 | using GridView = typename GridGeometry::GridView; | ||
| 99 | using Scalar = typename Detail::FieldType< std::decay_t<decltype(sol[0])> >; | ||
| 100 | |||
| 101 | Scalar integral(0.0); | ||
| 102 | for (const auto& element : elements(gg.gridView())) | ||
| 103 | { | ||
| 104 | const auto elemSol = elementSolution(element, sol, gg); | ||
| 105 | const auto geometry = element.geometry(); | ||
| 106 | const auto& quad = Dune::QuadratureRules<Scalar, GridView::dimension>::rule(geometry.type(), order); | ||
| 107 | for (auto&& qp : quad) | ||
| 108 | { | ||
| 109 | auto value = evalSolution(element, geometry, gg, elemSol, geometry.global(qp.position())); | ||
| 110 | value *= qp.weight()*geometry.integrationElement(qp.position()); | ||
| 111 | integral += value; | ||
| 112 | } | ||
| 113 | } | ||
| 114 | return integral; | ||
| 115 | } | ||
| 116 | |||
| 117 | /*! | ||
| 118 | * \brief Integrate a function over a grid view | ||
| 119 | * \param gg the grid geometry | ||
| 120 | * \param sol1 the first function | ||
| 121 | * \param sol2 the second function | ||
| 122 | * \param order the order of the quadrature rule | ||
| 123 | * \note dune functions currently doesn't support composing two functions | ||
| 124 | */ | ||
| 125 | template<class GridGeometry, class Sol1, class Sol2, | ||
| 126 | typename std::enable_if_t<!Detail::hasLocalFunction<Sol1>(), int> = 0> | ||
| 127 | 12 | auto integrateL2Error(const GridGeometry& gg, | |
| 128 | const Sol1& sol1, | ||
| 129 | const Sol2& sol2, | ||
| 130 | std::size_t order) | ||
| 131 | { | ||
| 132 | using GridView = typename GridGeometry::GridView; | ||
| 133 | using Scalar = typename Detail::FieldType< std::decay_t<decltype(sol1[0])> >; | ||
| 134 | |||
| 135 | 12 | Scalar l2norm(0.0); | |
| 136 |
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14824 | for (const auto& element : elements(gg.gridView())) |
| 137 | { | ||
| 138 | 7400 | const auto elemSol1 = elementSolution(element, sol1, gg); | |
| 139 | 7400 | const auto elemSol2 = elementSolution(element, sol2, gg); | |
| 140 | |||
| 141 | 7400 | const auto geometry = element.geometry(); | |
| 142 | 14800 | const auto& quad = Dune::QuadratureRules<Scalar, GridView::dimension>::rule(geometry.type(), order); | |
| 143 |
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52200 | for (auto&& qp : quad) |
| 144 | { | ||
| 145 |
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30000 | const auto& globalPos = geometry.global(qp.position()); |
| 146 |
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15000 | const auto value1 = evalSolution(element, geometry, gg, elemSol1, globalPos); |
| 147 |
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15000 | const auto value2 = evalSolution(element, geometry, gg, elemSol2, globalPos); |
| 148 | 15000 | const auto error = (value1 - value2); | |
| 149 | 60000 | l2norm += (error*error)*qp.weight()*geometry.integrationElement(qp.position()); | |
| 150 | } | ||
| 151 | } | ||
| 152 | |||
| 153 | using std::sqrt; | ||
| 154 | 12 | return sqrt(l2norm); | |
| 155 | } | ||
| 156 | |||
| 157 | #if HAVE_DUNE_FUNCTIONS | ||
| 158 | |||
| 159 | /*! | ||
| 160 | * \brief Integrate a grid function over a grid view | ||
| 161 | * \param gv the grid view | ||
| 162 | * \param f the grid function | ||
| 163 | * \param order the order of the quadrature rule | ||
| 164 | * \note overload for a Dune::Functions::GridFunction | ||
| 165 | */ | ||
| 166 | template<class GridView, class F, | ||
| 167 | typename std::enable_if_t<Detail::hasLocalFunction<F>(), int> = 0> | ||
| 168 | 1 | auto integrateGridFunction(const GridView& gv, | |
| 169 | const F& f, | ||
| 170 | std::size_t order) | ||
| 171 | { | ||
| 172 | 1 | auto fLocal = localFunction(f); | |
| 173 | |||
| 174 | using Element = typename GridView::template Codim<0>::Entity; | ||
| 175 | using LocalPosition = typename Element::Geometry::LocalCoordinate; | ||
| 176 | using Scalar = typename Detail::FieldType< std::decay_t<decltype(fLocal(std::declval<LocalPosition>()))> >; | ||
| 177 | |||
| 178 | 1 | Scalar integral(0.0); | |
| 179 |
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2180 | for (const auto& element : elements(gv)) |
| 180 | { | ||
| 181 |
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1089 | fLocal.bind(element); |
| 182 | |||
| 183 | 1089 | const auto geometry = element.geometry(); | |
| 184 | 2178 | const auto& quad = Dune::QuadratureRules<Scalar, GridView::dimension>::rule(geometry.type(), order); | |
| 185 |
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5445 | for (auto&& qp : quad) |
| 186 | { | ||
| 187 |
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2178 | auto value = fLocal(qp.position()); |
| 188 | 2178 | value *= qp.weight()*geometry.integrationElement(qp.position()); | |
| 189 | 1089 | integral += value; | |
| 190 | } | ||
| 191 | |||
| 192 |
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2178 | fLocal.unbind(); |
| 193 | } | ||
| 194 | 1 | return integral; | |
| 195 | } | ||
| 196 | |||
| 197 | /*! | ||
| 198 | * \brief Integrate a function over a grid view | ||
| 199 | * \param gv the grid view | ||
| 200 | * \param f the first function | ||
| 201 | * \param g the second function | ||
| 202 | * \param order the order of the quadrature rule | ||
| 203 | * \note overload for a Dune::Functions::GridFunction | ||
| 204 | * \note dune functions currently doesn't support composing two functions | ||
| 205 | */ | ||
| 206 | template<class GridView, class F, class G, | ||
| 207 | typename std::enable_if_t<Detail::hasLocalFunction<F>(), int> = 0> | ||
| 208 | 29 | auto integrateL2Error(const GridView& gv, | |
| 209 | const F& f, | ||
| 210 | const G& g, | ||
| 211 | std::size_t order) | ||
| 212 | { | ||
| 213 |
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42 | auto fLocal = localFunction(f); |
| 214 |
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29 | auto gLocal = localFunction(g); |
| 215 | |||
| 216 | using Element = typename GridView::template Codim<0>::Entity; | ||
| 217 | using LocalPosition = typename Element::Geometry::LocalCoordinate; | ||
| 218 | using Scalar = typename Detail::FieldType< std::decay_t<decltype(fLocal(std::declval<LocalPosition>()))> >; | ||
| 219 | |||
| 220 | 29 | Scalar l2norm(0.0); | |
| 221 |
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221829 | for (const auto& element : elements(gv)) |
| 222 | { | ||
| 223 |
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110900 | fLocal.bind(element); |
| 224 |
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110900 | gLocal.bind(element); |
| 225 | |||
| 226 |
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110900 | const auto geometry = element.geometry(); |
| 227 | 221800 | const auto& quad = Dune::QuadratureRules<Scalar, GridView::dimension>::rule(geometry.type(), order); | |
| 228 |
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1219900 | for (auto&& qp : quad) |
| 229 | { | ||
| 230 |
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887200 | const auto error = fLocal(qp.position()) - gLocal(qp.position()); |
| 231 | 1330800 | l2norm += (error*error)*qp.weight()*geometry.integrationElement(qp.position()); | |
| 232 | } | ||
| 233 | |||
| 234 |
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110900 | gLocal.unbind(); |
| 235 |
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221800 | fLocal.unbind(); |
| 236 | } | ||
| 237 | |||
| 238 | using std::sqrt; | ||
| 239 | 42 | return sqrt(l2norm); | |
| 240 | } | ||
| 241 | #endif | ||
| 242 | |||
| 243 | /*! | ||
| 244 | * \brief Integrate a scalar function | ||
| 245 | * \param f the integrand (invocable with a single scalar) | ||
| 246 | * \param lowerBound lower integral bound | ||
| 247 | * \param upperBound upper integral bound | ||
| 248 | * \param targetAbsoluteError desired absolute error in the result | ||
| 249 | * \return The value of the integral | ||
| 250 | */ | ||
| 251 | template<class Scalar, class Function, | ||
| 252 | typename std::enable_if_t<std::is_invocable_r_v<Scalar, Function, Scalar>>...> | ||
| 253 | ✗ | Scalar integrateScalarFunction(const Function& f, | |
| 254 | const Scalar lowerBound, | ||
| 255 | const Scalar upperBound, | ||
| 256 | const Scalar targetAbsoluteError = 1e-13) | ||
| 257 | { | ||
| 258 |
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2049663 | return DoubleExponentialIntegrator<Scalar>::integrate(f, lowerBound, upperBound, targetAbsoluteError); |
| 259 | } | ||
| 260 | |||
| 261 | } // end namespace Dumux | ||
| 262 | |||
| 263 | #endif | ||
| 264 |