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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 Geometry | ||
| 10 | * \brief Compute the volume of several common geometry types | ||
| 11 | */ | ||
| 12 | #ifndef DUMUX_GEOMETRY_VOLUME_HH | ||
| 13 | #define DUMUX_GEOMETRY_VOLUME_HH | ||
| 14 | |||
| 15 | #include <cmath> | ||
| 16 | #include <limits> | ||
| 17 | #include <type_traits> | ||
| 18 | |||
| 19 | #include <dune/common/exceptions.hh> | ||
| 20 | #include <dune/geometry/type.hh> | ||
| 21 | #include <dune/geometry/quadraturerules.hh> | ||
| 22 | |||
| 23 | #include <dumux/common/math.hh> | ||
| 24 | |||
| 25 | namespace Dumux { | ||
| 26 | |||
| 27 | /*! | ||
| 28 | * \ingroup Geometry | ||
| 29 | * \brief Compute the volume of several common geometry types | ||
| 30 | * \param type the geometry type | ||
| 31 | * \param c a function returning the ith corner (in Dune reference element order) | ||
| 32 | * e.g. `[&](unsigned int i){ return corners[i]; }`, where `corners` is a | ||
| 33 | * random access container storing the corners, and the returned corner is stored | ||
| 34 | * in a container (e.g. Dune::FieldVector) that exports `value_type` and `dimension`. | ||
| 35 | * \tparam dim the dimension of the geometry | ||
| 36 | * \tparam CornerF the function type (is deduced) | ||
| 37 | * \return volume of the geometry or NaN signalling not implemented | ||
| 38 | * \note This is only correct for convex polytopes (flat sides) | ||
| 39 | */ | ||
| 40 | template<int dim, class CornerF> | ||
| 41 | 43987463 | auto convexPolytopeVolume(Dune::GeometryType type, const CornerF& c) | |
| 42 | { | ||
| 43 | using ctype = typename std::decay_t<decltype(c(0))>::value_type; | ||
| 44 | static constexpr int coordDim = std::decay_t<decltype(c(0))>::dimension; | ||
| 45 | static_assert(coordDim >= dim, "Coordinate dimension has to be larger than geometry dimension"); | ||
| 46 | |||
| 47 | // not implemented for coordinate dimension larger than 3 | ||
| 48 | if constexpr (coordDim > 3) | ||
| 49 | return std::numeric_limits<ctype>::quiet_NaN(); | ||
| 50 | |||
| 51 | if constexpr (dim == 0) | ||
| 52 | ✗ | return 1.0; | |
| 53 | |||
| 54 | else if constexpr (dim == 1) | ||
| 55 | 25530022 | return (c(1)-c(0)).two_norm(); | |
| 56 | |||
| 57 | else if constexpr (dim == 2) | ||
| 58 | { | ||
| 59 |
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41828845 | if (type == Dune::GeometryTypes::triangle) |
| 60 | { | ||
| 61 | if constexpr (coordDim == 2) | ||
| 62 | { | ||
| 63 | // make sure we are using positive volumes | ||
| 64 | // the cross product of edge vectors might be negative, | ||
| 65 | // depending on the element orientation | ||
| 66 | using std::abs; | ||
| 67 | 4246954 | return 0.5*abs(Dumux::crossProduct(c(1)-c(0), c(2)-c(0))); | |
| 68 | } | ||
| 69 | else // coordDim == 3 | ||
| 70 | 936448 | return 0.5*Dumux::crossProduct(c(1)-c(0), c(2)-c(0)).two_norm(); | |
| 71 | |||
| 72 | } | ||
| 73 |
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41239875 | else if (type == Dune::GeometryTypes::quadrilateral) |
| 74 | { | ||
| 75 | if constexpr (coordDim == 2) | ||
| 76 | { | ||
| 77 | // make sure we are using positive volumes | ||
| 78 | // the cross product of diagonals might be negative, | ||
| 79 | // depending on the element orientation | ||
| 80 | using std::abs; | ||
| 81 | 340374193 | return 0.5*abs(Dumux::crossProduct(c(3)-c(0), c(2)-c(1))); | |
| 82 | } | ||
| 83 | else // coordDim == 3 | ||
| 84 | 27363920 | return 0.5*Dumux::crossProduct(c(3)-c(0), c(2)-c(1)).two_norm(); | |
| 85 | |||
| 86 | } | ||
| 87 | else | ||
| 88 | return std::numeric_limits<ctype>::quiet_NaN(); | ||
| 89 | } | ||
| 90 | |||
| 91 | else if constexpr (dim == 3) | ||
| 92 | { | ||
| 93 |
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1751192 | if (type == Dune::GeometryTypes::tetrahedron) |
| 94 | { | ||
| 95 | using std::abs; | ||
| 96 | 22080 | return 1.0/6.0 * abs( | |
| 97 | 220680 | Dumux::tripleProduct(c(3)-c(0), c(1)-c(0), c(2)-c(0)) | |
| 98 | 22080 | ); | |
| 99 | } | ||
| 100 |
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1729112 | else if (type == Dune::GeometryTypes::hexahedron) |
| 101 | { | ||
| 102 | // after Grandy 1997, Efficient computation of volume of hexahedron | ||
| 103 | 5077720 | const auto v = c(7)-c(0); | |
| 104 | using std::abs; | ||
| 105 | return 1.0/6.0 * ( | ||
| 106 | 13540688 | abs(Dumux::tripleProduct(v, c(1)-c(0), c(3)-c(5))) | |
| 107 | 13540688 | + abs(Dumux::tripleProduct(v, c(4)-c(0), c(5)-c(6))) | |
| 108 | 13540688 | + abs(Dumux::tripleProduct(v, c(2)-c(0), c(6)-c(3))) | |
| 109 | 1692624 | ); | |
| 110 | } | ||
| 111 |
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36488 | else if (type == Dune::GeometryTypes::pyramid) |
| 112 | { | ||
| 113 | // 1/3 * base * height | ||
| 114 | // for base see case Dune::GeometryTypes::quadrilateral above | ||
| 115 | // = 1/3 * (1/2 * norm(ADxBC)) * ((ADxBC)/norm(AD x BC) ⋅ AE) | ||
| 116 | // = 1/6 * (AD x BC) ⋅ AE | ||
| 117 | using std::abs; | ||
| 118 | 36484 | return 1.0/6.0 * abs( | |
| 119 | 364672 | Dumux::tripleProduct(c(3)-c(0), c(2)-c(1), c(4)-c(0)) | |
| 120 | 36484 | ); | |
| 121 | } | ||
| 122 |
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4 | else if (type == Dune::GeometryTypes::prism) |
| 123 | { | ||
| 124 | // compute as sum of a pyramid (0-1-3-4-5) and a tetrahedron (2-0-1-5) | ||
| 125 | using std::abs; | ||
| 126 | return 1.0/6.0 * ( | ||
| 127 | 20 | abs(Dumux::tripleProduct(c(3)-c(1), c(4)-c(0), c(5)-c(0))) | |
| 128 | 20 | + abs(Dumux::tripleProduct(c(5)-c(2), c(0)-c(2), c(1)-c(2))) | |
| 129 | 4 | ); | |
| 130 | } | ||
| 131 | else | ||
| 132 | return std::numeric_limits<ctype>::quiet_NaN(); | ||
| 133 | } | ||
| 134 | else | ||
| 135 | return std::numeric_limits<ctype>::quiet_NaN(); | ||
| 136 | } | ||
| 137 | |||
| 138 | /*! | ||
| 139 | * \ingroup Geometry | ||
| 140 | * \brief The volume of a given geometry | ||
| 141 | */ | ||
| 142 | template<class Geometry> | ||
| 143 | 292 | auto convexPolytopeVolume(const Geometry& geo) | |
| 144 | { | ||
| 145 | 292 | const auto v = convexPolytopeVolume<Geometry::mydimension>( | |
| 146 | 490 | geo.type(), [&](unsigned int i){ return geo.corner(i); } | |
| 147 | ); | ||
| 148 | |||
| 149 | // fall back to the method of the geometry if no specialized | ||
| 150 | // volume function is implemented for the geometry type | ||
| 151 |
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292 | return std::isnan(v) ? geo.volume() : v; |
| 152 | } | ||
| 153 | |||
| 154 | /*! | ||
| 155 | * \ingroup Geometry | ||
| 156 | * \brief The volume of a given geometry | ||
| 157 | */ | ||
| 158 | template<class Geometry> | ||
| 159 | 146 | auto volume(const Geometry& geo, unsigned int integrationOrder = 4) | |
| 160 | { | ||
| 161 | using ctype = typename Geometry::ctype; | ||
| 162 | 146 | ctype volume = 0.0; | |
| 163 | 292 | const auto rule = Dune::QuadratureRules<ctype, Geometry::mydimension>::rule(geo.type(), integrationOrder); | |
| 164 | 4938 | for (const auto& qp : rule) | |
| 165 | 4554 | volume += geo.integrationElement(qp.position())*qp.weight(); | |
| 166 | 292 | return volume; | |
| 167 | } | ||
| 168 | |||
| 169 | /*! | ||
| 170 | * \ingroup Geometry | ||
| 171 | * \brief The volume of a given geometry with an extrusion/transformation policy | ||
| 172 | * \note depending on the transformation this might not be an accurate quadrature rule anymore | ||
| 173 | */ | ||
| 174 | template<class Geometry, class Transformation> | ||
| 175 | 86517 | auto volume(const Geometry& geo, Transformation transformation, unsigned int integrationOrder = 4) | |
| 176 | { | ||
| 177 | using ctype = typename Geometry::ctype; | ||
| 178 | 86517 | ctype volume = 0.0; | |
| 179 |
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248268 | const auto rule = Dune::QuadratureRules<ctype, Geometry::mydimension>::rule(geo.type(), integrationOrder); |
| 180 |
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1816797 | for (const auto& qp : rule) |
| 181 |
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1557246 | volume += transformation.integrationElement(geo, qp.position())*qp.weight(); |
| 182 |
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173034 | return volume; |
| 183 | } | ||
| 184 | |||
| 185 | } // end namespace Dumux | ||
| 186 | |||
| 187 | #endif | ||
| 188 |