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5#ifndef DUNE_GEOMETRY_LOCALFINITEELEMENTGEOMETRY_HH \n-
6#define DUNE_GEOMETRY_LOCALFINITEELEMENTGEOMETRY_HH \n-
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14#include <dune/common/fmatrix.hh> \n+
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6#ifndef DUNE_GEOMETRY_AXISALIGNED_CUBE_GEOMETRY_HH \n+
7#define DUNE_GEOMETRY_AXISALIGNED_CUBE_GEOMETRY_HH \n+
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15#include <dune/common/fvector.hh> \n-
16#include <dune/common/math.hh> \n-
17#include <dune/common/typetraits.hh> \n-
18#include <dune/common/std/type_traits.hh> \n-
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38template <
class LFE,
int cdim>
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41 using LocalFiniteElement = LFE;
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42 using LocalBasis =
typename LFE::Traits::LocalBasisType;
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43 using LocalBasisTraits =
typename LocalBasis::Traits;
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47 using ctype =
typename LocalBasisTraits::DomainFieldType;
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16#include <dune/common/fmatrix.hh> \n+
17#include <dune/common/diagonalmatrix.hh> \n+
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48 template <
class CoordType,
unsigned int dim,
unsigned int coorddim>
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65 using Jacobian = FieldMatrix<ctype, coorddimension, mydimension>;
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104 const LocalFiniteElement& localFE,
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105 std::vector<GlobalCoordinate> vertices)
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106 : refElement_(refElement)
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108 , vertices_(
std::move(vertices))
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110 assert(localFE_.size() == vertices_.size());
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126 template <
class Param,
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127 std::enable_if_t<std::is_invocable_r_v<GlobalCoordinate,Param,LocalCoordinate>,
int> = 0>
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129 const LocalFiniteElement& localFE,
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130 Param&& parametrization)
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131 : refElement_(refElement)
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134 localFE_.localInterpolation().interpolate(parametrization, vertices_);
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143 template <
class... Args>
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79 typedef typename std::conditional<dim==coorddim,
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80 DiagonalMatrix<ctype,dim>,
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89 typedef typename std::conditional<dim==coorddim,
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90 DiagonalMatrix<ctype,dim>,
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100 using Jacobian = std::conditional_t<dim==coorddim, DiagonalMatrix<ctype,dim>, FieldMatrix<ctype,coorddim,dim> >;
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109 using JacobianInverse = std::conditional_t<dim==coorddim, DiagonalMatrix<ctype,dim>, FieldMatrix<ctype,dim,coorddim> >;
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125 const Dune::FieldVector<ctype,coorddim> upper)
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130 static_assert(dim==coorddim,
"Use this constructor only if dim==coorddim!");
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132 axes_ = (1<<coorddim)-1;
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143 const Dune::FieldVector<ctype,coorddim> upper,
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144 const std::bitset<coorddim>& axes)
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149 assert(axes.count()==dim);
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150 for (
size_t i=0; i<coorddim; i++)
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152 upper_[i] = lower_[i];
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162 affine_.emplace(affineImpl());
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169 return refElement_.type();
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181 assert( (i >= 0) && (i <
corners()) );
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188 return global(refElement_.position(0, 0));
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204 thread_local std::vector<typename LocalBasisTraits::RangeType> shapeValues;
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206 assert(shapeValues.size() == vertices_.size());
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209 for (std::size_t i = 0; i < shapeValues.size(); ++i)
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210 out.axpy(shapeValues[i], vertices_[i]);
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235 Impl::GaussNewtonErrorCode err = Impl::gaussNewton(
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241 if (err != Impl::GaussNewtonErrorCode::OK)
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242 DUNE_THROW(Dune::Exception,
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243 "Local coordinate can not be recovered from global coordinate, error code = " <<
int(err) <<
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244 <<
" (global(x) - y).two_norm() = " << (
global(x) - y).two_norm()
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245 <<
" > tol = " << opts.absTol);
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283 for (
int p = 2; p < opts.maxIt; ++p) {
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285 if (abs(vol1 - vol0) < opts.absTol)
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297 for (
const auto& qp : quadRule)
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309 thread_local std::vector<typename LocalBasisTraits::JacobianType> shapeJacobians;
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311 assert(shapeJacobians.size() == vertices_.size());
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314 for (std::size_t i = 0; i < shapeJacobians.size(); ++i) {
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315 for (
int j = 0; j < Jacobian::rows; ++j) {
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316 shapeJacobians[i].umtv(vertices_[i][j], out[j]);
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361 return geometry.refElement_;
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166 return GeometryTypes::cube(dim);
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173 if (dim == coorddim) {
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174 for (
size_t i=0; i<coorddim; i++)
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175 result[i] = lower_[i] +
local[i]*(upper_[i] - lower_[i]);
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176 }
else if (dim == 0) {
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180 for (
size_t i=0; i<coorddim; i++)
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181 result[i] = (axes_[i])
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182 ? lower_[i] +
local[lc++]*(upper_[i] - lower_[i])
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192 if (dim == coorddim) {
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193 for (
size_t i=0; i<dim; i++)
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194 result[i] = (
global[i] - lower_[i]) / (upper_[i] - lower_[i]);
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195 }
else if (dim != 0) {
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197 for (
size_t i=0; i<coorddim; i++)
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199 result[lc++] = (
global[i] - lower_[i]) / (upper_[i] - lower_[i]);
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256 for (
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257 result[i] = CoordType(0.5) * (lower_[i] + upper_[i]);
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272 if (dim == coorddim) {
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273 for (
size_t i=0; i<coorddim; i++)
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274 result[i] = (k & (1<<i)) ? upper_[i] : lower_[i];
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275 }
else if (dim == 0) {
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278 unsigned int mask = 1;
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280 for (
size_t i=0; i<coorddim; i++) {
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282 result[i] = lower_[i];
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284 result[i] = (k & mask) ? upper_[i] : lower_[i];
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298 if (dim == coorddim) {
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299 for (
size_t i=0; i<dim; i++)
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300 vol *= upper_[i] - lower_[i];
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302 }
else if (dim != 0) {
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303 for (
size_t i=0; i<coorddim; i++)
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305 vol *= upper_[i] - lower_[i];
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325 for (
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336 for (
size_t i=0; i<coorddim; i++)
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344 for (
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355 for (
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360 Dune::FieldVector<ctype,coorddim> lower_;
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362 Dune::FieldVector<ctype,coorddim> upper_;
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379 return localFE_.localBasis();
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384 bool affineImpl ()
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405 auto refSimplex = referenceElement<ctype,mydimension>(GeometryTypes::simplex(
mydimension));
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406 auto simplexIndices = Dune::range(refSimplex.size(
mydimension));
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407 auto simplexCorners = Dune::transformedRangeView(simplexIndices,
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409 AffineGeometry<ctype,mydimension,coorddimension> affineGeo(refSimplex,simplexCorners);
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411 const ctype tol = sqrt(std::numeric_limits<ctype>::epsilon());
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412 for (
int i = 0; i <
corners(); ++i) {
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427 LocalFiniteElement localFE_{};
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430 std::vector<GlobalCoordinate> vertices_{};
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432 mutable std::optional<bool> affine_ = std::nullopt;
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439using LocalCoordinate_t
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440 = FieldVector<
typename LFE::Traits::LocalBasisType::Traits::DomainFieldType,
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441 LFE::Traits::LocalBasisType::Traits::dimDomain>;
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447template <
class I,
class LFE,
class GlobalCoordinate>
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451template <
class I,
class LFE,
class F,
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452 class Range = std::invoke_result_t<F,Impl::LocalCoordinate_t<LFE>>>
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456template <
class LFE,
class GlobalCoordinate>
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460template <
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461 class Range = std::invoke_result_t<F,Impl::LocalCoordinate_t<LFE>>>
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An implementation of the Geometry interface for affine geometries.
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A unique label for each type of element that can occur in a grid.
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364 std::bitset<coorddim> axes_;
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A unique label for each type of element that can occur in a grid.
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Definition affinegeometry.hh:21
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This class provides access to geometric and topological properties of a reference element.
Definition referenceelement.hh:52
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Class providing access to the singletons of the reference elements.
Definition referenceelements.hh:128
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typename Container::ReferenceElement ReferenceElement
The reference element type.
Definition referenceelements.hh:146
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Geometry implementation based on local-basis function parametrization.
Definition localfiniteelementgeometry.hh:40
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GeometryType type() const
Obtain the name of the reference element.
Definition localfiniteelementgeometry.hh:167
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decltype(power(std::declval< ctype >(), mydimension)) Volume
type of volume
Definition localfiniteelementgeometry.hh:62
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LocalCoordinate local(const GlobalCoordinate &y, Impl::GaussNewtonOptions< ctype > opts={}) const
Evaluate the inverse coordinate mapping.
Definition localfiniteelementgeometry.hh:232
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LocalFiniteElementGeometry(const ReferenceElement &refElement, const LocalFiniteElement &localFE, std::vector< GlobalCoordinate > vertices)
Constructor from a vector of coefficients of the LocalBasis parametrizing the geometry.
Definition localfiniteelementgeometry.hh:103
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JacobianTransposed jacobianTransposed(const LocalCoordinate &local) const
Obtain the transposed of the Jacobian.
Definition localfiniteelementgeometry.hh:327
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const LocalBasis & localBasis() const
The local basis of the stored local finite-element.
Definition localfiniteelementgeometry.hh:377
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typename LocalBasisTraits::DomainFieldType ctype
coordinate type
Definition localfiniteelementgeometry.hh:47
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JacobianInverseTransposed jacobianInverseTransposed(const LocalCoordinate &local) const
Obtain the transposed of the Jacobian's inverse.
Definition localfiniteelementgeometry.hh:353
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friend ReferenceElement referenceElement(const LocalFiniteElementGeometry &geometry)
Obtain the reference-element related to this geometry.
Definition localfiniteelementgeometry.hh:359
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LocalFiniteElementGeometry()=default
Default constructed geometry results in an empty/invalid representation.
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bool affine() const
Is this mapping affine? Geometries of order 1 might be affine, but it needs to be checked on non-simp...
Definition localfiniteelementgeometry.hh:159
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Jacobian jacobian(const LocalCoordinate &local) const
Obtain the Jacobian.
Definition localfiniteelementgeometry.hh:307
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Volume volume(const QuadratureRule< ctype, mydimension > &quadRule) const
Obtain the volume of the mapping's image by given quadrature rules.
Definition localfiniteelementgeometry.hh:294
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const std::vector< GlobalCoordinate > & coefficients() const
Obtain the coefficients of the parametrization.
Definition localfiniteelementgeometry.hh:371
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LocalFiniteElementGeometry(GeometryType gt, Args &&... args)
Constructor, forwarding to the other constructors that take a reference-element.
Definition localfiniteelementgeometry.hh:144
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static const int coorddimension
coordinate dimension
Definition localfiniteelementgeometry.hh:53
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int corners() const
Obtain number of corners of the corresponding reference element.
Definition localfiniteelementgeometry.hh:173
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GlobalCoordinate center() const
Obtain the centroid of the mapping's image.
Definition localfiniteelementgeometry.hh:186
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const LocalFiniteElement & finiteElement() const
Obtain the local finite-element.
Definition localfiniteelementgeometry.hh:365
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GlobalCoordinate global(const LocalCoordinate &local) const
Evaluate the coordinate mapping.
Definition localfiniteelementgeometry.hh:202
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Impl::FieldMatrixHelper< ctype > MatrixHelper
Definition localfiniteelementgeometry.hh:82
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typename ReferenceElements::ReferenceElement ReferenceElement
Definition localfiniteelementgeometry.hh:79
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GlobalCoordinate corner(int i) const
Obtain coordinates of the i-th corner.
Definition localfiniteelementgeometry.hh:179
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Volume volume(Impl::ConvergenceOptions< ctype > opts={}) const
Obtain the volume of the mapping's image.
Definition localfiniteelementgeometry.hh:276
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static const int mydimension
geometry dimension
Definition localfiniteelementgeometry.hh:50
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JacobianInverse jacobianInverse(const LocalCoordinate &local) const
Obtain the Jacobian's inverse.
Definition localfiniteelementgeometry.hh:339
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FieldVector< ctype, coorddimension > GlobalCoordinate
type of global coordinates
Definition localfiniteelementgeometry.hh:59
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FieldMatrix< ctype, coorddimension, mydimension > Jacobian
type of jacobian
Definition localfiniteelementgeometry.hh:65
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FieldMatrix< ctype, coorddimension, mydimension > JacobianInverseTransposed
type of jacobian inverse transposed
Definition localfiniteelementgeometry.hh:74
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FieldMatrix< ctype, mydimension, coorddimension > JacobianInverse
type of jacobian inverse
Definition localfiniteelementgeometry.hh:71
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ctype integrationElement(const LocalCoordinate &local) const
Obtain the integration element.
Definition localfiniteelementgeometry.hh:260
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int order() const
Obtain the (highest) polynomial order of the parametrization.
Definition localfiniteelementgeometry.hh:149
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FieldVector< ctype, mydimension > LocalCoordinate
type of local coordinates
Definition localfiniteelementgeometry.hh:56
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FieldMatrix< ctype, mydimension, coorddimension > JacobianTransposed
type of jacobian transposed
Definition localfiniteelementgeometry.hh:68
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LocalFiniteElementGeometry(const ReferenceElement &refElement, const LocalFiniteElement &localFE, Param &¶metrization)
Constructor from a local parametrization function, mapping local to (curved) global coordinates.
Definition localfiniteelementgeometry.hh:128
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Abstract base class for quadrature rules.
Definition quadraturerules.hh:214
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A container for all quadrature rules of dimension dim
Definition quadraturerules.hh:260
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static const ReferenceElement & cube()
get hypercube reference elements
Definition referenceelements.hh:168
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A geometry implementation for axis-aligned hypercubes.
Definition axisalignedcubegeometry.hh:50
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Volume volume() const
Return the element volume.
Definition axisalignedcubegeometry.hh:295
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AxisAlignedCubeGeometry(const Dune::FieldVector< ctype, coorddim > lower, const Dune::FieldVector< ctype, coorddim > upper, const std::bitset< coorddim > &axes)
Constructor from a lower left and an upper right corner.
Definition axisalignedcubegeometry.hh:142
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AxisAlignedCubeGeometry(const Dune::FieldVector< ctype, coorddim > lower, const Dune::FieldVector< ctype, coorddim > upper)
Constructor from a lower left and an upper right corner.
Definition axisalignedcubegeometry.hh:124
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JacobianInverse jacobianInverse(const LocalCoordinate &local) const
Inverse Jacobian of the transformation from local to global coordinates.
Definition axisalignedcubegeometry.hh:235
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JacobianInverseTransposed jacobianInverseTransposed(const LocalCoordinate &local) const
Inverse Jacobian transposed of the transformation from local to global coordinates.
Definition axisalignedcubegeometry.hh:217
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std::conditional< dim==coorddim, DiagonalMatrix< ctype, dim >, FieldMatrix< ctype, dim, coorddim > >::type JacobianTransposed
Return type of jacobianTransposed.
Definition axisalignedcubegeometry.hh:81
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AxisAlignedCubeGeometry(const Dune::FieldVector< ctype, coorddim > lower)
Constructor from a single point only.
Definition axisalignedcubegeometry.hh:159
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static constexpr int mydimension
Dimension of the cube element.
Definition axisalignedcubegeometry.hh:56
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friend Dune::ReferenceElements< ctype, dim >::ReferenceElement referenceElement(const AxisAlignedCubeGeometry &)
Definition axisalignedcubegeometry.hh:316
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static constexpr int coorddimension
Dimension of the world space that the cube element is embedded in.
Definition axisalignedcubegeometry.hh:59
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GlobalCoordinate corner(int k) const
Return world coordinates of the k-th corner of the element.
Definition axisalignedcubegeometry.hh:269
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ctype Volume
Type used for volume.
Definition axisalignedcubegeometry.hh:71
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FieldVector< ctype, dim > LocalCoordinate
Type used for a vector of element coordinates.
Definition axisalignedcubegeometry.hh:65
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JacobianTransposed jacobianTransposed(const LocalCoordinate &local) const
Jacobian transposed of the transformation from local to global coordinates.
Definition axisalignedcubegeometry.hh:205
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FieldVector< ctype, coorddim > GlobalCoordinate
Type used for a vector of world coordinates.
Definition axisalignedcubegeometry.hh:68
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LocalCoordinate local(const GlobalCoordinate &global) const
Map a point in global (world) coordinates to element coordinates.
Definition axisalignedcubegeometry.hh:189
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CoordType ctype
Type used for single coordinate coefficients.
Definition axisalignedcubegeometry.hh:62
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std::conditional_t< dim==coorddim, DiagonalMatrix< ctype, dim >, FieldMatrix< ctype, coorddim, dim > > Jacobian
Return type of jacobian.
Definition axisalignedcubegeometry.hh:100
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GeometryType type() const
Type of the cube. Here: a hypercube of the correct dimension.
Definition axisalignedcubegeometry.hh:164
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int corners() const
Return the number of corners of the element.
Definition axisalignedcubegeometry.hh:263
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Jacobian jacobian(const LocalCoordinate &local) const
Jacobian of the transformation from local to global coordinates.
Definition axisalignedcubegeometry.hh:229
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std::conditional< dim==coorddim, DiagonalMatrix< ctype, dim >, FieldMatrix< ctype, coorddim, dim > >::type JacobianInverseTransposed
Return type of jacobianInverseTransposed.
Definition axisalignedcubegeometry.hh:91
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Volume integrationElement(const LocalCoordinate &local) const
Return the integration element, i.e., the determinant term in the integral transformation formula.
Definition axisalignedcubegeometry.hh:243
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GlobalCoordinate center() const
Return center of mass of the element.
Definition axisalignedcubegeometry.hh:249
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AxisAlignedCubeGeometry()=default
Constructs an empty geometry.
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bool affine() const
Return if the element is affine. Here: yes.
Definition axisalignedcubegeometry.hh:311
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std::conditional_t< dim==coorddim, DiagonalMatrix< ctype, dim >, FieldMatrix< ctype, dim, coorddim > > JacobianInverse
Return type of jacobianInverse.
Definition axisalignedcubegeometry.hh:109
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GlobalCoordinate global(const LocalCoordinate &local) const
Map a point in local (element) coordinates to world coordinates.
Definition axisalignedcubegeometry.hh:170
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Unique label for each type of entities that can occur in DUNE grids.
Definition type.hh:114
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constexpr bool isSimplex() const
Return true if entity is a simplex of any dimension.
Definition type.hh:319
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