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Commit 7f8a2779 authored by Praetorius, Simon's avatar Praetorius, Simon
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corrected the exact derivative of sphere function and wrapped CurvedGeometry... 

corrected the exact derivative of sphere function and wrapped CurvedGeometry to support localtransformation of local coordinates
parent db972060
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dune/curvedsurfacegrid/entity.hh
View file @ 7f8a2779
......@@ -205,31 +205,49 @@ namespace Dune
using Super = EntityBase<codim, G>;
using Traits = typename std::remove_const_t<G>::Traits;
//! type of host elements, i.e., of host entities of codimension 0
using HostElement = typename Traits::HostGrid::template Codim<0>::Entity;
using GridFunction = typename Super::GridFunction;
public:
//! type of corresponding geometry
using Geometry = typename Traits::template Codim<codim>::Geometry;
using ctype = typename Geometry::ctype;
public:
using Super::Super;
// construct the entity from a subentity of a host-entity
EntityBaseGeometry (const GridFunction& gridFunction, const HostElement& hostElement, int i)
: Super(gridFunction, hostElement, i)
, hostElement_(hostElement)
, subEntity_(i)
{}
//! obtain the geometry of this entity
Geometry geometry () const
{
if (!geo_) {
auto localFct = localFunction(Super::gridFunction());
// localFct.bind(Super::hostEntity());
if (hostElement_) {
localFct.bind(*hostElement_);
// construct a fake local geometry for transformations.
// auto refElem = referenceElement<typename Geometry::ctype, Super::dimension>(GeometryTypes::simplex(Super::dimension));
geo_ = std::make_shared<GeometryImpl>(Super::type(), localFct);
auto refElem = referenceElement<ctype, Super::dimension>(hostElement_->type());
auto localGeometry = refElem.template geometry<codim>(subEntity_);
geo_ = std::make_shared<GeometryImpl>(Super::type(), localFct, localGeometry);
}
else {
DUNE_THROW(Dune::NotImplemented, "Geometry of entities of codim!=0 not implemented");
}
}
return Geometry(*geo_);
//return Super::hostEntity().geometry();
}
private:
Std::optional<HostElement> hostElement_;
int subEntity_ = -1;
using GeometryImpl = typename Traits::template Codim<codim>::GeometryImpl;
mutable std::shared_ptr<GeometryImpl> geo_;
};
......@@ -265,7 +283,8 @@ namespace Dune
if (!geo_) {
auto localFct = localFunction(Super::gridFunction());
localFct.bind(Super::hostEntity());
geo_ = std::make_shared<GeometryImpl>(Super::type(), localFct, Dune::CGeo::Impl::DefaultLocalGeometry{});
auto fakeDefaultGeometry = Dune::CGeo::Impl::DefaultLocalGeometry{};
geo_ = std::make_shared<GeometryImpl>(Super::type(), localFct, fakeDefaultGeometry);
}
return Geometry(*geo_);
......
dune/curvedsurfacegrid/geometry.hh
View file @ 7f8a2779
......@@ -16,6 +16,8 @@
#include <dune/common/std/optional.hh>
#include <dune/common/std/type_traits.hh>
#include <dune/curvedgeometry/curvedgeometry.hh>
#include <dune/geometry/affinegeometry.hh>
#include <dune/geometry/multilineargeometry.hh>
#include <dune/geometry/quadraturerules.hh>
......@@ -90,6 +92,7 @@ namespace Dune
}
// efficient implementation of a trivial local geometry for elements
struct DefaultLocalGeometry
{
template <class LocalCoordinate>
......@@ -104,23 +107,93 @@ namespace Dune
return {};
}
};
// type-erased wrapper for local geometries
template <class LG>
struct LocalGeometryInterface
{
using LocalCoordinate = typename LG::LocalCoordinate;
using GlobalCoordinate = typename LG::GlobalCoordinate;
using JacobianTransposed = typename LG::JacobianTransposed;
template <class LocalGeometry>
LocalGeometryInterface(const LocalGeometry& lg)
: global([lg](auto const& local) { return lg.global(local); })
, jacobianTransposed([lg](auto const& local) { return lg.jacobianTransposed(local); })
{}
template <class GlobalFct, class JacobianTransposedFct>
LocalGeometryInterface(GlobalFct&& g, JacobianTransposedFct&& jt)
: global(std::forward<GlobalFct>(g))
, jacobianTransposed(std::forward<JacobianTransposedFct>(jt))
{}
std::function<GlobalCoordinate(LocalCoordinate)> global;
std::function<JacobianTransposed(LocalCoordinate)> jacobianTransposed;
};
}
/// \brief Curved geometry implementation based on local basis function parametrization
/**
* Parametrization of the geometry by any localfunction given by a finite-element cache
* defined in the Traits class. See \ref LagrangeGeometry for an example instantiation
* of this class with local lagrange basis functions.
* Parametrization of the geometry by a differentiable localFunction
*
* \tparam ct coordinate type
* \tparam mydim geometry dimension
* \tparam cdim coordinate dimension
*
* The requirements on the traits are documented along with their default,
* GeometryTraits.
* \tparam LF localFunction parametrizing the geometry
* \tparam LG localGeometry for coordinate transform from subEntity to element,
* see \ref Impl::DefaultLocalGeometry and \ref Impl::LocalGeometryInterface
* \tparam order Polynomial order of lagrange parametrization. If order < 0 use localFunction.
*/
template <class ct, int mydim, int cdim, class LocalFunction, class LocalGeometry = Impl::DefaultLocalGeometry>
template <class ct, int mydim, int cdim, class LF, class LG, int order>
class Geometry
: public Dune::LagrangeCurvedGeometry<ct, mydim, cdim, (order > 0 ? order : 1)>
{
using Super = Dune::LagrangeCurvedGeometry<ct, mydim, cdim, (order > 0 ? order : 1)>;
//! type of the localFunction representation the geometry parametrization
using LocalFunction = LF;
//! type of coordinate transformation for subEntities to codim=0 entities
using LocalGeometry = LG;
/// type of reference element
using ReferenceElements = Dune::ReferenceElements<ct, mydim>;
using ReferenceElement = typename ReferenceElements::ReferenceElement;
public:
/// \brief constructor from localFunction to parametrize the geometry
/**
* \param[in] refElement reference element for the geometry
* \param[in] localFunction localFunction for the parametrization of the geometry
* (stored by value)
* \param[in] args... argument to construct the local geometry
*
*/
template <class... Args>
Geometry (const ReferenceElement& refElement, const LocalFunction& localFunction, Args&&... args)
: Super(refElement, [localFunction, localGeometry=LocalGeometry{std::forward<Args>(args)...}](auto const& local)
{
return localFunction(localGeometry.global(local));
})
{}
/// \brief constructor, forwarding to the other constructor that take a reference-element
/**
* \param[in] gt geometry type
* \param[in] localFunction localFunction for the parametrization of the geometry
* (stored by value)
* \param[in] args... argument to construct the local geometry
*/
template <class... Args>
Geometry (Dune::GeometryType gt, const LocalFunction& localFunction, Args&&... args)
: Geometry(ReferenceElements::general(gt), localFunction, std::forward<Args>(args)...)
{}
};
template <class ct, int mydim, int cdim, class LF, class LG>
class Geometry<ct,mydim,cdim,LF,LG,-1>
{
public:
/// coordinate type
......@@ -156,9 +229,14 @@ namespace Dune
//! helper structure containing some matrix routines. See affinegeometry.hh
using MatrixHelper = Dune::Impl::FieldMatrixHelper<ct>;
//! type of coordinate transformation for subEntities to codim=0 entities
using LocalGeometry = LG;
//! type of the localFunction representation the geometry parametrization
using LocalFunction = LF;
//! type of the LocalFunction representing the derivative
using DerivativeLocalFunction
= std::decay_t<decltype(derivative(std::declval<LocalFunction>()))>;
using DerivativeLocalFunction = std::decay_t<decltype(derivative(std::declval<LF>()))>;
//! tolerance to numerical algorithms
static ct tolerance () { return ct(16) * std::numeric_limits<ct>::epsilon(); }
......@@ -167,31 +245,31 @@ namespace Dune
static int maxIteration () { return 100; }
public:
/// \brief constructor from a vector of coefficients of the LocalBasis parametrizing
/// the geometry
/// \brief constructor from localFunction to parametrize the geometry
/**
* \param[in] refElement reference element for the geometry
* \param[in] vertices vertices to store internally
* \param[in] localFunction localFunction for the parametrization of the geometry
* (stored by value)
* \param[in] args... argument to construct the local geometry
*
* \note The vertices are stored internally, so if possible move an external vertex
* storedge to this constructor
*/
Geometry (const ReferenceElement& refElement, const LocalFunction& localFunction,
Std::optional<LocalGeometry> localGeometry = {})
template <class... Args>
Geometry (const ReferenceElement& refElement, const LocalFunction& localFunction, Args&&... args)
: refElement_(refElement)
, localFunction_(localFunction)
, localGeometry_(localGeometry)
, localGeometry_(std::forward<Args>(args)...)
{}
/// \brief constructor, forwarding to the other constructor that take a reference-element
/**
* \param[in] gt geometry type
* \param[in] localFunction Function that can be evaluated in local coordinates and
* can be differentiated
* \param[in] localFunction localFunction for the parametrization of the geometry
* (stored by value)
* \param[in] args... argument to construct the local geometry
*/
Geometry (Dune::GeometryType gt, const LocalFunction& localFunction,
Std::optional<LocalGeometry> localGeometry = {})
: Geometry(ReferenceElements::general(gt), localFunction, localGeometry)
template <class... Args>
Geometry (Dune::GeometryType gt, const LocalFunction& localFunction, Args&&... args)
: Geometry(ReferenceElements::general(gt), localFunction, std::forward<Args>(args)...)
{}
/// \brief is this mapping affine? No!
......@@ -200,7 +278,7 @@ namespace Dune
return false;
}
/// \brief obtain the name of the reference element
/// \brief obtain the element type from the reference element
Dune::GeometryType type () const
{
return refElement_.type();
......@@ -213,10 +291,6 @@ namespace Dune
}
/// \brief obtain coordinates of the i-th corner
/**
* \todo In some local-bases, the corners are part of the stored vertices, and sometimes
* even stored first before higher order vertices. Maybe this can be utilized somehow.
*/
GlobalCoordinate corner (int i) const
{
assert( (i >= 0) && (i < corners()) );
......@@ -247,6 +321,9 @@ namespace Dune
* \param[in] globalCoord global coordinate to map
*
* \return corresponding local coordinate
* \throws in case of an error indicating that the local coordinate can not be obtained,
* an exception is thrown. See \ref checkedLocal for a variant that returns
* an optional instead.
*
* \note For given global coordinate `y` the returned local coordinate `x` that minimizes
* the following function over the local coordinate space spanned by the reference element.
......@@ -258,11 +335,19 @@ namespace Dune
{
auto localCoord = checkedLocal(globalCoord);
if (!localCoord)
DUNE_THROW(Exception, "local coordinate can not be recovered from given global coordinate " << globalCoord);
DUNE_THROW(Dune::Exception,
"local coordinate can not be recovered from given global coordinate " << globalCoord);
return *localCoord;
}
/// \brief Evaluate the inverse coordinate mapping
/**
* \param[in] globalCoord global coordinate to map
*
* \return corresponding local coordinate or nothing, in case the local coordinate
* could not be calculated. The return value is wrapped in an optional.
**/
Std::optional<LocalCoordinate> checkedLocal (const GlobalCoordinate& globalCoord) const
{
LocalCoordinate x = flatGeometry().local(globalCoord);
......@@ -317,9 +402,6 @@ namespace Dune
* \param[in] local local coordinate to evaluate the integration element in
*
* \returns the integration element \f$\mu(x)\f$.
*
* \todo Implement caching of the jacobianTransposed matrix, since it is used for the
* integrationElement and the jacobianInverseTransposed
*/
ctype integrationElement (const LocalCoordinate& local) const
{
......@@ -356,11 +438,13 @@ namespace Dune
derivativeLocalFunction_->bind(localFunction().localContext());
}
// TODO: maybe multiply with localGeometry().jacobianTransposed()
auto j0 = localGeometry().jacobianTransposed(local);
auto jt = hostGeometry().jacobianTransposed(localGeometry().global(local));
auto jacobian = (*derivativeLocalFunction_)(localGeometry().global(local));
return Impl::AB(j0,Impl::ABt(jt,jacobian));
// coordinate in the localContext of the localFunction
auto&& elementLocal = localGeometry().global(local);
auto jLocal = localGeometry().jacobianTransposed(local);
auto jGlobal = hostGeometry().jacobianTransposed(elementLocal);
auto jacobian = (*derivativeLocalFunction_)(elementLocal);
return Impl::AB(jLocal,Impl::ABt(jGlobal,jacobian));
}
/// \brief obtain the transposed of the Jacobian's inverse
......@@ -410,7 +494,7 @@ namespace Dune
return res /= res.two_norm();
}
public:
private:
const LocalFunction& localFunction () const
{
return localFunction_;
......@@ -418,7 +502,7 @@ namespace Dune
const LocalGeometry& localGeometry () const
{
return localGeometry_.value();
return localGeometry_;
}
using FlatGeometry = MultiLinearGeometry<ctype, mydim, cdim>;
......@@ -436,7 +520,7 @@ namespace Dune
return *flatGeometry_;
}
using HostGeometry = std::decay_t<decltype(std::declval<LocalFunction>().localContext().geometry())>;
using HostGeometry = std::decay_t<decltype(std::declval<LF>().localContext().geometry())>;
const HostGeometry& hostGeometry () const
{
if (!hostGeometry_)
......@@ -453,7 +537,7 @@ namespace Dune
LocalFunction localFunction_;
//! transformation of local coordinates to element-local coordinates
Std::optional<LocalGeometry> localGeometry_;
LocalGeometry localGeometry_;
// some data optionally provided
mutable Std::optional<DerivativeLocalFunction> derivativeLocalFunction_;
......@@ -465,15 +549,20 @@ namespace Dune
#ifndef DOXYGEN
// Specialization for vertex geometries
template <class ct, int cdim, class Localfunction>
class Geometry<ct,0,cdim,Localfunction>
template <class ct, int cdim, class LF, class LG>
class VertexGeometry
: public AffineGeometry<ct,0,cdim>
{
using Super = AffineGeometry<ct,0,cdim>;
using LocalFunction = LF;
using LocalGeometry = LG;
//! tolerance to numerical algorithms
static ct tolerance () { return ct(16) * std::numeric_limits<ct>::epsilon(); }
struct Construct {};
public:
/// type of reference element
using ReferenceElements = Dune::ReferenceElements<ct, 0>;
......@@ -486,17 +575,21 @@ namespace Dune
using GlobalCoordinate = FieldVector<ct, cdim>;
protected:
Geometry (const ReferenceElement& refElement, std::vector<GlobalCoordinate> vertices)
: Super(refElement, std::move(vertices))
VertexGeometry (Construct, const ReferenceElement& refElement, const LocalFunction& localFunction,
const LocalGeometry& lg)
: Super(refElement, std::vector<GlobalCoordinate>{localFunction(lg.global(refElement.position(0,0)))})
{}
public:
Geometry (const ReferenceElement& refElement, const Localfunction& localFunction)
: Geometry(refElement, std::vector<GlobalCoordinate>{localFunction(refElement.position(0,0))})
template <class... Args>
VertexGeometry (const ReferenceElement& refElement, const LocalFunction& lf, Args&&... args)
: VertexGeometry(Construct{}, refElement, lf, LocalGeometry(std::forward<Args>(args)...))
{}
Geometry (Dune::GeometryType gt, const Localfunction& localFunction)
: Geometry(ReferenceElements::general(gt), localFunction)
template <class... Args>
VertexGeometry (Dune::GeometryType gt, const LocalFunction& lf, Args&&... args)
: VertexGeometry(Construct{}, ReferenceElements::general(gt), lf,
LocalGeometry(std::forward<Args>(args)...))
{}
Std::optional<LocalCoordinate> checkedLocal (const GlobalCoordinate& globalCoord) const
......@@ -515,8 +608,28 @@ namespace Dune
return GlobalCoordinate(0);
}
private:
VertexGeometry const& flatGeometry () const { return *this; }
};
// Specialization for vertex geometries
template <class ct, int cdim, class LF, class LG, int order>
class Geometry<ct,0,cdim,LF,LG,order>
: public VertexGeometry<ct,cdim,LF,LG>
{
using Super = VertexGeometry<ct,cdim,LF,LG>;
public:
using Super::Super;
};
template <class ct, int cdim, class LF, class LG>
class Geometry<ct,0,cdim,LF,LG,-1>
: public VertexGeometry<ct,cdim,LF,LG>
{
using Super = VertexGeometry<ct,cdim,LF,LG>;
public:
Geometry const& flatGeometry () const { return *this; }
using Super::Super;
};
#endif // DOXYGEN
......
dune/curvedsurfacegrid/gridfamily.hh
View file @ 7f8a2779
......@@ -4,7 +4,6 @@
#define DUNE_CURVED_SURFACE_GRID_GRIDFAMILY_HH
#include <dune/grid/common/grid.hh>
#include <dune/curvedgeometry/curvedgeometry.hh>
#include <dune/curvedsurfacegrid/capabilities.hh>
#include <dune/curvedsurfacegrid/entity.hh>
#include <dune/curvedsurfacegrid/entityseed.hh>
......@@ -90,26 +89,17 @@ namespace Dune
{
using LocalGeometry = typename HostGrid::template Codim<codim>::LocalGeometry;
using LocalTransformation = std::conditional_t<(codim == 0),
CGeo::Impl::DefaultLocalGeometry,
CGeo::Impl::LocalGeometryInterface<LocalGeometry>>;
template < int mydim, int cdim, class GridImpl >
using GeometryImplTemplate = std::conditional_t<(differentiableLocalFunction || (order > 0)),
CGeo::Geometry<ctype, mydim, cdim, LocalFunction,
std::conditional_t<(codim == 0), CGeo::Impl::DefaultLocalGeometry, LocalGeometry>>,
Dune::LagrangeCurvedGeometry<ctype, mydim, cdim, (order > 0 ? order : 1)>>;
using GeometryImplTemplate
= CGeo::Geometry<ctype, mydim, cdim, LocalFunction, LocalTransformation, order>;
// geometry types
using GeometryImpl = GeometryImplTemplate<dimension-codim, dimensionworld, const Grid>;
using Geometry = //std::conditional_t<(codim == 0),
Dune::Geometry<dimension-codim, dimensionworld, const Grid, GeometryImplTemplate>/*,
typename HostGrid::Traits::template Codim<codim>::Geometry>*/;
// template < int mydim, int cdim, class GridImpl >
// using IntersectionGeometryImplTemplate = std::conditional_t<(differentiableLocalFunction || (order > 0)),
// CGeo::Geometry<ctype, mydim, cdim, LocalFunction,
// std::conditional_t<(codim == 0), CGeo::Impl::DefaultLocalGeometry, LocalGeometry>>,
// Dune::LagrangeCurvedGeometry<ctype, mydim, cdim, (order > 0 ? order : 1)>>;
// using IntersectionGeometryImpl = IntersectionGeometryImplTemplate<dimension-codim, dimensionworld, const Grid>;
// using IntersectionGeometry = Dune::Geometry<dimension-codim, dimensionworld, const Grid,
// IntersectionGeometryImplTemplate>;
using Geometry = Dune::Geometry<dimension-codim, dimensionworld, const Grid, GeometryImplTemplate>;
// entity types
using EntityImpl = CGeo::Entity<codim, dimension, const Grid>;
......
dune/curvedsurfacegrid/intersection.hh
View file @ 7f8a2779
......@@ -103,7 +103,6 @@ namespace Dune
geo_.emplace(type(), localFct, hostIntersection().geometryInInside());
}
return Geometry(*geo_);
// return hostIntersection().geometry();
}
GeometryType type () const { return hostIntersection().type(); }
......
dune/curvedsurfacegrid/test/convergence.cc
View file @ 7f8a2779
......@@ -196,11 +196,11 @@ int main(int argc, char** argv)
return x / x.two_norm();
},
[](auto const& x) {
double nrmInv = 1.0/x.two_norm();
double nrm = x.two_norm();
FieldMatrix<double,3,3> out;
for (int i = 0; i < 3; ++i)
for (int j = 0; j < 3; ++j)
out[i][j] = nrmInv * (i == j ? 1 : 0) + x[i] * x[j];
out[i][j] = ((i == j ? 1 : 0) - (x[i]/nrm) * (x[j]/nrm)) / nrm;
return out;
}
);
......
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