From 85d33d4c7e750ebbb3891282819d9ba222d64dda Mon Sep 17 00:00:00 2001
From: Oliver Sander <sander@igpm.rwth-aachen.de>
Date: Mon, 24 Mar 2014 15:48:08 +0000
Subject: [PATCH] New interpolation function that interpolates in a Euclidean
space and projects onto the manifold
[[Imported from SVN: r9682]]
---
dune/gfe/Makefile.am | 1 +
dune/gfe/localprojectedfefunction.hh | 128 +++++++++++++++++++++++++++
2 files changed, 129 insertions(+)
create mode 100644 dune/gfe/localprojectedfefunction.hh
diff --git a/dune/gfe/Makefile.am b/dune/gfe/Makefile.am
index ad63f329..97b5f27c 100644
--- a/dune/gfe/Makefile.am
+++ b/dune/gfe/Makefile.am
@@ -21,6 +21,7 @@ srcinclude_HEADERS = adolcnamespaceinjections.hh \
localgeodesicfefunction.hh \
localgeodesicfestiffness.hh \
localgfetestfunctionbasis.hh \
+ localprojectedfefunction.hh \
maxnormtrustregion.hh \
orthogonalmatrix.hh \
pktop1mgtransfer.hh \
diff --git a/dune/gfe/localprojectedfefunction.hh b/dune/gfe/localprojectedfefunction.hh
new file mode 100644
index 00000000..5971b33d
--- /dev/null
+++ b/dune/gfe/localprojectedfefunction.hh
@@ -0,0 +1,128 @@
+#ifndef DUNE_GFE_LOCALPROJECTEDFEFUNCTION_HH
+#define DUNE_GFE_LOCALPROJECTEDFEFUNCTION_HH
+
+#include <vector>
+
+#include <dune/common/fvector.hh>
+
+#include <dune/geometry/type.hh>
+
+namespace Dune {
+
+ namespace GFE {
+
+ /** \brief Interpolate in an embedding Euclidean space, and project back onto the Riemannian manifold
+ *
+ * \tparam dim Dimension of the reference element
+ * \tparam ctype Type used for coordinates on the reference element
+ * \tparam LocalFiniteElement A Lagrangian finite element whose shape functions define the interpolation weights
+ * \tparam TargetSpace The manifold that the function takes its values in
+ */
+ template <int dim, class ctype, class LocalFiniteElement, class TargetSpace>
+ class LocalProjectedFEFunction
+ {
+ typedef typename TargetSpace::ctype RT;
+
+ typedef typename TargetSpace::EmbeddedTangentVector EmbeddedTangentVector;
+ static const int embeddedDim = EmbeddedTangentVector::dimension;
+
+ static const int spaceDim = TargetSpace::TangentVector::dimension;
+
+ public:
+
+ /** \brief The type used for derivatives */
+ typedef Dune::FieldMatrix<RT, embeddedDim, dim> DerivativeType;
+
+ /** \brief Constructor
+ * \param localFiniteElement A Lagrangian finite element that provides the interpolation points
+ * \param coefficients Values of the function at the Lagrange points
+ */
+ LocalProjectedFEFunction(const LocalFiniteElement& localFiniteElement,
+ const std::vector<TargetSpace>& coefficients)
+ : localFiniteElement_(localFiniteElement),
+ coefficients_(coefficients)
+ {
+ assert(localFiniteElement_.localBasis().size() == coefficients_.size());
+ }
+
+ /** \brief The number of Lagrange points */
+ unsigned int size() const
+ {
+ return localFiniteElement_.localBasis().size();
+ }
+
+ /** \brief The type of the reference element */
+ Dune::GeometryType type() const
+ {
+ return localFiniteElement_.type();
+ }
+
+ /** \brief Evaluate the function */
+ TargetSpace evaluate(const Dune::FieldVector<ctype, dim>& local) const;
+
+ /** \brief Evaluate the derivative of the function */
+ DerivativeType evaluateDerivative(const Dune::FieldVector<ctype, dim>& local) const;
+
+ /** \brief Evaluate the derivative of the function, if you happen to know the function value (much faster!)
+ * \param local Local coordinates in the reference element where to evaluate the derivative
+ * \param q Value of the local gfe function at 'local'. If you provide something wrong here the result will be wrong, too!
+ */
+ DerivativeType evaluateDerivative(const Dune::FieldVector<ctype, dim>& local,
+ const TargetSpace& q) const;
+
+ /** \brief Get the i'th base coefficient. */
+ TargetSpace coefficient(int i) const
+ {
+ return coefficients_[i];
+ }
+ private:
+
+ /** \brief The scalar local finite element, which provides the weighting factors
+ * \todo We really only need the local basis
+ */
+ const LocalFiniteElement& localFiniteElement_;
+
+ /** \brief The coefficient vector */
+ std::vector<TargetSpace> coefficients_;
+
+ };
+
+ template <int dim, class ctype, class LocalFiniteElement, class TargetSpace>
+ TargetSpace LocalProjectedFEFunction<dim,ctype,LocalFiniteElement,TargetSpace>::
+ evaluate(const Dune::FieldVector<ctype, dim>& local) const
+ {
+ // Evaluate the weighting factors---these are the Lagrangian shape function values at 'local'
+ std::vector<Dune::FieldVector<ctype,1> > w;
+ localFiniteElement_.localBasis().evaluateFunction(local,w);
+
+ typename TargetSpace::CoordinateType c(0);
+ for (size_t i=0; i<coefficients_.size(); i++)
+ c.axpy(w[i][0], coefficients_[i].globalCoordinates());
+
+ return TargetSpace(c);
+ }
+
+ template <int dim, class ctype, class LocalFiniteElement, class TargetSpace>
+ typename LocalProjectedFEFunction<dim,ctype,LocalFiniteElement,TargetSpace>::DerivativeType
+ LocalProjectedFEFunction<dim,ctype,LocalFiniteElement,TargetSpace>::
+ evaluateDerivative(const Dune::FieldVector<ctype, dim>& local) const
+ {
+ // the function value at the point where we are evaluating the derivative
+ TargetSpace q = evaluate(local);
+
+ // Actually compute the derivative
+ return evaluateDerivative(local,q);
+ }
+
+ template <int dim, class ctype, class LocalFiniteElement, class TargetSpace>
+ typename LocalProjectedFEFunction<dim,ctype,LocalFiniteElement,TargetSpace>::DerivativeType
+ LocalProjectedFEFunction<dim,ctype,LocalFiniteElement,TargetSpace>::
+ evaluateDerivative(const Dune::FieldVector<ctype, dim>& local, const TargetSpace& q) const
+ {
+ DUNE_THROW(NotImplemented, "Not implemented yet!");
+ }
+
+ }
+
+}
+#endif
--
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