From f28dd6919966601d4c308686c78e089ab08d4d00 Mon Sep 17 00:00:00 2001
From: Oliver Sander <sander@igpm.rwth-aachen.de>
Date: Thu, 13 Oct 2011 16:37:27 +0000
Subject: [PATCH] prototype implementation of geodesic fe test functions. Not
seriously tested yet
[[Imported from SVN: r7899]]
---
dune/gfe/Makefile.am | 1 +
dune/gfe/localgfetestfunction.hh | 104 +++++++++++++++++++++++++++++++
2 files changed, 105 insertions(+)
create mode 100644 dune/gfe/localgfetestfunction.hh
diff --git a/dune/gfe/Makefile.am b/dune/gfe/Makefile.am
index 9b9e8d03..af9a2dd9 100644
--- a/dune/gfe/Makefile.am
+++ b/dune/gfe/Makefile.am
@@ -14,6 +14,7 @@ srcinclude_HEADERS = averagedistanceassembler.hh \
linearalgebra.hh \
localgeodesicfefunction.hh \
localgeodesicfestiffness.hh \
+ localgfetestfunction.hh \
maxnormtrustregion.hh \
quaternion.hh \
realtuple.hh \
diff --git a/dune/gfe/localgfetestfunction.hh b/dune/gfe/localgfetestfunction.hh
new file mode 100644
index 00000000..6d40cd67
--- /dev/null
+++ b/dune/gfe/localgfetestfunction.hh
@@ -0,0 +1,104 @@
+#ifndef LOCAL_GFE_TEST_FUNCTION_HH
+#define LOCAL_GFE_TEST_FUNCTION_HH
+
+#include <vector>
+
+#include <dune/common/fvector.hh>
+
+#include <dune/gfe/localgeodesicfefunction.hh>
+#include <dune/gfe/tensor3.hh>
+#include <dune/gfe/linearalgebra.hh>
+
+/** \brief A function defined by simplicial geodesic interpolation
+ from the reference element to a 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 LocalGFETestFunction
+{
+
+ typedef typename TargetSpace::EmbeddedTangentVector EmbeddedTangentVector;
+ static const int embeddedDim = EmbeddedTangentVector::dimension;
+
+ static const int spaceDim = TargetSpace::TangentVector::dimension;
+
+public:
+
+ /** \brief Constructor
+ */
+ LocalGFETestFunction(const LocalFiniteElement& localFiniteElement,
+ const std::vector<TargetSpace>& baseCoefficients,
+ const std::vector<typename TargetSpace::TangentVector>& tangentCoefficients)
+ : localGFEFunction_(localFiniteElement, baseCoefficients),
+ tangentCoefficients_(tangentCoefficients)
+ {}
+
+ /** \brief Evaluate the function */
+ typename TargetSpace::EmbeddedTangentVector evaluate(const Dune::FieldVector<ctype, dim>& local) const;
+
+ /** \brief Evaluate the derivative of the function */
+ Dune::FieldMatrix<ctype, EmbeddedTangentVector::dimension, dim> evaluateDerivative(const Dune::FieldVector<ctype, dim>& local) const;
+
+private:
+
+ /** \brief The scalar local finite element, which provides the weighting factors
+ */
+ const LocalGeodesicFEFunction<dim,ctype,LocalFiniteElement,TargetSpace> localGFEFunction_;
+
+ std::vector<typename TargetSpace::TangentVector> tangentCoefficients_;
+
+};
+
+template <int dim, class ctype, class LocalFiniteElement, class TargetSpace>
+typename TargetSpace::EmbeddedTangentVector LocalGFETestFunction<dim,ctype,LocalFiniteElement,TargetSpace>::
+evaluate(const Dune::FieldVector<ctype, dim>& local) const
+{
+ typename TargetSpace::EmbeddedTangentVector result(0);
+
+ for (size_t i=0; i<tangentCoefficients_.size(); i++) {
+
+ Dune::FieldMatrix< double, embeddedDim, embeddedDim > derivative;
+
+ localGFEFunction_.evaluateDerivativeOfValueWRTCoefficient (local,
+ i,
+ derivative);
+
+ derivative.umv(tangentCoefficients_, result);
+
+ }
+
+ return result;
+}
+
+template <int dim, class ctype, class LocalFiniteElement, class TargetSpace>
+Dune::FieldMatrix<ctype, TargetSpace::EmbeddedTangentVector::dimension, dim> LocalGFETestFunction<dim,ctype,LocalFiniteElement,TargetSpace>::
+evaluateDerivative(const Dune::FieldVector<ctype, dim>& local) const
+{
+ typename Dune::FieldMatrix<ctype, TargetSpace::EmbeddedTangentVector::dimension, dim> result(0);
+
+ for (size_t i=0; i<tangentCoefficients_.size(); i++) {
+
+ Tensor3< double, embeddedDim, embeddedDim, dim > derivative;
+ localGFEFunction_.evaluateDerivativeOfGradientWRTCoefficient (local,
+ i,
+ derivative);
+
+ // Contract the second index of the derivative with the tangent vector at the i-th Lagrange point.
+ // Add that to the result.
+ for (size_t j=0; j<embeddedDim; j++)
+ for (size_t k=0; k<embeddedDim; k++)
+ for (size_t l=0; l<dim; l++)
+ result[j][l] += derivative[j][k][l] * tangentCoefficients_[i][k];
+
+ }
+
+ return result;
+
+}
+
+
+#endif
--
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