From db27a71bfaac1377d383adecbd79672dc62a2bdc Mon Sep 17 00:00:00 2001
From: Oliver Sander <sander@igpm.rwth-aachen.de>
Date: Mon, 20 Apr 2009 09:53:16 +0000
Subject: [PATCH] Local interpolation for geodesic finite element functions
centralized in one class
[[Imported from SVN: r4057]]
---
src/localgeodesicfefunction.hh | 125 +++++++++++++++++++++++++++++++++
1 file changed, 125 insertions(+)
create mode 100644 src/localgeodesicfefunction.hh
diff --git a/src/localgeodesicfefunction.hh b/src/localgeodesicfefunction.hh
new file mode 100644
index 00000000..5ae292a1
--- /dev/null
+++ b/src/localgeodesicfefunction.hh
@@ -0,0 +1,125 @@
+#ifndef LOCAL_GEODESIC_FE_FUNCTION
+#define LOCAL_GEODESIC_FE_FUNCTION
+
+#include <vector>
+
+#include <dune/common/fvector.hh>
+#include <dune/common/geometrytype.hh>
+
+
+/** \brief A geodesic function from the reference element to a manifold
+
+\tparam dim Dimension of the reference element
+\tparam ctype Type used for coordinates on the reference element
+\tparam TargetSpace The manifold that the function takes its values in
+*/
+template <int dim, class ctype, class TargetSpace>
+class LocalGeodesicFEFunction
+{
+
+ typedef typename TargetSpace::EmbeddedTangentVector EmbeddedTangentVector;
+
+public:
+
+ /** \brief Constructor */
+ LocalGeodesicFEFunction(const Dune::GeometryType& type,
+ const std::vector<TargetSpace>& coefficients)
+ : type_(type), coefficients_(coefficients)
+ {
+ // currently only simplices are implemented
+ assert(type.isSimplex());
+ }
+
+ /** \brief Evaluate the function */
+ TargetSpace evaluate(const Dune::FieldVector<ctype, dim>& local);
+
+ /** \brief Evaluate the derivative of the function */
+ Dune::FieldMatrix<ctype, EmbeddedTangentVector::size, dim> evaluateDerivative(const Dune::FieldVector<ctype, dim>& local);
+
+private:
+
+ /** \brief Compute the derivate of geodesic interpolation wrt to the initial point
+ and return it as an _embedded_ tangent vector
+
+ \todo This is group-specific and should not really be here
+ */
+ static Dune::FieldMatrix<ctype, EmbeddedTangentVector::size, EmbeddedTangentVector::size>
+ derivativeWRTFirstPoint(const Rotation<3,ctype>& a, const Rotation<3,ctype>& b, double s);
+
+ /** \brief The type of the reference element */
+ Dune::GeometryType type_;
+
+ /** \brief The coefficient vector */
+ std::vector<TargetSpace> coefficients_;
+
+};
+
+template <int dim, class ctype, class TargetSpace>
+Dune::FieldMatrix<ctype, TargetSpace::EmbeddedTangentVector::size, TargetSpace::EmbeddedTangentVector::size>
+LocalGeodesicFEFunction<dim,ctype,TargetSpace>::
+derivativeWRTFirstPoint(const Rotation<3,ctype>& a, const Rotation<3,ctype>& b, double s)
+{
+ DUNE_THROW(Dune::NotImplemented, "derivativeWRTFirstPoint");
+}
+
+
+template <int dim, class ctype, class TargetSpace>
+TargetSpace LocalGeodesicFEFunction<dim,ctype,TargetSpace>::
+evaluate(const Dune::FieldVector<ctype, dim>& local)
+{
+ TargetSpace result = TargetSpace::interpolate(coefficients_[0], coefficients_[1], local[0]);
+
+ for (int i=1; i<dim; i++)
+ result = TargetSpace::interpolate(result, coefficients_[i+1], local[i]);
+
+ return result;
+}
+
+template <int dim, class ctype, class TargetSpace>
+Dune::FieldMatrix<ctype, TargetSpace::EmbeddedTangentVector::size, dim> LocalGeodesicFEFunction<dim,ctype,TargetSpace>::
+evaluateDerivative(const Dune::FieldVector<ctype, dim>& local)
+{
+ Dune::FieldMatrix<ctype, EmbeddedTangentVector::size, dim> result;
+
+ if (dim==1) {
+
+ EmbeddedTangentVector tmp = TargetSpace::interpolateDerivative(coefficients_[0], coefficients_[1], local[0]);
+
+ for (int i=0; i<EmbeddedTangentVector::size; i++)
+ result[i][0] = tmp[i];
+
+ }
+
+ if (dim==2) {
+
+ TargetSpace firstPoint = TargetSpace::interpolate(coefficients_[0], coefficients_[1], local[0]);
+
+ // Derivative with respect to \xi_0
+
+ // -- Outer derivative
+ Dune::FieldMatrix<ctype, EmbeddedTangentVector::size, EmbeddedTangentVector::size> outerDerivative
+ = derivativeWRTFirstPoint(firstPoint, coefficients_[2], local[1]);
+
+ // -- Inner derivative
+ EmbeddedTangentVector innerDerivative = TargetSpace::interpolateDerivative(coefficients_[0], coefficients_[1], local[0]);
+
+ EmbeddedTangentVector der;
+ outerDerivative.mv(innerDerivative, der);
+
+ for (int i=0; i<EmbeddedTangentVector::size; i++)
+ result[i][0] = der[i];
+
+
+ // Derivative with respect to \xi_1
+ EmbeddedTangentVector tmp = TargetSpace::interpolateDerivative(firstPoint, coefficients_[2], local[1]);
+
+ for (int i=0; i<EmbeddedTangentVector::size; i++)
+ result[i][1] = tmp[i];
+
+ }
+
+ assert(dim==1 || dim==2);
+
+}
+
+#endif
--
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