New interpolation function that interpolates in a Euclidean space and projects onto the manifold

[[Imported from SVN: r9682]]

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 \

dune/gfe/localprojectedfefunction.hh

+#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