A global geodesic finite element grid function. Not tested yet.

[[Imported from SVN: r7914]]

dune/gfe/globalgeodesicfefunction.hh

+#ifndef GLOBAL_GEODESIC_FINITE_ELEMENT_FUNCTION_HH
+#define GLOBAL_GEODESIC_FINITE_ELEMENT_FUNCTION_HH
+
+#include <vector>
+
+#include <dune/common/fvector.hh>
+#include <dune/common/fmatrix.hh>
+
+#include <dune/gfe/localgeodesicfefunction.hh>
+
+
+/** \brief Global geodesic finite element function. 
+ *
+ *  \tparam Basis  - The global basis type.
+ *  \tparam TargetSpace - The manifold that this functions takes its values in.
+ */
+template<class Basis, class TargetSpace>
+GlobalGeodesicFEFunction {
+
+    typedef typename Basis::LocalFiniteElement LocalFiniteElement;
+    typedef typename Basis::GridView GridView;
+    typedef typename GridView::template Codim<0>::Entity Element;
+    typedef typename GridView::Grid::ctype  ctype;
+
+    typedef LocalGeodesicFEFunction<GridView::dimension, ctype, LocalFiniteElement, TargetSpace> LocalGFEFunction;
+    typedef typename TargetSpace::EmbeddedTangentVector EmbeddedTangentVector;
+
+    //! Dimension of the grid.
+    enum { gridDim = GridView::dimension };
+    
+    //! Dimension of the embedded tanget space
+    enum { embeddedDim = EmbeddedTangentVector::dimension };
+
+    //! Create global function by a global basis and the corresponding coefficient vector
+    GlobalGeodesicFEFunction(const Basis& basis, const std::vector<TargetSpace>& coefficients) :
+        basis_(basis),
+        coefficients_(coefficients)
+    {}
+
+    /** \brief Evaluate the function at local coordinates. */
+    void evaluateLocal(const Element& element, const Dune::FieldVector<gridDim,ctype>& local, TargetSpace& out) 
+    {
+        int numOfBasisFct = basis_.getLocalFiniteElement(element).size(); 
+
+        // Extract local solution
+        std::vector<TargetSpace> localSolution(numOfBaseFct);
+        
+        for (int i=0; i<numOfBaseFct; i++)
+            localCoeff[i] = coefficients_[basis_.index(element,i)];
+
+        // create local gfe function
+        LocalGFEFunction localGFE(basis_.getLocalFiniteElement(element),localCoeff);
+        out = localGFE.evaluate(local);
+    }
+
+    /** \brief Evaluate the derivative of the function at local coordinates. */
+    void evaluateDerivativeLocal(const Element& element, const Dune::FieldVector<gridDim,ctype>& local, 
+                                 Dune::FieldMatrix<ctype, embeddedDim, gridDim>& out)
+    {
+        int numOfBasisFct = basis_.getLocalFiniteElement(element).size(); 
+
+        // Extract local solution
+        std::vector<TargetSpace> localSolution(numOfBaseFct);
+        
+        for (int i=0; i<numOfBaseFct; i++)
+            localCoeff[i] = coefficients_[basis_.index(element,i)];
+
+        // create local gfe function
+        LocalGFEFunction localGFE(basis_.getLocalFiniteElement(element),localCoeff);
+    
+        // use it to evaluate the derivative
+        out = localGFE.evaluateDerivative(local);
+    }
+
+private:
+    //! The global basis
+    const Basis& basis_;
+    //! The coefficient vector
+    const std::vector<TargetSpace>& coefficients_;
+};
+#endif