Add localintegralenergy.hh and neumannenergy.hh, they assemble the energy for...

Add localintegralenergy.hh and neumannenergy.hh, they assemble the energy for a single element and work with a CompositeBasis

These classes work similarly to Dune::Elasticity::LocalIntegralEnergy and Dune::Elasticity::NeumannEnergy,
where the ones in Dune::Elasticity with a power basis (for the displacement function) and
Dune::GFE::LocalIntegralEnergy / Dune::GFE::NeumannEnergy work with a CompositeBasis (for the displacement AND the rotation),
so the indices to access the different parts of the basis are different.

dune/gfe/localintegralenergy.hh

+#ifndef DUNE_GFE_LOCALINTEGRALENERGY_HH
+#define DUNE_GFE_LOCALINTEGRALENERGY_HH
+
+#include <dune/common/fmatrix.hh>
+#include <dune/common/fmatrixev.hh>
+
+#include <dune/geometry/quadraturerules.hh>
+
+#include <dune/gfe/localenergy.hh>
+#include <dune/gfe/realtuple.hh>
+#include <dune/gfe/rigidbodymotion.hh>
+
+#include <dune/elasticity/materials/localdensity.hh>
+
+namespace Dune::GFE {
+
+  /**
+    \brief Assembles the elastic energy for a single element integrating the localdensity over one element.
+
+           This class works similarly to the class Dune::Elasticity::LocalIntegralEnergy, where Dune::Elasticity::LocalIntegralEnergy extends
+           Dune::Elasticity::LocalEnergy and Dune::GFE::LocalIntegralEnergy extends Dune::GFE::LocalEnergy.
+  */
+template<class Basis, class... TargetSpaces>
+class LocalIntegralEnergy
+  : public Dune::GFE::LocalEnergy<Basis,TargetSpaces...>
+{
+  using LocalView = typename Basis::LocalView;
+  using GridView = typename LocalView::GridView;
+  using DT = typename GridView::Grid::ctype;
+  using RT = typename Dune::GFE::LocalEnergy<Basis,TargetSpaces...>::RT;
+
+  enum {gridDim=GridView::dimension};
+
+public:
+
+  /** \brief Constructor with a local energy density
+    */
+  LocalIntegralEnergy(const std::shared_ptr<Dune::Elasticity::LocalDensity<gridDim,RT,DT>>& ld)
+  : localDensity_(ld)
+  {}
+
+  /** \brief Assemble the energy for a single element */
+  RT energy(const typename Basis::LocalView& localView,
+            const std::vector<TargetSpaces>&... localSolutions) const
+  { 
+    static_assert(sizeof...(TargetSpaces) > 0, "LocalIntegralEnergy needs at least one TargetSpace!");
+
+    using TargetSpace = typename std::tuple_element<0, std::tuple<TargetSpaces...> >::type;
+    static_assert( (std::is_same<TargetSpace, RigidBodyMotion<RT,gridDim>>::value)
+      or (std::is_same<TargetSpace, RealTuple<RT,gridDim>>::value), "The first TargetSpace of LocalIntegralEnergy needs to be RigidBodyMotion or RealTuple!" );
+    
+    const std::vector<TargetSpace>& localSolution = std::get<0>(std::forward_as_tuple(localSolutions...));
+
+    using namespace Dune::Indices;
+    // powerBasis: grab the finite element of the first child
+    const auto& localFiniteElement = localView.tree().child(_0,0).finiteElement();
+    const auto& element = localView.element();
+
+    RT energy = 0;
+
+    // store gradients of shape functions and base functions
+    std::vector<FieldMatrix<DT,1,gridDim> > referenceGradients(localFiniteElement.size());
+    std::vector<FieldVector<DT,gridDim> > gradients(localFiniteElement.size());
+
+    int quadOrder = (element.type().isSimplex()) ? localFiniteElement.localBasis().order()
+                                                 : localFiniteElement.localBasis().order() * gridDim;
+
+    const auto& quad = Dune::QuadratureRules<DT, gridDim>::rule(element.type(), quadOrder);
+
+    for (const auto& qp : quad)
+    {
+      const DT integrationElement = element.geometry().integrationElement(qp.position());
+
+      const auto jacobianInverseTransposed = element.geometry().jacobianInverseTransposed(qp.position());
+
+      // Global position
+      auto x = element.geometry().global(qp.position());
+
+      // Get gradients of shape functions
+      localFiniteElement.localBasis().evaluateJacobian(qp.position(), referenceGradients);
+
+      // compute gradients of base functions
+      for (size_t i=0; i<gradients.size(); ++i)
+        jacobianInverseTransposed.mv(referenceGradients[i][0], gradients[i]);
+
+      // Deformation gradient
+      FieldMatrix<RT,gridDim,gridDim> deformationGradient(0);
+      for (size_t i=0; i<gradients.size(); i++)
+        for (int j=0; j<gridDim; j++)
+          deformationGradient[j].axpy(localSolution[i][j], gradients[i]);
+      // Integrate the energy density
+      energy += qp.weight() * integrationElement * (*localDensity_)(x, deformationGradient);
+    }
+
+    return energy;
+  }
+
+protected:
+  const std::shared_ptr<Dune::Elasticity::LocalDensity<gridDim,RT,DT>> localDensity_ = nullptr;
+
+};
+
+}  // namespace Dune::GFE
+
+#endif   //#ifndef DUNE_GFE_LOCALINTEGRALENERGY_HH

dune/gfe/neumannenergy.hh

+#ifndef DUNE_GFE_NEUMANNENERGY_HH
+#define DUNE_GFE_NEUMANNENERGY_HH
+
+#include <dune/geometry/quadraturerules.hh>
+
+#include <dune/fufem/functions/virtualgridfunction.hh>
+#include <dune/fufem/boundarypatch.hh>
+
+#include <dune/elasticity/assemblers/localenergy.hh>
+
+namespace Dune::GFE {
+  /**
+    \brief Assembles the Neumann energy for a single element on the Neumann Boundary using the Neumann Function.
+    
+           This class works similarly to the class Dune::Elasticity::NeumannEnergy, where Dune::Elasticity::NeumannEnergy extends
+           Dune::Elasticity::LocalEnergy and Dune::GFE::NeumannEnergy extends Dune::GFE::LocalEnergy.
+  */
+template<class Basis, class... TargetSpaces>
+class NeumannEnergy
+  : public Dune::GFE::LocalEnergy<Basis,TargetSpaces...>
+{
+  using LocalView = typename Basis::LocalView;
+  using GridView = typename LocalView::GridView;
+  using DT = typename GridView::Grid::ctype;
+  using RT = typename Dune::GFE::LocalEnergy<Basis,TargetSpaces...>::RT;
+
+  enum {dim=GridView::dimension};
+
+public:
+
+  /** \brief Constructor with a set of material parameters
+   * \param parameters The material parameters
+   */
+  NeumannEnergy(const std::shared_ptr<BoundaryPatch<GridView>>& neumannBoundary,
+                std::function<Dune::FieldVector<double,dim>(Dune::FieldVector<DT,dim>)> neumannFunction)
+  : neumannBoundary_(neumannBoundary),
+    neumannFunction_(neumannFunction)
+  {}
+
+  /** \brief Assemble the energy for a single element */
+  RT energy(const typename Basis::LocalView& localView,
+            const std::vector<TargetSpaces>&... localSolutions) const
+  { 
+    static_assert(sizeof...(TargetSpaces) > 0, "NeumannEnergy needs at least one TargetSpace!");
+
+    using namespace Dune::Indices;
+    using TargetSpace = typename std::tuple_element<0, std::tuple<TargetSpaces...> >::type;
+    const std::vector<TargetSpace>& localSolution = std::get<0>(std::forward_as_tuple(localSolutions...));
+
+    const auto& localFiniteElement = localView.tree().child(_0,0).finiteElement();
+    const auto& element = localView.element();
+
+    RT energy = 0;
+
+    for (auto&& intersection : intersections(neumannBoundary_->gridView(), element)) {
+
+      if (not neumannBoundary_ or not neumannBoundary_->contains(intersection))
+        continue;
+
+      int quadOrder = localFiniteElement.localBasis().order();
+
+      const auto& quad = Dune::QuadratureRules<DT, dim-1>::rule(intersection.type(), quadOrder);
+
+      for (size_t pt=0; pt<quad.size(); pt++) {
+
+        // Local position of the quadrature point
+        const Dune::FieldVector<DT,dim>& quadPos = intersection.geometryInInside().global(quad[pt].position());
+
+        const auto integrationElement = intersection.geometry().integrationElement(quad[pt].position());
+
+        // The value of the local function
+        std::vector<Dune::FieldVector<DT,1> > shapeFunctionValues;
+        localFiniteElement.localBasis().evaluateFunction(quadPos, shapeFunctionValues);
+
+        Dune::FieldVector<RT,dim> value(0);
+        for (size_t i=0; i<localFiniteElement.size(); i++)
+          for (int j=0; j<dim; j++)
+            value[j] += shapeFunctionValues[i] * localSolution[i][j];
+
+        // Value of the Neumann data at the current position
+        auto neumannValue = neumannFunction_( intersection.geometry().global(quad[pt].position()) );
+
+        // Only translational dofs are affected by the Neumann force
+        for (size_t i=0; i<neumannValue.size(); i++)
+          energy += (neumannValue[i] * value[i]) * quad[pt].weight() * integrationElement;
+
+      }
+
+    }
+
+    return energy;
+  }
+
+private:
+  /** \brief The Neumann boundary */
+  const std::shared_ptr<BoundaryPatch<GridView>> neumannBoundary_;
+
+  /** \brief The function implementing the Neumann data */
+  std::function<Dune::FieldVector<double,dim>(Dune::FieldVector<DT,dim>)> neumannFunction_;
+};
+}  // namespace Dune::GFE
+
+#endif   //#ifndef DUNE_GFE_NEUMANNENERGY_HH