Add SubEntityQuadratureRule for quadrature on a subentity

This wraps a quadrature rule for a subentity with smaller dimension
as quadrature rule on an entity/element, by mapping quadrature
points from local subentity coordinates to local entity coordinates.

Although this rule looks like a quadrature rule on the entity it does
in fact integrate over the subentity. This e.g. has the advantage, that
integration over faces can use the same infrastructure as integration
over entities for caching.

dune/fufem/quadraturerules/CMakeLists.txt

@@ -3,4 +3,5 @@ install(FILES
     lumpingquadraturerule.hh
     quadraturerulecache.hh
     refinedquadraturerule.hh
+    subentityquadraturerule.hh
     DESTINATION ${CMAKE_INSTALL_INCLUDEDIR}/dune/fufem/quadraturerules)

dune/fufem/quadraturerules/subentityquadraturerule.hh

+// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
+// vi: set et ts=4 sw=2 sts=2:
+#ifndef DUNE_FUFEM_QUADRATURERULES_SUBENTITYQUADRATURERULE_HH
+#define DUNE_FUFEM_QUADRATURERULES_SUBENTITYQUADRATURERULE_HH
+
+#include <dune/geometry/type.hh>
+#include <dune/geometry/referenceelements.hh>
+#include <dune/geometry/quadraturerules.hh>
+
+namespace Dune::Fufem {
+
+/**
+ * \brief Quadrature rule for a subentity of some given geometry type.
+ *
+ * Wrap a quadrature rule for a subentity with smaller dimension
+ * as quadrature rule on an entity/element, by mapping quadrature
+ * points from local subentity coordinates to local entity coordinates.
+ *
+ * Although this rule looks like a quadrature rule on the entity it does
+ * in fact integrate over the subentity. This e.g. has the advantage, that
+ * integration over faces can use the same infrastructure as integration
+ * over entities for caching.
+ */
+template <class ct, int dim, int codim>
+class SubEntityQuadratureRule:
+  public Dune::QuadratureRule<ct,dim>
+{
+  using Base = Dune::QuadratureRule<ct,dim>;
+
+public:
+
+  using Base::type;
+
+  /**
+   * \brief Create SubEntityQuadratureRule for entity of given GeometryType
+   *
+   * \param gt GeometryType of the entity the rule is defined on
+   * \param subEntityIndex Index of codim subentity that the rule should integrate
+   * \param rule A (dim-codim)-dimensional rule on the subEntityIndex-th subentity of codimension codim
+   */
+  SubEntityQuadratureRule(Dune::GeometryType gt, std::size_t subEntityIndex, const Dune::QuadratureRule<ct, dim-codim>& rule)
+    : Base(gt),
+      subEntityRule_(&rule)
+  {
+    auto subEntityGeometryType = Dune::referenceElement<ct,dim>(type()).type(subEntityIndex, codim);
+    assert(subEntityGeometryType == subEntityRule().type());
+    auto subEntityGeometry = Dune::referenceElement<ct,dim>(type()).template geometry<codim>(subEntityIndex);
+    for(auto qp : subEntityRule())
+      this->emplace_back(subEntityGeometry.global(qp.position()), qp.weight());
+    this->delivered_order = subEntityRule().order();
+  }
+
+  const Dune::QuadratureRule<ct, dim-1>& subEntityRule() const
+  {
+    return *subEntityRule_;
+  }
+
+protected:
+  const Dune::QuadratureRule<ct, dim-1>* subEntityRule_;
+};
+
+
+} // namespace Dune::Fufem
+
+#endif // DUNE_FUFEM_QUADRATURERULES_SUBENTITYQUADRATURERULE_HH