Start writing of simplicial Gauss-Lengendre quadrature formulae

Only sets 1d formulae which is trivially set as the tensorial ones

src/analysis/CMakeLists.txt

@@ -2,5 +2,6 @@
 
 add_library(
   PugsAnalysis
+  SimplicialGaussLegendreQuadrature.cpp
   TensorialGaussLegendreQuadrature.cpp
   TensorialGaussLobattoQuadrature.cpp)

src/analysis/SimplicialGaussLegendreQuadrature.cpp

+#include <analysis/SimplicialGaussLegendreQuadrature.hpp>
+#include <analysis/TensorialGaussLegendreQuadrature.hpp>
+#include <utils/Exceptions.hpp>
+
+template <>
+void
+SimplicialGaussLegendreQuadrature<1>::_buildPointAndWeightLists()
+{
+  TensorialGaussLegendreQuadrature<1> gauss(m_order);
+
+  m_point_list  = gauss.pointList();
+  m_weight_list = gauss.weightList();
+}
+
+template <>
+void
+SimplicialGaussLegendreQuadrature<2>::_buildPointAndWeightLists()
+{
+  throw NotImplementedError("gauss legendre quadrature on 2d simplex");
+}
+
+template <>
+void
+SimplicialGaussLegendreQuadrature<3>::_buildPointAndWeightLists()
+{
+  throw NotImplementedError("gauss legendre quadrature on 3d simplex");
+}

src/analysis/SimplicialGaussLegendreQuadrature.hpp

+#ifndef SIMPLICIAL_GAUSS_LEGENDRE_QUADRATURE_HPP
+#define SIMPLICIAL_GAUSS_LEGENDRE_QUADRATURE_HPP
+
+#include <analysis/QuadratureFormula.hpp>
+
+/**
+ * Defines Gauss Legendre quadrature on the reference simplex element
+ * - in 1d, the segment \f$]-1,1[\f$
+ * - in 2d, the triangle defined by \f$(-1,-1)\f$,  \f$(1,-1)\f$ and \f$(-1,1)\f$
+ * - in 3d, the tetrahedron joining \f$(-1,-1-1)\f$, \f$(1,-1,-1)\f$, \f$(-1,1,-1)\f$ and \f$(-1,1-,1)\f$
+ *
+ * \note formulae are extracted from High-order Finite Element Method [2004 -  Chapman & Hall]
+ */
+template <size_t Dimension>
+class SimplicialGaussLegendreQuadrature final : public QuadratureForumla<Dimension>
+{
+ private:
+  void _buildPointAndWeightLists();
+
+ public:
+  SimplicialGaussLegendreQuadrature(SimplicialGaussLegendreQuadrature&&)      = default;
+  SimplicialGaussLegendreQuadrature(const SimplicialGaussLegendreQuadrature&) = default;
+
+  explicit SimplicialGaussLegendreQuadrature(const size_t order) : QuadratureForumla<Dimension>(order)
+  {
+    this->_buildPointAndWeightLists();
+  }
+
+  SimplicialGaussLegendreQuadrature()  = delete;
+  ~SimplicialGaussLegendreQuadrature() = default;
+};
+
+#endif   // SIMPLICIAL_GAUSS_LEGENDRE_QUADRATURE_HPP

tests/CMakeLists.txt

@@ -99,6 +99,7 @@ add_executable (unit_tests
   test_PugsUtils.cpp
   test_Q1Transformation.cpp
   test_RevisionInfo.cpp
+  test_SimplicialGaussLegendreQuadrature.cpp
   test_SmallArray.cpp
   test_SmallVector.cpp
   test_SymbolTable.cpp