Merge branch 'feature/more-examples' into 'master'

Add example for flat torus and graph parametrization

See merge request !15

src/example5.cc

@@ -77,16 +77,16 @@ void graph()
   YaspGrid<2> refGrid({4.0*M_PI, 4.0*M_PI}, {8, 8});
 
   // 2. Define the geometry mapping
-  auto torus = [](const FieldVector<double,2>& u)
+  auto g = [](const FieldVector<double,2>& u)
   {
     return FieldVector<double,3>{u[0], u[1],
       std::sin(u[0])*std::cos(u[1])
     };
   };
-  auto torusGF = analyticDiscreteFunction(torus, refGrid, /*order*/ 3);
+  auto gGF = analyticDiscreteFunction(g, refGrid, /*order*/ 3);
 
   // 3. Wrap the reference grid to build a curved grid
-  CurvedGrid grid{refGrid, torusGF};
+  CurvedGrid grid{refGrid, gGF};
 
   write_grid<3>(grid, "graph.vtu");
 }

src/example6.cc

@@ -19,10 +19,41 @@
 #include <dune/grid/yaspgrid.hh>
 #include <dune/grid/io/file/vtk.hh>
 
-using namespace Dune;
+namespace Dune {
+namespace Curved {
+
+struct Torus
+{
+  double const r1 = 2.0, r2 = 1.0;
+
+  auto operator() (FieldVector<double,2> const& u) const
+  {
+    return FieldVector<double,3>{
+      (r1 + r2*std::cos(u[0])) * std::cos(u[1]),
+      (r1 + r2*std::cos(u[0])) * std::sin(u[1]),
+            r2*std::sin(u[0])
+    };
+  }
+
+  friend auto derivative (Torus t)
+  {
+    return [r1=t.r1,r2=t.r2](FieldVector<double,2> const& u)
+    {
+      return FieldMatrix<double,3,2>{
+        {-r2*std::sin(u[0])*std::cos(u[1]),-(r1 + r2*std::cos(u[0]))*std::sin(u[1])},
+        {-r2*std::sin(u[0])*std::sin(u[1]), (r1 + r2*std::cos(u[0]))*std::cos(u[1])},
+        { r2*std::cos(u[0]),                0.0}
+      };
+    };
+  }
+};
+
+}}
 
 int main(int argc, char** argv)
 {
+  using namespace Dune;
+
   MPIHelper::instance(argc, argv);
 
   // 1. Construct a reference grid [0,1]x[0,1]
@@ -32,16 +63,10 @@ int main(int argc, char** argv)
   CurvedGrid grid1{grid0, [](auto const& x) { return (2.0*M_PI)*x; }, 1};
 
   // 2. Define the geometry mapping
-  auto torus = [](FieldVector<double,2> const& u) {
-    return FieldVector<double,3>{
-      (2 + std::cos(u[0])) * std::cos(u[1]),
-      (2 + std::cos(u[0])) * std::sin(u[1]),
-           std::sin(u[0])
-    };
-  };
+  auto torus = Curved::Torus{};
 
   // 3. Wrap the reference grid to build a curved grid, with Lagrange elements of order 3
-  CurvedGrid grid2{grid1, torus, 3};
+  CurvedGrid grid2{grid1, torus};
 
   // 4. Write grid to vtu file
   SubsamplingVTKWriter writer{grid2.leafGridView(), refinementIntervals(3)};