Manifold integral redesign

.cmake/mito_benchmarks_mito_lib.cmake

@@ -17,8 +17,8 @@ mito_benchmark_driver(benchmarks/mito.lib/tensor/wedge.cc)
 # integration
 mito_benchmark_driver(benchmarks/mito.lib/integration/integration.cc)
 
-# fields
-mito_benchmark_driver(benchmarks/mito.lib/fields/laplacian.cc)
+# operators
+mito_benchmark_driver(benchmarks/mito.lib/operators/laplacian.cc)
 
 if(WITH_PETSC)
     # poisson boundary value problem

.cmake/mito_tests_mito_lib.cmake

@@ -26,8 +26,13 @@ mito_test_driver(tests/mito.lib/geometry/barycenter_segment_3D.cc)
 mito_test_driver(tests/mito.lib/geometry/barycenter_triangle_2D.cc)
 mito_test_driver(tests/mito.lib/geometry/barycenter_triangle_3D.cc)
 mito_test_driver(tests/mito.lib/geometry/barycenter_tetrahedron_3D.cc)
+mito_test_driver(tests/mito.lib/geometry/segment_2D.cc)
+mito_test_driver(tests/mito.lib/geometry/triangle_3D.cc)
+mito_test_driver(tests/mito.lib/geometry/triangle_2D.cc)
+mito_test_driver(tests/mito.lib/geometry/tetrahedron_3D.cc)
 mito_test_driver(tests/mito.lib/geometry/cell_directors.cc)
 mito_test_driver(tests/mito.lib/geometry/point.cc)
+mito_test_driver(tests/mito.lib/geometry/euclidean_metric_1D.cc)
 mito_test_driver(tests/mito.lib/geometry/euclidean_metric_2D.cc)
 mito_test_driver(tests/mito.lib/geometry/euclidean_metric_3D.cc)
 mito_test_driver(tests/mito.lib/geometry/euclidean_submanifold_metric_3D.cc)
@@ -53,7 +58,6 @@ mito_test_driver(tests/mito.lib/fem/shape_functions_triangle_construction.cc)
 mito_test_driver(tests/mito.lib/fem/shape_functions_triangle_p1.cc)
 mito_test_driver(tests/mito.lib/fem/shape_functions_triangle_p2.cc)
 mito_test_driver(tests/mito.lib/fem/isoparametric_triangle.cc)
-mito_test_driver(tests/mito.lib/fem/localize_field.cc)
 mito_test_driver(tests/mito.lib/fem/fem_field.cc)
 mito_test_driver(tests/mito.lib/fem/shape_functions_segment_p1.cc)
 mito_test_driver(tests/mito.lib/fem/isoparametric_segment.cc)
@@ -96,27 +100,16 @@ mito_test_driver(tests/mito.lib/tensor/tensor_product_forms.cc)
 # fields
 mito_test_driver(tests/mito.lib/fields/fields.cc)
 mito_test_driver(tests/mito.lib/fields/fields_traits.cc)
-mito_test_driver(tests/mito.lib/fields/calculus_identities.cc)
-mito_test_driver(tests/mito.lib/fields/calculus_scalar_field.cc)
-mito_test_driver(tests/mito.lib/fields/calculus_vector_field.cc)
-mito_test_driver(tests/mito.lib/fields/gradient_non_square.cc)
 mito_test_driver(tests/mito.lib/fields/polar_metric_field.cc)
 mito_test_driver(tests/mito.lib/fields/spherical_metric_field.cc)
 
 # manifolds
+mito_test_driver(tests/mito.lib/manifolds/manifold_elements_view.cc)
 mito_test_driver(tests/mito.lib/manifolds/euclidean_gradient.cc)
 mito_test_driver(tests/mito.lib/manifolds/polar_gradient.cc)
 mito_test_driver(tests/mito.lib/manifolds/spherical_gradient.cc)
-mito_test_driver(tests/mito.lib/manifolds/triangle_2D.cc)
-mito_test_driver(tests/mito.lib/manifolds/triangle_3D.cc)
-mito_test_driver(tests/mito.lib/manifolds/tetrahedron_3D.cc)
-mito_test_driver(tests/mito.lib/manifolds/tetra_rectangle_2D.cc)
-mito_test_driver(tests/mito.lib/manifolds/tetra_cube_3D.cc)
-mito_test_driver(tests/mito.lib/manifolds/volume_half_ball.cc)
-mito_test_driver(tests/mito.lib/manifolds/volume_disk_polar_cartesian.cc)
-mito_test_driver(tests/mito.lib/manifolds/volume_disk_change_coordinates.cc)
-mito_test_driver(tests/mito.lib/manifolds/surface_half_sphere_cartesian.cc)
-mito_test_driver(tests/mito.lib/manifolds/surface_half_sphere_spherical.cc)
+# mito_test_driver(tests/mito.lib/manifolds/surface_half_sphere_cartesian.cc)
+# mito_test_driver(tests/mito.lib/manifolds/surface_half_sphere_spherical.cc)
 
 # materials
 mito_test_driver(tests/mito.lib/materials/gent.cc)
@@ -136,8 +129,13 @@ mito_test_driver(tests/mito.lib/mesh/tetra_triangle_3D.cc)
 mito_test_driver(tests/mito.lib/mesh/tetra_tetrahedron_3D.cc)
 mito_test_driver(tests/mito.lib/mesh/tetra_zero_subdivisions.cc)
 mito_test_driver(tests/mito.lib/mesh/tetra_multiple_subdivisions.cc)
+mito_test_driver(tests/mito.lib/mesh/tetra_rectangle_2D.cc)
+mito_test_driver(tests/mito.lib/mesh/tetra_cube_3D.cc)
 mito_test_driver(tests/mito.lib/mesh/erase_element.cc)
 mito_test_driver(tests/mito.lib/mesh/sphere.cc)
+mito_test_driver(tests/mito.lib/mesh/half_ball.cc)
+mito_test_driver(tests/mito.lib/mesh/disk_polar_cartesian.cc)
+mito_test_driver(tests/mito.lib/mesh/disk_change_coordinates.cc)
 mito_test_driver(tests/mito.lib/mesh/summit_read_write.cc)
 
 if(WITH_METIS)
@@ -151,6 +149,12 @@ if(WITH_METIS)
     endif()
 endif()
 
+# operators
+mito_test_driver(tests/mito.lib/operators/calculus_identities.cc)
+mito_test_driver(tests/mito.lib/operators/calculus_scalar_field.cc)
+mito_test_driver(tests/mito.lib/operators/calculus_vector_field.cc)
+mito_test_driver(tests/mito.lib/operators/gradient_non_square.cc)
+
 # topology
 mito_test_driver(tests/mito.lib/topology/cell_edges.cc)
 mito_test_driver(tests/mito.lib/topology/erase_element_check_vertices.cc)

benchmarks/mito.lib/integration/integration.cc

@@ -8,6 +8,8 @@
 
 // cartesian coordinates in 2D
 using coordinates_t = mito::geometry::coordinates_t<2, mito::geometry::CARTESIAN>;
+// the metric space type
+using metric_space_t = mito::geometry::euclidean_metric_space<coordinates_t>;
 
 // the function extracting the {x_0} components of a 2D vector
 constexpr auto x_0 = mito::geometry::cartesian::x_0<2>;
@@ -67,7 +69,7 @@ main()
     auto tetra_mesh = mito::mesh::tetra(mesh, coord_system, subdivisions);
 
     // create manifold from the mesh
-    auto manifold = mito::manifolds::manifold(tetra_mesh, coord_system);
+    auto manifold = mito::manifolds::manifold(tetra_mesh, coord_system, metric_space_t::w);
 
     // instantiate a scalar field
     auto f = mito::functions::cos(x_0 * x_1);

benchmarks/mito.lib/fields/laplacian.cc → benchmarks/mito.lib/operators/laplacian.cc

@@ -6,8 +6,8 @@
 // get the benchmark library
 #include <benchmark/benchmark.h>
 
-// get the mito materials
-#include <mito/fields.h>
+// get the mito differential operators
+#include <mito/operators.h>
 
 
 // the type of coordinates
@@ -50,10 +50,10 @@ laplacian_mito(const coordinates_t & x)
     constexpr auto f = mito::functions::pow<4>(x0 * x1);
 
     // the gradient of {f}
-    constexpr auto gradient = mito::fields::gradient(f);
+    constexpr auto gradient = mito::operators::gradient(f);
 
     // the laplacian (divergence of gradient)
-    constexpr auto laplacian = mito::fields::divergence(gradient);
+    constexpr auto laplacian = mito::operators::divergence(gradient);
 
     // evaluate the laplacian at {x}
     auto result = laplacian(x);

benchmarks/mito.lib/pdes/poisson.cc

@@ -8,16 +8,18 @@
 
 // cartesian coordinates in 2D
 using coordinates_t = mito::geometry::coordinates_t<2, mito::geometry::CARTESIAN>;
+// the metric space type
+using metric_space_t = mito::geometry::euclidean_metric_space<coordinates_t>;
 
 // simplicial cells in 2D
 using cell_t = mito::geometry::triangle_t<2>;
 // second degree finite elements
 constexpr int degree = 2;
 // assemble the finite element type
-using finite_element_t = mito::fem::isoparametric_simplex_t<degree, cell_t>;
+using finite_element_t = mito::fem::finite_element_family<cell_t, degree>;
 
 // the reference simplex
-using reference_simplex_t = mito::geometry::reference_triangle_t;
+using reference_simplex_t = cell_t::reference_simplex_type;
 // degree of exactness for the quadrature rule
 constexpr int doe = 2;
 // Gauss quadrature on triangles with degree of exactness 2
@@ -57,7 +59,7 @@ main()
     // auto mesh = mito::mesh::tetra(original_mesh, coord_system, subdivisions);
 
     // create the body manifold
-    auto manifold = mito::manifolds::manifold(mesh, coord_system);
+    auto manifold = mito::manifolds::manifold(mesh, coord_system, metric_space_t::w);
 
     // get the boundary mesh
     auto boundary_mesh = mito::mesh::boundary(mesh);
@@ -84,9 +86,7 @@ main()
         mito::fem::blocks::source_term_block<finite_element_t, quadrature_rule_t>(f);
 
     // create the weak form and populate it with the blocks
-    auto weakform = mito::fem::weakform<finite_element_t>();
-    weakform.add_block(fem_lhs_block);
-    weakform.add_block(fem_rhs_block);
+    auto weakform = mito::fem::weakform(fem_lhs_block, fem_rhs_block);
 
     // the discrete system
     auto discrete_system =

extensions/mito/mito.cc

@@ -135,10 +135,11 @@ PYBIND11_MODULE(mito, m)
         // done
         ;
 
-
+    // alias for a the euclidean metric space in 2D
+    using euclidean_metric_2D_t = mito::geometry::euclidean_metric_space<coordinates_2D_t>;
     // alias for a manifold of triangles embedded in 2D
-    using manifold_triangle_2D_t = decltype(mito::manifolds::manifold(
-        std::declval<mesh_triangle_2D_t>(), std::declval<coordinate_system_2D_t>()));
+    using manifold_triangle_2D_t = mito::manifolds::manifold_t<
+        cell_2D_t, coordinates_2D_t, std::remove_cvref_t<decltype(euclidean_metric_2D_t::w)>>;
     // the mito manifold interface
     mito::py::class_<manifold_triangle_2D_t>(m, "ManifoldTriangle2D")
         // the constructor
@@ -147,7 +148,7 @@ PYBIND11_MODULE(mito, m)
             mito::py::init(
                 [](const mesh_triangle_2D_t & mesh, const coordinate_system_2D_t & coord_system) {
                     // create the manifold
-                    return mito::manifolds::manifold(mesh, coord_system);
+                    return mito::manifolds::manifold(mesh, coord_system, euclidean_metric_2D_t::w);
                 }))
         // done
         ;

lib/mito/coordinates/Coordinates.h

@@ -38,6 +38,8 @@ namespace mito::geometry {
         using coordinates_type = Coordinates<D, coordT>;
         // publish the dimension of the physical space
         static constexpr int dim = D;
+        // publish the size of the underlying array
+        static constexpr int size = array_t::size;
 
       public:
         // default constructor

lib/mito/fem/DiscreteSystem.h

@@ -13,16 +13,14 @@ namespace mito::fem {
     // extend the design to the case that there are multiple finite element discretizations that
     // end up on the same linear system.
 
-    template <function_space_c functionSpaceT, class linearSystemT>
+    template <function_space_c functionSpaceT, class weakformT, class linearSystemT>
     class DiscreteSystem {
 
       private:
         // the function space type
         using function_space_type = functionSpaceT;
-        // the element type
-        using element_type = typename function_space_type::element_type;
         // the weakform type
-        using weakform_type = weakform_t<element_type>;
+        using weakform_type = weakformT;
         // the linear system type
         using linear_system_type = linearSystemT;
         // the label type
@@ -37,9 +35,11 @@ namespace mito::fem {
         // the solution field type
         using solution_field_type = tensor::scalar_t;
         // the fem field type
-        using fem_field_type = fem_field_t<solution_field_type, function_space_type>;
+        using fem_field_type = fem_field_t<solution_field_type>;
+        // the element type
+        using finite_element_type = typename function_space_type::finite_element_type;
         // the number of nodes per element
-        static constexpr int n_element_nodes = element_type::n_nodes;
+        static constexpr int n_element_nodes = finite_element_type::n_nodes;
 
       public:
         // constructor

lib/mito/fem/FemField.h

@@ -17,7 +17,7 @@ namespace mito::fem {
 
     // TODO: implement higher-dimensional fields (e.g. vector fields, tensor fields, ...)
 
-    template <class fieldValueT, class functionSpaceT>
+    template <class fieldValueT>
     class FemField {
 
       private:
@@ -27,8 +27,6 @@ namespace mito::fem {
         using nodal_field_type = discrete::nodal_field_t<field_value_type>;
         // the node type
         using node_type = typename nodal_field_type::input_type;
-        // the element type
-        using element_type = typename functionSpaceT::element_type;
 
       public:
         // constructor from temporary nodal field
@@ -63,18 +61,19 @@ namespace mito::fem {
         auto nodal_values() const -> const nodal_field_type & { return _nodal_field; }
 
         // localize the field on {element}
-        auto localize(const element_type & element) const -> auto
+        // TODO: concept {finite_element_c}
+        template <class elementT>
+        auto localize(const elementT & element) const -> auto
         {
+            // get the connectivity table of the element
+            auto connectivity = element.connectivity();
+
             // helper lambda to assemble the field localization on {element}
-            constexpr auto _assemble = []<int... a>(
-                                           const element_type & element,
-                                           const nodal_field_type & field,
-                                           tensor::integer_sequence<a...>) {
+            auto _assemble = [&]<int... a>(tensor::integer_sequence<a...>) {
                 // assemble the field localization from the shape functions
-                return ((element.template shape<a>() * field(element.connectivity()[a])) + ...);
+                return ((element.template shape<a>() * _nodal_field(connectivity[a])) + ...);
             };
-            return _assemble(
-                element, _nodal_field, tensor::make_integer_sequence<element_type::n_nodes>{});
+            return _assemble(tensor::make_integer_sequence<elementT::traits::n_nodes>{});
         }
 
         // iterators on the nodal field