feat(mean_field): added dimensions, discritization, and start of eos

The full rewrite of mean_field into something maintainable is progressing. dimensions is mostly done, discritization (domain, blocks, and fields) is done, and eos is progressing quickly

src/include/serif/discretization/domain/schema/validation/all.hpp

@@ -0,0 +1,33 @@
+#pragma once
+
+#include <mfem.hpp>
+
+#include "serif/discretization/domain/mesh/topology.hpp"
+#include "serif/discretization/domain/schema/concepts.hpp"
+#include "serif/discretization/domain/schema/validation/results.hpp"
+#include "serif/discretization/domain/schema/validation/validator.hpp"
+
+// Every RelationValidator specialization must be visible before
+// SchemaRelationValidator is instantiated, so they are all included here and
+// validate_schema is defined only in this header. Include this file to validate
+// a mesh; including validator.hpp alone is not enough.
+#include "serif/discretization/domain/schema/validation/boundary.hpp"
+#include "serif/discretization/domain/schema/validation/connected.hpp"
+#include "serif/discretization/domain/schema/validation/inscribed.hpp"
+
+namespace serif::discretization::domain::schema::validation {
+    // Validate against connectivity that has already been extracted. Prefer
+    // this overload when validating several schemas against the same mesh.
+    template <IsSchema SchemaT>
+    [[nodiscard]] SchemaValidationResult validate_schema(const mesh::MeshTopology &topology) {
+        using RelationsT = typename SchemaT::relations_type;
+        return SchemaRelationValidator<SchemaT, RelationsT>::validate(topology);
+    }
+
+    // Extract the mesh connectivity once, then check every relation against it.
+    template <IsSchema SchemaT>
+    [[nodiscard]] SchemaValidationResult validate_schema(const mfem::Mesh &mfemMesh) {
+        const mesh::MeshTopology topology{mfemMesh};
+        return validate_schema<SchemaT>(topology);
+    }
+}