feat(stroid): first working version

stroid generates o-grid topologies with proper boundary conditions applied. Currently the external domain does not work, this will be addressed in the next commit.

src/lib/utils/mesh_utils.cpp

@@ -0,0 +1,64 @@
+#include "stroid/utils/mesh_utils.h"
+#include "mfem.hpp"
+#include <print>
+
+namespace stroid::utils {
+    void MarkFlippedElements(mfem::Mesh& mesh) {
+        size_t total_flipped = 0;
+        size_t total_elements = mesh.GetNE();
+        for (int i = 0; i < mesh.GetNE(); i++) {
+            mfem::ElementTransformation *T = mesh.GetElementTransformation(i);
+
+            const mfem::IntegrationRule &ir = mfem::IntRules.Get(T->GetGeometryType(), 2 * T->Order());
+
+            bool is_flipped = false;
+            for (int j = 0; j < ir.GetNPoints(); j++) {
+                T->SetIntPoint(&ir.IntPoint(j));
+                if (T->Jacobian().Det() < 0.0) {
+                    is_flipped = true;
+                    break;
+                }
+            }
+
+            if (is_flipped) {
+                mesh.SetAttribute(i, 999);
+                total_flipped++;
+            }
+
+
+        }
+        std::println("Marked {}/{} elements as flipped.", total_flipped, total_elements);
+    }
+
+    void MarkFlippedBoundaryElements(mfem::Mesh& mesh) {
+        size_t total_flipped = 0;
+        size_t total_boundary_elements = mesh.GetNBE();
+        for (int i = 0; i < mesh.GetNBE(); i++) {
+            mfem::ElementTransformation *T = mesh.GetBdrElementTransformation(i);
+            const mfem::IntegrationRule &ir = mfem::IntRules.Get(T->GetGeometryType(), 2 * T->Order());
+
+            bool is_flipped = false;
+            for (int j = 0; j < ir.GetNPoints(); j++) {
+                T->SetIntPoint(&ir.IntPoint(j));
+                const mfem::DenseMatrix &J = T->Jacobian();
+                mfem::Vector pos;
+                T->Transform(ir.IntPoint(j), pos);
+
+                const double nx = J(1,0) * J(2,1) - J(2,0) * J(1,1);
+                const double ny = J(2,0) * J(0,1) - J(0,0) * J(2,1);
+                const double nz = J(0,0) * J(1,1) - J(1,0) * J(0,1);
+
+                if (nx * pos(0) + ny * pos(1) + nz * pos(2) < 0.0) {
+                    is_flipped = true;
+                    break;
+                }
+            }
+
+            if (is_flipped) {
+                mesh.SetBdrAttribute(i, 500);
+                total_flipped++;
+            }
+        }
+        std::println("Marked {}/{} boundary elements as flipped.", total_flipped, total_boundary_elements);
+    }
+}