fix(integrate): sort boundary edges as pairs

Assisted-by: GLM 5.3 Flash

integrate/fem2d_test.go

@@ -434,6 +434,34 @@ func TestTriangleMesh2DBoundaryEdges(t *testing.T) {
 	}
 }
 
+// TestTriangleMesh2DBoundaryEdgesAreMeshEdges pins the pair contract of
+// BoundaryEdges: every returned pair must be an edge the mesh actually
+// carries, and the pairs must come out sorted, which a sort of the flat
+// index list cannot deliver (it interleaves unrelated endpoints).
+func TestTriangleMesh2DBoundaryEdgesAreMeshEdges(t *testing.T) {
+	mesh, err := GridTriangleMesh2D(0, 0, 1, 1, 1, 1)
+	if err != nil {
+		t.Fatalf("GridTriangleMesh2D: %v", err)
+	}
+	edges := mesh.BoundaryEdges()
+	// The square's four sides: (0,1), (0,2), (1,3), (2,3) in sorted
+	// pair order.
+	want := []int{0, 1, 0, 2, 1, 3, 2, 3}
+	if len(edges) != len(want) {
+		t.Fatalf("boundary edge count %d, want %d", len(edges)/2, len(want)/2)
+	}
+	for p := 0; p < len(edges); p += 2 {
+		if edges[p] > edges[p+1] {
+			t.Fatalf("edge [%d,%d] is not sorted as a pair", edges[p], edges[p+1])
+		}
+	}
+	for p := range len(want) {
+		if edges[p] != want[p] {
+			t.Fatalf("boundary edges %v, want %v", edges, want)
+		}
+	}
+}
+
 // TestSolvePoissonFEM2DDuplicateDirichletNode pins the documented rule
 // for a node listed more than once: the last value is the prescribed
 // one and the node enters the assembled system exactly once, so the