rustytorch/crates/specialized/rtx-fea/tests/hexahedron_finite_element_tdd.rs

//! TDD Tests for Hexahedron FiniteElement Implementations
//! Following strict Red-Green-Refactor cycle
//! No mocks, stubs, or TODOs - only full implementations

#[cfg(test)]
mod hexahedron20_tests {
    use nalgebra::Vector3;
    use rtx_fea::elements::shape_functions::shape_3d::Hexahedron20;
    use rtx_fea::elements::{FiniteElement, NaturalCoords};
    use rtx_fea::mesh::ElementType;

    #[test]
    fn test_hex20_element_type() {
        // RED: Test that Hexahedron20 implements FiniteElement and returns correct type
        let hex20 = Hexahedron20::new();

        // GREEN: Hexahedron20 should return ElementType::Hex20
        assert_eq!(hex20.element_type(), ElementType::Hex20);
    }

    #[test]
    fn test_hex20_num_nodes() {
        // RED: Test that Hexahedron20 correctly reports number of nodes
        let hex20 = Hexahedron20::new();

        // GREEN: Hexahedron20 has 20 nodes (8 corners + 12 mid-edges)
        assert_eq!(hex20.num_nodes(), 20);
    }

    #[test]
    fn test_hex20_dimensions() {
        // RED: Test spatial and parametric dimensions
        let hex20 = Hexahedron20::new();

        // GREEN: Hexahedron20 is 3D element with 3D parametric space
        assert_eq!(hex20.spatial_dimension(), 3);
        assert_eq!(hex20.parametric_dimension(), 3);
    }

    #[test]
    fn test_hex20_shape_functions_at_corner() {
        // RED: Test shape function evaluation at corner node
        let hex20 = Hexahedron20::new();

        // Test at corner (−1,−1,−1) - should be 1 at node 0, 0 at others
        let coords = NaturalCoords::new_3d(-1.0, -1.0, -1.0);
        let shape = hex20.shape_functions(&coords).unwrap();

        // GREEN: Verify shape function properties
        assert!((shape.value(0).unwrap() - 1.0).abs() < 1e-10);
        for i in 1..20 {
            assert!(shape.value(i).unwrap().abs() < 1e-10);
        }
    }

    #[test]
    fn test_hex20_jacobian() {
        // RED: Test Jacobian computation
        let hex20 = Hexahedron20::new();

        // The reference cube spanning [-1, 1] in each direction, in the node
        // order the shape functions are written in: four bottom corners
        // counter-clockwise, four top corners, then the bottom, top and
        // vertical mid-edges.
        //
        // This previously listed the corners in lexicographic order and put
        // *all twelve* mid-edge nodes at the origin, commented "simplified
        // for test". That is not a degenerate hexahedron so much as not a
        // hexahedron: collapsing the mid-side nodes to a point makes the
        // mapping genuinely singular. It only passed because the dN/dr and
        // dN/ds derivatives carried sign errors at nodes 1, 3, 5 and 7, which
        // produced a non-zero determinant for a geometry that has none.
        let node_coords = vec![
            // Bottom corners
            Vector3::new(-1.0, -1.0, -1.0),
            Vector3::new(1.0, -1.0, -1.0),
            Vector3::new(1.0, 1.0, -1.0),
            Vector3::new(-1.0, 1.0, -1.0),
            // Top corners
            Vector3::new(-1.0, -1.0, 1.0),
            Vector3::new(1.0, -1.0, 1.0),
            Vector3::new(1.0, 1.0, 1.0),
            Vector3::new(-1.0, 1.0, 1.0),
            // Bottom mid-edges
            Vector3::new(0.0, -1.0, -1.0),
            Vector3::new(1.0, 0.0, -1.0),
            Vector3::new(0.0, 1.0, -1.0),
            Vector3::new(-1.0, 0.0, -1.0),
            // Top mid-edges
            Vector3::new(0.0, -1.0, 1.0),
            Vector3::new(1.0, 0.0, 1.0),
            Vector3::new(0.0, 1.0, 1.0),
            Vector3::new(-1.0, 0.0, 1.0),
            // Vertical mid-edges
            Vector3::new(-1.0, -1.0, 0.0),
            Vector3::new(1.0, -1.0, 0.0),
            Vector3::new(1.0, 1.0, 0.0),
            Vector3::new(-1.0, 1.0, 0.0),
        ];

        let coords = NaturalCoords::new_3d(0.0, 0.0, 0.0);
        let jac = hex20.jacobian(&coords, &node_coords).unwrap();

        // The element occupies its own reference domain, so the mapping is the
        // identity and the Jacobian determinant is exactly 1.
        assert!((jac.determinant() - 1.0).abs() < 1e-10);
    }

    #[test]
    fn test_hex20_quadrature() {
        // RED: Test quadrature rule generation
        let hex20 = Hexahedron20::new();

        // GREEN: Get default quadrature rule
        let quad_rule = hex20.quadrature_rule(None).unwrap();
        assert!(quad_rule.points.len() > 0);

        // For order 3, should have at least 8 points (2x2x2)
        let quad_rule_3 = hex20.quadrature_rule(Some(3)).unwrap();
        assert!(quad_rule_3.points.len() >= 8);
    }
}

#[cfg(test)]
mod hexahedron27_tests {
    use nalgebra::Vector3;
    use rtx_fea::elements::shape_functions::shape_3d::Hexahedron27;
    use rtx_fea::elements::{FiniteElement, NaturalCoords};
    use rtx_fea::mesh::ElementType;

    #[test]
    fn test_hex27_element_type() {
        // RED: Test that Hexahedron27 implements FiniteElement
        let hex27 = Hexahedron27::new();

        // GREEN: Hexahedron27 should return ElementType::Hex27
        assert_eq!(hex27.element_type(), ElementType::Hex27);
    }

    #[test]
    fn test_hex27_num_nodes() {
        // RED: Test node count
        let hex27 = Hexahedron27::new();

        // GREEN: Hexahedron27 has 27 nodes (8 corners + 12 mid-edges + 6 face-centers + 1 center)
        assert_eq!(hex27.num_nodes(), 27);
    }

    #[test]
    fn test_hex27_partition_of_unity() {
        // RED: Test that shape functions sum to 1 everywhere
        let hex27 = Hexahedron27::new();

        let test_points = vec![
            (0.0, 0.0, 0.0),   // Center
            (0.5, 0.5, 0.5),   // Random point
            (-0.5, 0.3, -0.7), // Another random point
        ];

        for (x, y, z) in test_points {
            let coords = NaturalCoords::new_3d(x, y, z);
            let shape = hex27.shape_functions(&coords).unwrap();

            // GREEN: Sum of all shape functions should be 1
            let sum: f64 = (0..27).map(|i| shape.value(i).unwrap()).sum();
            assert!((sum - 1.0).abs() < 1e-10);
        }
    }
}

#[cfg(test)]
mod integration_tests {
    use rtx_fea::elements::shape_functions::shape_3d::{Hexahedron20, Hexahedron27};
    use rtx_fea::elements::{FiniteElement, NaturalCoords};

    #[test]
    fn test_hex20_numerical_integration() {
        // RED: Test numerical integration over element
        let hex20 = Hexahedron20::new();
        let quad_rule = hex20.quadrature_rule(Some(3)).unwrap();

        // Integrate constant function f=1 over reference element [-1,1]^3
        let mut integral = 0.0;
        for point in &quad_rule.points {
            let coords =
                NaturalCoords::new_3d(point.coords.xi(), point.coords.eta(), point.coords.zeta());
            let _shape = hex20.shape_functions(&coords).unwrap();
            integral += 1.0 * point.weight;
        }

        // GREEN: Volume of reference hex should be 8
        assert!((integral - 8.0).abs() < 1e-10);
    }

    #[test]
    fn test_hex27_derivative_consistency() {
        // RED: Test that shape function derivatives are consistent
        let hex27 = Hexahedron27::new();

        let test_points = vec![(0.1, 0.2, 0.3), (-0.3, 0.4, -0.2)];

        for (x, y, z) in test_points {
            let coords = NaturalCoords::new_3d(x, y, z);
            let shape_eval = hex27.shape_functions(&coords).unwrap();

            // GREEN: Sum of derivatives should be zero (constant preservation)
            let mut sum_dxi = 0.0;
            let mut sum_deta = 0.0;
            let mut sum_dzeta = 0.0;

            for i in 0..27 {
                sum_dxi += shape_eval.derivative(i, 0).unwrap();
                sum_deta += shape_eval.derivative(i, 1).unwrap();
                sum_dzeta += shape_eval.derivative(i, 2).unwrap();
            }

            assert!(sum_dxi.abs() < 1e-10);
            assert!(sum_deta.abs() < 1e-10);
            assert!(sum_dzeta.abs() < 1e-10);
        }
    }
}