Tri6.hpp

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#pragma once
// Auto-generated by tools/gen_shape_functions -- DO NOT EDIT
// Element: Tri6
// Regenerate: /usr/bin/python3 -m tools.gen_shape_functions.generate
 
#include "DNDS/Defines.hpp"
#include "Geom/Geometric.hpp"
#include "Geom/ElemEnum.hpp"
#include "Geom/ElementTraitsBase.hpp"
 
namespace DNDS::Geom::Elem
{
 
    // Forward declaration (primary template is in ElementTraitsBase.hpp)
    template <ElemType> struct ShapeFuncImpl;
 
    // <GEN_SHAPE_FUNCS_BEGIN>
    template <>
    struct ShapeFuncImpl<Tri6>
    {
        template <class TPoint, class TArray>
        DNDS_DEVICE_CALLABLE static inline void Diff0(const TPoint &p, TArray &&v)
        {
            t_real xi = p[0];
            t_real et = p[1];
            const t_real _t0 = et + xi - 1;
            const t_real _t1 = 2*et;
            const t_real _t2 = 2*xi - 1;
            const t_real _t3 = -_t0;
            const t_real _t4 = 4*xi;
            v(0, 0) = _t0*(_t1 + _t2);
            v(0, 1) = _t2*xi;
            v(0, 2) = et*(_t1 - 1);
            v(0, 3) = _t3*_t4;
            v(0, 4) = _t4*et;
            v(0, 5) = 4*_t3*et;
        }
 
        template <class TPoint, class TArray>
        DNDS_DEVICE_CALLABLE static inline void Diff1(const TPoint &p, TArray &&v)
        {
            t_real xi = p[0];
            t_real et = p[1];
            const t_real _t0 = 4*et;
            const t_real _t1 = 4*xi;
            const t_real _t2 = _t0 + _t1 - 3;
            v(0, 0) = _t2;
            v(0, 1) = _t1 - 1;
            v(0, 3) = -_t0 - 8*xi + 4;
            v(0, 4) = _t0;
            v(0, 5) = -_t0;
            v(1, 0) = _t2;
            v(1, 2) = _t0 - 1;
            v(1, 3) = -_t1;
            v(1, 4) = _t1;
            v(1, 5) = -_t1 - 8*et + 4;
        }
 
        template <class TPoint, class TArray>
        DNDS_DEVICE_CALLABLE static inline void Diff2(const TPoint &p, TArray &&v)
        {
            t_real xi = p[0];
            t_real et = p[1];
            v(0, 0) = 4;
            v(0, 1) = 4;
            v(0, 3) = -8;
            v(1, 0) = 4;
            v(1, 3) = -4;
            v(1, 4) = 4;
            v(1, 5) = -4;
            v(2, 0) = 4;
            v(2, 2) = 4;
            v(2, 5) = -8;
        }
 
        template <class TPoint, class TArray>
        DNDS_DEVICE_CALLABLE static inline void Diff3(const TPoint &p, TArray &&v)
        {
            t_real xi = p[0];
            t_real et = p[1];
            // all zero
        }
    };
    // <GEN_SHAPE_FUNCS_END>
 
 
    /**
     * @brief Element traits for 6-node quadratic triangle (Tri6)
     *
     * Tri6 is a high-order 2D triangular element with:
     * - 3 corner nodes (vertices)
     * - 3 edge mid-nodes
     *
     * Used for high-order finite element methods and curved boundary representation.
     */
    template <>
    struct ElementTraits<Tri6>
    {
        // ============================================================
        // Core Element Identification
        // ============================================================
 
        static constexpr ElemType elemType = Tri6;
        static constexpr int dim = 2;
        static constexpr int order = 2;
        static constexpr int numVertices = 3;
        static constexpr int numNodes = 6;
        static constexpr int numFaces = 3;
        static constexpr ParamSpace paramSpace = TriSpace;
        static constexpr t_real paramSpaceVol = 0.5;
 
        // ============================================================
        // Geometry Definition
        // ============================================================
 
        /**
         * @brief Standard coordinates of nodes in parametric space
         *
         * Reference triangle with nodes:
         * Nodes 0-2: vertices (same as Tri3)
         * Nodes 3-5: edge midpoints
         */
        static constexpr std::array<t_real, 3 * 6> standardCoords = {
            0,   0,   0,   // Node 0: vertex
            1,   0,   0,   // Node 1: vertex
            0,   1,   0,   // Node 2: vertex
            0.5, 0,   0,   // Node 3: edge 0-1 midpoint
            0.5, 0.5, 0,   // Node 4: edge 1-2 midpoint
            0,   0.5, 0};  // Node 5: edge 2-0 midpoint
 
        // ============================================================
        // Face/Edge Definitions
        // ============================================================
 
        /**
         * @brief Get the element type of a face (edge)
         * @return Line3 (all edges are quadratic lines with 3 nodes)
         */
        static constexpr ElemType GetFaceType(t_index /*iFace*/) { return Line3; }
 
        /**
         * @brief Node indices for each face (edge)
         *
         * Each edge has 3 nodes: 2 vertices + 1 midpoint
         * Edge 0: nodes 0-1-3
         * Edge 1: nodes 1-2-4
         * Edge 2: nodes 2-0-5
         */
        static constexpr std::array<std::array<t_index, 10>, 3> faceNodes = {{
            {0, 1, 3},     // Edge 0: bottom
            {1, 2, 4},     // Edge 1: hypotenuse
            {2, 0, 5}}};   // Edge 2: left
 
        // ============================================================
        // Order Elevation (P-Refinement)
        // ============================================================
 
        /// @brief Element type after order elevation (O2 has no higher elevation defined)
        static constexpr ElemType elevatedType = UnknownElem;
 
        /// @brief Number of additional nodes created during elevation (none for O2)
        static constexpr int numElevNodes = 0;
 
        // ============================================================
        // Bisection (Adaptive Refinement)
        // ============================================================
 
        /// @brief Number of sub-elements created when bisecting (4 Tri3 elements)
        static constexpr int numBisect = 4;
 
        /// @brief Number of bisection variants (only 1 way to uniformly bisect)
        static constexpr int numBisectVariants = 1;
 
        /**
         * @brief Get the element type of a sub-element after bisection
         * @return Tri3 (all sub-elements are linear triangles)
         */
        static constexpr ElemType GetBisectElemType(t_index /*i*/) { return Tri3; }
 
        /**
         * @brief Node indices for each sub-element created by bisection
         *
         * Bisecting creates 4 sub-triangles by connecting edge midpoints:
         *   Sub-element 0: corner at node 0
         *   Sub-element 1: corner at node 1
         *   Sub-element 2: corner at node 2
         *   Sub-element 3: center triangle
         */
        static constexpr std::array<tBisectSub, 4> bisectElements = {{
            {0, 3, 5},     // Corner triangle at vertex 0
            {3, 1, 4},     // Corner triangle at vertex 1
            {5, 3, 4},     // Center triangle
            {5, 4, 2}}};   // Corner triangle at vertex 2
 
        // ============================================================
        // VTK/Visualization Support
        // ============================================================
 
        /// @brief VTK cell type identifier (22 = VTK_QUADRATIC_TRIANGLE)
        static constexpr int vtkCellType = 22;
 
        /**
         * @brief VTK node ordering map
         *
         * VTK uses the same ordering as DNDS for Tri6:
         *   VTK nodes 0-2 = corner nodes 0-2
         *   VTK nodes 3-5 = edge mid-nodes 3-5
         */
        static constexpr std::array<int, 6> vtkNodeOrder = {0, 1, 2, 3, 4, 5};
    };
 
} // namespace DNDS::Geom::Elem