DNDSR/doxygen/Pyramid14_8hpp_source.html

#pragma once

// Auto-generated by tools/gen_shape_functions -- DO NOT EDIT

// Element: Pyramid14

// 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<Pyramid14>

    {

        template <class TPoint, class TArray>


        static inline void Diff0(const TPoint &p, TArray &&v)

        {

            t_real xi = p[0];

            t_real et = p[1];

            t_real zt = p[2];

            // singularity guard

            if (std::abs(1 - zt) < 1e-15)

                zt -= DNDS::signP(1 - zt) * 1e-15;

            const t_real _t0 = zt - 1;

            const t_real _t1 = _t0 + xi;

            const t_real _t2 = _t0 + et;

            const t_real _t3 = ((0.25))*_t2;

            const t_real _t4 = _t1*_t3;

            const t_real _t5 = 2*zt - 1;

            const t_real _t6 = _t5/((_t0) * (_t0) * (_t0));

            const t_real _t7 = _t6*xi;

            const t_real _t8 = _t7*et;

            const t_real _t9 = 1 - zt;

            const t_real _t10 = _t9 + xi;

            const t_real _t11 = _t10*_t7;

            const t_real _t12 = _t11*et;

            const t_real _t13 = _t9 + et;

            const t_real _t14 = ((0.25))*_t13;

            const t_real _t15 = _t1*_t14;

            const t_real _t16 = ((_t0) * (_t0));

            const t_real _t17 = -_t16;

            const t_real _t18 = _t6*(_t17 + ((xi) * (xi)));

            const t_real _t19 = ((0.5))*_t18*et;

            const t_real _t20 = _t17 + ((et) * (et));

            const t_real _t21 = ((0.5))*_t20;

            const t_real _t22 = (((_t5) * (_t5)) - 1)/_t16;

            const t_real _t23 = _t10*_t22;

            v(0, 0) = _t4*_t8;

            v(0, 1) = _t12*_t3;

            v(0, 2) = _t12*_t14;

            v(0, 3) = _t15*_t8;

            v(0, 4) = _t5*zt;

            v(0, 5) = -_t19*_t2;

            v(0, 6) = -_t11*_t21;

            v(0, 7) = -_t13*_t19;

            v(0, 8) = -_t1*_t21*_t7;

            v(0, 9) = -_t22*_t4;

            v(0, 10) = _t23*_t3;

            v(0, 11) = -_t14*_t23;

            v(0, 12) = _t15*_t22;

            v(0, 13) = _t18*_t20;

        }


        template <class TPoint, class TArray>


        static inline void Diff1(const TPoint &p, TArray &&v)

        {

            t_real xi = p[0];

            t_real et = p[1];

            t_real zt = p[2];

            // singularity guard

            if (std::abs(1 - zt) < 1e-15)

                zt -= DNDS::signP(1 - zt) * 1e-15;

            const t_real _t0 = 2*xi;

            const t_real _t1 = zt - 1;

            const t_real _t2 = _t0 + _t1;

            const t_real _t3 = _t1 + et;

            const t_real _t4 = 2*zt - 1;

            const t_real _t5 = (1.0 / ((_t1) * (_t1) * (_t1)));

            const t_real _t6 = _t4*_t5;

            const t_real _t7 = _t6*et;

            const t_real _t8 = ((0.25))*_t7;

            const t_real _t9 = _t3*_t8;

            const t_real _t10 = 1 - zt;

            const t_real _t11 = _t0 + _t10;

            const t_real _t12 = _t10 + et;

            const t_real _t13 = _t12*_t8;

            const t_real _t14 = _t3*xi;

            const t_real _t15 = ((et) * (et));

            const t_real _t16 = ((_t1) * (_t1));

            const t_real _t17 = -_t16;

            const t_real _t18 = _t15 + _t17;

            const t_real _t19 = _t18*_t6;

            const t_real _t20 = ((0.5))*_t19;

            const t_real _t21 = _t12*xi;

            const t_real _t22 = zt/_t1;

            const t_real _t23 = _t1 + xi;

            const t_real _t24 = 2*et;

            const t_real _t25 = _t1 + _t24;

            const t_real _t26 = _t6*xi;

            const t_real _t27 = ((0.25))*_t26;

            const t_real _t28 = _t25*_t27;

            const t_real _t29 = _t10 + xi;

            const t_real _t30 = _t10 + _t24;

            const t_real _t31 = _t27*_t30;

            const t_real _t32 = ((xi) * (xi));

            const t_real _t33 = _t17 + _t32;

            const t_real _t34 = _t33*_t6;

            const t_real _t35 = ((0.5))*_t34;

            const t_real _t36 = _t29*et;

            const t_real _t37 = _t23*et;

            const t_real _t38 = 4*zt;

            const t_real _t39 = _t38 - 3;

            const t_real _t40 = _t23*_t3;

            const t_real _t41 = _t14 + _t37;

            const t_real _t42 = (1.0 / ((_t1) * (_t1) * (_t1) * (_t1)));

            const t_real _t43 = ((0.25))*_t42*et*xi;

            const t_real _t44 = _t29*_t3;

            const t_real _t45 = _t14 + _t36;

            const t_real _t46 = _t12*_t29;

            const t_real _t47 = _t21 + _t36;

            const t_real _t48 = _t12*_t23;

            const t_real _t49 = _t21 + _t37;

            const t_real _t50 = -_t39;

            const t_real _t51 = _t3*_t33;

            const t_real _t52 = 2*_t32;

            const t_real _t53 = _t33*et;

            const t_real _t54 = ((0.5))*_t42;

            const t_real _t55 = _t54*et;

            const t_real _t56 = _t18*_t29;

            const t_real _t57 = 2*_t15;

            const t_real _t58 = _t18*xi;

            const t_real _t59 = _t54*xi;

            const t_real _t60 = _t12*_t33;

            const t_real _t61 = _t18*_t23;

            const t_real _t62 = _t1*_t4;

            const t_real _t63 = ((_t4) * (_t4)) - 1;

            const t_real _t64 = ((0.25))*_t63;

            const t_real _t65 = (1.0 / (_t16));

            const t_real _t66 = _t15*_t32*_t42;

            v(0, 0) = _t2*_t9;

            v(0, 1) = _t11*_t9;

            v(0, 2) = _t11*_t13;

            v(0, 3) = _t13*_t2;

            v(0, 5) = -_t14*_t7;

            v(0, 6) = -_t11*_t20;

            v(0, 7) = -_t21*_t7;

            v(0, 8) = -_t2*_t20;

            v(0, 9) = -_t22*_t3;

            v(0, 10) = _t22*_t3;

            v(0, 11) = -_t12*_t22;

            v(0, 12) = _t12*_t22;

            v(0, 13) = _t0*_t19;

            v(1, 0) = _t23*_t28;

            v(1, 1) = _t28*_t29;

            v(1, 2) = _t29*_t31;

            v(1, 3) = _t23*_t31;

            v(1, 5) = -_t25*_t35;

            v(1, 6) = -_t26*_t36;

            v(1, 7) = -_t30*_t35;

            v(1, 8) = -_t26*_t37;

            v(1, 9) = -_t22*_t23;

            v(1, 10) = _t22*_t29;

            v(1, 11) = -_t22*_t29;

            v(1, 12) = _t22*_t23;

            v(1, 13) = _t24*_t34;

            v(2, 0) = _t43*(_t23*_t3*_t39 - _t4*(2*_t40 + _t41));

            v(2, 1) = _t43*(_t29*_t3*_t39 - _t4*(2*_t44 + _t45));

            v(2, 2) = _t43*(_t12*_t29*_t39 - _t4*(2*_t46 + _t47));

            v(2, 3) = _t43*(_t12*_t23*_t39 - _t4*(2*_t48 + _t49));

            v(2, 4) = _t38 - 1;

            v(2, 5) = _t55*(_t4*(_t3*_t52 + _t51 + _t53) + _t50*_t51);

            v(2, 6) = _t59*(_t4*(_t29*_t57 + _t56 + _t58) + _t50*_t56);

            v(2, 7) = _t55*(_t4*(_t12*_t52 + _t53 + _t60) + _t50*_t60);

            v(2, 8) = _t59*(_t4*(_t23*_t57 + _t58 + _t61) + _t50*_t61);

            v(2, 9) = _t5*(-_t40*_t62 + ((0.25))*_t41*_t63);

            v(2, 10) = _t5*(_t44*_t62 - _t45*_t64);

            v(2, 11) = _t5*(-_t46*_t62 + ((0.25))*_t47*_t63);

            v(2, 12) = _t5*(_t48*_t62 - _t49*_t64);

            v(2, 13) = _t15*_t65 + _t32*_t65 - _t38*_t66 + _t39 + _t66;

        }


        template <class TPoint, class TArray>


        static inline void Diff2(const TPoint &p, TArray &&v)

        {

            t_real xi = p[0];

            t_real et = p[1];

            t_real zt = p[2];

            // singularity guard

            if (std::abs(1 - zt) < 1e-15)

                zt -= DNDS::signP(1 - zt) * 1e-15;

            const t_real _t0 = zt - 1;

            const t_real _t1 = _t0 + et;

            const t_real _t2 = 2*zt;

            const t_real _t3 = _t2 - 1;

            const t_real _t4 = _t3/((_t0) * (_t0) * (_t0));

            const t_real _t5 = _t4*et;

            const t_real _t6 = _t1*_t5;

            const t_real _t7 = ((0.5))*_t6;

            const t_real _t8 = 1 - zt;

            const t_real _t9 = _t8 + et;

            const t_real _t10 = _t5*_t9;

            const t_real _t11 = ((0.5))*_t10;

            const t_real _t12 = ((et) * (et));

            const t_real _t13 = ((_t0) * (_t0));

            const t_real _t14 = -_t13;

            const t_real _t15 = _t4*(_t12 + _t14);

            const t_real _t16 = -_t15;

            const t_real _t17 = _t0 + xi;

            const t_real _t18 = _t4*xi;

            const t_real _t19 = _t17*_t18;

            const t_real _t20 = ((0.5))*_t19;

            const t_real _t21 = _t8 + xi;

            const t_real _t22 = _t18*_t21;

            const t_real _t23 = ((0.5))*_t22;

            const t_real _t24 = ((xi) * (xi));

            const t_real _t25 = _t4*(_t14 + _t24);

            const t_real _t26 = -_t25;

            const t_real _t27 = ((zt) * (zt));

            const t_real _t28 = _t27*xi;

            const t_real _t29 = 2*_t28;

            const t_real _t30 = -_t2 + _t27 + 1;

            const t_real _t31 = _t29 + _t30;

            const t_real _t32 = -xi;

            const t_real _t33 = xi*zt;

            const t_real _t34 = et*zt;

            const t_real _t35 = 6*_t34;

            const t_real _t36 = _t35*xi;

            const t_real _t37 = _t32 - _t33 + _t36;

            const t_real _t38 = -et;

            const t_real _t39 = _t27*et;

            const t_real _t40 = 2*_t39;

            const t_real _t41 = -_t34 + _t38 + _t40;

            const t_real _t42 = ((zt) * (zt) * (zt) * (zt) * (zt));

            const t_real _t43 = ((zt) * (zt) * (zt));

            const t_real _t44 = ((zt) * (zt) * (zt) * (zt));

            const t_real _t45 = (1.0 / (-10*_t27 + _t42 + 10*_t43 - 5*_t44 + 5*zt - 1));

            const t_real _t46 = et*xi;

            const t_real _t47 = ((0.5))*_t45*_t46;

            const t_real _t48 = -_t27 + _t3;

            const t_real _t49 = _t48 + et;

            const t_real _t50 = -_t40;

            const t_real _t51 = _t34 + _t50;

            const t_real _t52 = _t30 + xi;

            const t_real _t53 = -_t29;

            const t_real _t54 = _t33 + _t36 + _t53;

            const t_real _t55 = _t48 + xi;

            const t_real _t56 = _t24*_t35;

            const t_real _t57 = _t24*zt;

            const t_real _t58 = _t24*_t27;

            const t_real _t59 = _t24 + _t57 - 2*_t58;

            const t_real _t60 = _t2*et;

            const t_real _t61 = -_t60;

            const t_real _t62 = _t39 + _t61 + et;

            const t_real _t63 = _t45*et;

            const t_real _t64 = 6*_t12*_t33;

            const t_real _t65 = _t12*zt;

            const t_real _t66 = _t12*_t27;

            const t_real _t67 = _t12 + _t65 - 2*_t66;

            const t_real _t68 = _t2*xi;

            const t_real _t69 = -_t28 + _t32 + _t68;

            const t_real _t70 = _t45*xi;

            const t_real _t71 = _t38 - _t39 + _t60;

            const t_real _t72 = -_t68;

            const t_real _t73 = _t28 + _t72 + xi;

            const t_real _t74 = 3*zt;

            const t_real _t75 = 3*_t27;

            const t_real _t76 = _t43 + _t74 - _t75 - 1;

            const t_real _t77 = 2/_t76;

            const t_real _t78 = _t77*(-_t46 - _t76);

            const t_real _t79 = -_t74;

            const t_real _t80 = _t77*(-_t43 + _t46 + _t75 + _t79 + 1);

            const t_real _t81 = _t17*et;

            const t_real _t82 = _t1*xi + _t46;

            const t_real _t83 = ((0.25))*_t4;

            const t_real _t84 = _t21*et;

            const t_real _t85 = _t46 + _t9*xi;

            const t_real _t86 = 2*et;

            const t_real _t87 = 2*xi;

            const t_real _t88 = zt/_t0;

            const t_real _t89 = -_t88;

            const t_real _t90 = 4*_t34;

            const t_real _t91 = 4*_t39;

            const t_real _t92 = -_t90 + _t91;

            const t_real _t93 = 8*_t34;

            const t_real _t94 = _t93*xi;

            const t_real _t95 = _t94 - 2*et*xi;

            const t_real _t96 = _t31 + _t72;

            const t_real _t97 = 4*zt;

            const t_real _t98 = 6*_t27 - 4*_t43 + _t44 - _t97 + 1;

            const t_real _t99 = (1.0 / (_t98));

            const t_real _t100 = ((0.25))*_t99;

            const t_real _t101 = _t100*xi;

            const t_real _t102 = 2*_t46 - _t94;

            const t_real _t103 = _t30 + _t53 + _t68;

            const t_real _t104 = _t90 - _t91;

            const t_real _t105 = _t24*et;

            const t_real _t106 = -_t57 + _t58 + _t98;

            const t_real _t107 = 3 - _t97;

            const t_real _t108 = 4*xi;

            const t_real _t109 = _t79 + 3;

            const t_real _t110 = (1.0 / ((_t0) * (_t0) * (_t0) * (_t0)));

            const t_real _t111 = _t110*_t46;

            const t_real _t112 = _t74 - 3;

            const t_real _t113 = (1.0 / (_t30));

            const t_real _t114 = (1.0 / (_t13));

            const t_real _t115 = _t110*_t24;

            const t_real _t116 = _t30 + _t95;

            const t_real _t117 = _t40 + _t61;

            const t_real _t118 = 4*_t33;

            const t_real _t119 = 4*_t28;

            const t_real _t120 = -_t118 + _t119;

            const t_real _t121 = _t100*et;

            const t_real _t122 = _t118 - _t119;

            const t_real _t123 = _t102 + _t30;

            const t_real _t124 = _t50 + _t60;

            const t_real _t125 = 4*et;

            const t_real _t126 = _t12*xi;

            const t_real _t127 = -_t65 + _t66 + _t98;

            const t_real _t128 = _t30 + et;

            const t_real _t129 = _t110*_t12;

            v(0, 0) = _t7;

            v(0, 1) = _t7;

            v(0, 2) = _t11;

            v(0, 3) = _t11;

            v(0, 5) = -_t6;

            v(0, 6) = _t16;

            v(0, 7) = -_t10;

            v(0, 8) = _t16;

            v(0, 13) = 2*_t15;

            v(1, 0) = _t20;

            v(1, 1) = _t23;

            v(1, 2) = _t23;

            v(1, 3) = _t20;

            v(1, 5) = _t26;

            v(1, 6) = -_t22;

            v(1, 7) = _t26;

            v(1, 8) = -_t19;

            v(1, 13) = 2*_t25;

            v(2, 0) = _t47*(_t31 + _t37 + _t41);

            v(2, 1) = _t47*(_t29 + _t37 + _t49 + _t51);

            v(2, 2) = _t47*(_t51 + _t52 + _t54 + et);

            v(2, 3) = _t47*(_t41 + _t54 + _t55);

            v(2, 4) = 4;

            v(2, 5) = _t63*(-_t56 + _t59 + _t62);

            v(2, 6) = _t70*(-_t64 - _t67 - _t69);

            v(2, 7) = _t63*(-_t56 - _t59 - _t71);

            v(2, 8) = _t70*(-_t64 + _t67 + _t73);

            v(2, 9) = _t78;

            v(2, 10) = _t80;

            v(2, 11) = _t78;

            v(2, 12) = _t80;

            v(2, 13) = 2*_t45*(6*_t12*_t24*zt + 2*_t12*zt - _t12 + 2*_t24*zt - _t24 - 20*_t27 + 2*_t42 + 20*_t43 - 10*_t44 - _t58 - _t66 + 10*zt - 2);

            v(3, 0) = _t83*(_t1*_t17 + _t81 + _t82);

            v(3, 1) = _t83*(_t1*_t21 + _t82 + _t84);

            v(3, 2) = _t83*(_t21*_t9 + _t84 + _t85);

            v(3, 3) = _t83*(_t17*_t9 + _t81 + _t85);

            v(3, 5) = _t18*(-_t0 - _t86);

            v(3, 6) = _t5*(-_t8 - _t87);

            v(3, 7) = _t18*(-_t8 - _t86);

            v(3, 8) = _t5*(-_t0 - _t87);

            v(3, 9) = _t89;

            v(3, 10) = _t88;

            v(3, 11) = _t89;

            v(3, 12) = _t88;

            v(3, 13) = 4*_t4*_t46;

            v(4, 0) = _t101*(-_t92 - _t95 - _t96);

            v(4, 1) = _t101*(_t102 + _t103 + _t92);

            v(4, 2) = _t101*(-_t103 - _t104 - _t95);

            v(4, 3) = _t101*(_t102 + _t104 + _t96);

            v(4, 5) = _t99*(-_t105 + _t106 + _t24*_t90 + _t71);

            v(4, 6) = _t111*(_t107*_t21 + _t3*(_t108 + _t109));

            v(4, 7) = _t99*(-_t105 - _t106 + 4*_t24*et*zt - _t62);

            v(4, 8) = _t111*(_t107*_t17 + _t3*(_t108 + _t112));

            v(4, 9) = _t113*_t55;

            v(4, 10) = -_t113*_t52;

            v(4, 11) = _t113*_t52;

            v(4, 12) = -_t113*_t55;

            v(4, 13) = _t114*_t86 + _t115*_t86 - _t115*_t93;

            v(5, 0) = _t121*(-_t116 - _t117 - _t120);

            v(5, 1) = _t121*(_t117 + _t122 + _t123);

            v(5, 2) = _t121*(-_t116 - _t122 - _t124);

            v(5, 3) = _t121*(_t120 + _t123 + _t124);

            v(5, 5) = _t111*(_t1*_t107 + _t3*(_t112 + _t125));

            v(5, 6) = _t99*(4*_t12*xi*zt - _t126 - _t127 - _t73);

            v(5, 7) = _t111*(_t107*_t9 + _t3*(_t109 + _t125));

            v(5, 8) = _t99*(_t118*_t12 - _t126 + _t127 + _t69);

            v(5, 9) = _t113*_t49;

            v(5, 10) = -_t113*_t49;

            v(5, 11) = _t113*_t128;

            v(5, 12) = -_t113*_t128;

            v(5, 13) = _t114*_t87 - 8*_t129*_t33 + _t129*_t87;

        }


        template <class TPoint, class TArray>


        static inline void Diff3(const TPoint &p, TArray &&v)

        {

            t_real xi = p[0];

            t_real et = p[1];

            t_real zt = p[2];

            // singularity guard

            if (std::abs(1 - zt) < 1e-15)

                zt -= DNDS::signP(1 - zt) * 1e-15;

            const t_real _t0 = 2*et;

            const t_real _t1 = _t0*xi;

            const t_real _t2 = xi*zt;

            const t_real _t3 = 8*et;

            const t_real _t4 = _t2*_t3;

            const t_real _t5 = 2*zt;

            const t_real _t6 = ((zt) * (zt));

            const t_real _t7 = -_t5 + _t6 + 1;

            const t_real _t8 = _t1 + _t4 + _t7;

            const t_real _t9 = -_t0;

            const t_real _t10 = 2*xi;

            const t_real _t11 = _t10*_t6;

            const t_real _t12 = _t11 + _t9;

            const t_real _t13 = _t0*_t6;

            const t_real _t14 = -_t10;

            const t_real _t15 = _t13 + _t14;

            const t_real _t16 = 6*zt;

            const t_real _t17 = ((zt) * (zt) * (zt));

            const t_real _t18 = ((zt) * (zt) * (zt) * (zt));

            const t_real _t19 = ((zt) * (zt) * (zt) * (zt) * (zt));

            const t_real _t20 = (1.0 / (-_t16 - 20*_t17 + 15*_t18 - 6*_t19 + 15*_t6 + ((zt) * (zt) * (zt) * (zt) * (zt) * (zt)) + 1));

            const t_real _t21 = et*xi;

            const t_real _t22 = ((1.5))*_t20*_t21;

            const t_real _t23 = -_t13;

            const t_real _t24 = _t0 + _t23;

            const t_real _t25 = -_t6;

            const t_real _t26 = _t5 - 1;

            const t_real _t27 = _t25 + _t26;

            const t_real _t28 = _t1 + _t27 + _t4;

            const t_real _t29 = -_t11;

            const t_real _t30 = _t10 + _t29;

            const t_real _t31 = ((xi) * (xi));

            const t_real _t32 = 2*_t31;

            const t_real _t33 = _t32*_t6;

            const t_real _t34 = -et;

            const t_real _t35 = _t6*et;

            const t_real _t36 = -_t35;

            const t_real _t37 = _t0*zt;

            const t_real _t38 = _t31*zt;

            const t_real _t39 = _t0*_t31 + _t3*_t38 + _t34 + _t36 + _t37;

            const t_real _t40 = 3*_t20;

            const t_real _t41 = _t40*et;

            const t_real _t42 = ((et) * (et));

            const t_real _t43 = 2*_t42;

            const t_real _t44 = _t43*_t6;

            const t_real _t45 = -_t44;

            const t_real _t46 = -xi;

            const t_real _t47 = _t6*xi;

            const t_real _t48 = -_t47;

            const t_real _t49 = _t10*zt;

            const t_real _t50 = 8*_t42;

            const t_real _t51 = _t10*_t42 + _t2*_t50 + _t46 + _t48 + _t49;

            const t_real _t52 = _t40*xi;

            const t_real _t53 = -_t33;

            const t_real _t54 = 4*zt;

            const t_real _t55 = (1.0 / (-4*_t17 + _t18 - _t54 + 6*_t6 + 1));

            const t_real _t56 = 6*_t21*_t55;

            const t_real _t57 = -_t56;

            const t_real _t58 = zt - 1;

            const t_real _t59 = _t0 + _t58;

            const t_real _t60 = _t26/((_t58) * (_t58) * (_t58));

            const t_real _t61 = ((0.5))*_t60;

            const t_real _t62 = _t59*_t61;

            const t_real _t63 = -zt;

            const t_real _t64 = _t63 + 1;

            const t_real _t65 = _t0 + _t64;

            const t_real _t66 = _t61*_t65;

            const t_real _t67 = -_t0*_t60;

            const t_real _t68 = 4*et;

            const t_real _t69 = _t10 + _t58;

            const t_real _t70 = _t61*_t69;

            const t_real _t71 = _t10 + _t64;

            const t_real _t72 = _t61*_t71;

            const t_real _t73 = -_t10*_t60;

            const t_real _t74 = 4*xi;

            const t_real _t75 = _t58 + xi;

            const t_real _t76 = _t54 - 3;

            const t_real _t77 = 3*zt;

            const t_real _t78 = _t77 - 3;

            const t_real _t79 = _t74 + _t78;

            const t_real _t80 = (1.0 / ((_t58) * (_t58) * (_t58) * (_t58)));

            const t_real _t81 = _t80*xi;

            const t_real _t82 = ((0.5))*_t81;

            const t_real _t83 = _t82*(-_t26*_t79 + _t75*_t76);

            const t_real _t84 = _t64 + xi;

            const t_real _t85 = 3 - _t77;

            const t_real _t86 = _t74 + _t85;

            const t_real _t87 = _t82*(-_t26*_t86 + _t76*_t84);

            const t_real _t88 = (1.0 / ((_t58) * (_t58)));

            const t_real _t89 = _t31*_t80;

            const t_real _t90 = 4*_t31*_t80*zt - _t88 - _t89;

            const t_real _t91 = -_t76;

            const t_real _t92 = 2*_t88;

            const t_real _t93 = 12*et;

            const t_real _t94 = _t2*_t93;

            const t_real _t95 = _t7 + _t94;

            const t_real _t96 = -_t2;

            const t_real _t97 = _t46 + _t96;

            const t_real _t98 = 4*_t35;

            const t_real _t99 = -_t37 + _t98;

            const t_real _t100 = (1.0 / (10*_t17 - 5*_t18 + _t19 - 10*_t6 + 5*zt - 1));

            const t_real _t101 = ((0.5))*_t100;

            const t_real _t102 = _t101*xi;

            const t_real _t103 = _t27 + _t94;

            const t_real _t104 = _t0 + _t37 - _t98;

            const t_real _t105 = _t2 + _t29 + xi;

            const t_real _t106 = _t54*et;

            const t_real _t107 = _t38*_t93;

            const t_real _t108 = _t31 + _t38 + _t53;

            const t_real _t109 = _t16*xi;

            const t_real _t110 = 2*_t6;

            const t_real _t111 = -_t110 + zt + 1;

            const t_real _t112 = _t1*_t100;

            const t_real _t113 = _t110 + _t63 - 1;

            const t_real _t114 = (1.0 / (_t17 - 3*_t6 + _t77 - 1));

            const t_real _t115 = _t10*_t114;

            const t_real _t116 = -_t115;

            const t_real _t117 = 4*_t47;

            const t_real _t118 = _t117 - _t49;

            const t_real _t119 = et*zt;

            const t_real _t120 = -_t119;

            const t_real _t121 = _t120 + _t34;

            const t_real _t122 = _t101*et;

            const t_real _t123 = _t119 + _t23 + et;

            const t_real _t124 = _t10 - _t117 + _t49;

            const t_real _t125 = _t16*et;

            const t_real _t126 = _t54*xi;

            const t_real _t127 = 12*_t2*_t42;

            const t_real _t128 = _t42*zt;

            const t_real _t129 = _t128 + _t42 + _t45;

            const t_real _t130 = _t0*_t114;

            const t_real _t131 = -_t130;

            const t_real _t132 = _t58 + et;

            const t_real _t133 = _t68 + _t78;

            const t_real _t134 = _t80*et;

            const t_real _t135 = ((0.5))*_t134;

            const t_real _t136 = _t135*(_t132*_t76 - _t133*_t26);

            const t_real _t137 = _t64 + et;

            const t_real _t138 = _t68 + _t85;

            const t_real _t139 = _t135*(_t137*_t76 - _t138*_t26);

            const t_real _t140 = 4*_t42*_t80*zt - _t42*_t80 - _t88;

            const t_real _t141 = -(0.5)*zt;

            const t_real _t142 = ((0.25))*_t6;

            const t_real _t143 = _t120 + _t141 + _t142 + _t35 + (0.25);

            const t_real _t144 = _t21*_t54;

            const t_real _t145 = _t144 - et*xi;

            const t_real _t146 = _t47 + _t96;

            const t_real _t147 = _t2 + _t48;

            const t_real _t148 = -_t144 + _t21;

            const t_real _t149 = _t119 + _t141 + _t142 + _t36 + (0.25);

            const t_real _t150 = _t106 + _t34;

            const t_real _t151 = _t6 + _t63;

            const t_real _t152 = _t10*_t55;

            const t_real _t153 = _t25 + zt;

            const t_real _t154 = _t126 + _t46;

            const t_real _t155 = _t0*_t55;

            const t_real _t156 = (1.0 / (_t7));

            const t_real _t157 = -_t156;

            v(2, 0) = _t22*(-_t12 - _t15 - _t8);

            v(2, 1) = _t22*(-_t11 - _t14 - _t24 - _t28);

            v(2, 2) = _t22*(-_t24 - _t30 - _t8);

            v(2, 3) = _t22*(-_t13 - _t28 - _t30 - _t9);

            v(2, 5) = _t41*(-_t32 + _t33 + _t39);

            v(2, 6) = _t52*(_t43 + _t45 + _t51);

            v(2, 7) = _t41*(_t32 + _t39 + _t53);

            v(2, 8) = _t52*(-_t43 + _t44 + _t51);

            v(2, 9) = _t56;

            v(2, 10) = _t57;

            v(2, 11) = _t56;

            v(2, 12) = _t57;

            v(2, 13) = 6*_t20*(-_t31*_t5 + _t31*_t6 + _t31 - _t32*_t42 - _t38*_t50 - _t42*_t5 + _t42*_t6 + _t42);

            v(3, 0) = _t62;

            v(3, 1) = _t62;

            v(3, 2) = _t66;

            v(3, 3) = _t66;

            v(3, 5) = -_t59*_t60;

            v(3, 6) = _t67;

            v(3, 7) = -_t60*_t65;

            v(3, 8) = _t67;

            v(3, 13) = _t60*_t68;

            v(4, 0) = _t70;

            v(4, 1) = _t72;

            v(4, 2) = _t72;

            v(4, 3) = _t70;

            v(4, 5) = _t73;

            v(4, 6) = -_t60*_t71;

            v(4, 7) = _t73;

            v(4, 8) = -_t60*_t69;

            v(4, 13) = _t60*_t74;

            v(5, 0) = _t83;

            v(5, 1) = _t87;

            v(5, 2) = _t87;

            v(5, 3) = _t83;

            v(5, 5) = _t90;

            v(5, 6) = _t81*(_t26*_t86 + _t84*_t91);

            v(5, 7) = _t90;

            v(5, 8) = _t81*(_t26*_t79 + _t75*_t91);

            v(5, 13) = _t32*_t80 - 8*_t89*zt + _t92;

            v(6, 0) = _t102*(_t12 + _t95 + _t97 + _t99);

            v(6, 1) = _t102*(_t103 + _t104 + _t11 + _t97);

            v(6, 2) = _t102*(_t104 + _t105 + _t95);

            v(6, 3) = _t102*(_t103 + _t105 + _t9 + _t99);

            v(6, 5) = _t100*(_t0 - _t106 - _t107 + _t108 + _t13);

            v(6, 6) = _t112*(-_t109 - _t111);

            v(6, 7) = _t100*(-_t106 - _t107 - _t108 - _t23 - _t9);

            v(6, 8) = _t112*(-_t109 - _t113);

            v(6, 9) = _t116;

            v(6, 10) = _t115;

            v(6, 11) = _t116;

            v(6, 12) = _t115;

            v(6, 13) = _t100*_t68*(_t16*_t31 + _t27);

            v(7, 0) = _t122*(_t118 + _t121 + _t15 + _t95);

            v(7, 1) = _t122*(_t103 + _t118 + _t123 + _t14);

            v(7, 2) = _t122*(_t123 + _t124 + _t95);

            v(7, 3) = _t122*(_t103 + _t121 + _t124 + _t13);

            v(7, 5) = _t112*(-_t113 - _t125);

            v(7, 6) = _t100*(-_t126 - _t127 - _t129 - _t14 - _t29);

            v(7, 7) = _t112*(-_t111 - _t125);

            v(7, 8) = _t100*(_t10 + _t11 - _t126 - _t127 + _t129);

            v(7, 9) = _t131;

            v(7, 10) = _t130;

            v(7, 11) = _t131;

            v(7, 12) = _t130;

            v(7, 13) = _t100*_t74*(_t16*_t42 + _t27);

            v(8, 0) = _t136;

            v(8, 1) = _t136;

            v(8, 2) = _t139;

            v(8, 3) = _t139;

            v(8, 5) = _t134*(_t132*_t91 + _t133*_t26);

            v(8, 6) = _t140;

            v(8, 7) = _t134*(_t137*_t91 + _t138*_t26);

            v(8, 8) = _t140;

            v(8, 13) = -8*_t128*_t80 + _t43*_t80 + _t92;

            v(9, 0) = _t55*(-_t143 - _t145 - _t146);

            v(9, 1) = _t55*(_t143 + _t147 + _t148);

            v(9, 2) = _t55*(-_t145 - _t147 - _t149);

            v(9, 3) = _t55*(_t146 + _t148 + _t149);

            v(9, 5) = _t152*(_t150 + _t151);

            v(9, 6) = _t155*(_t153 + _t154);

            v(9, 7) = _t152*(_t150 + _t153);

            v(9, 8) = _t155*(_t151 + _t154);

            v(9, 9) = _t156;

            v(9, 10) = _t157;

            v(9, 11) = _t156;

            v(9, 12) = _t157;

            v(9, 13) = _t134*_t74*(1 - _t54);

        }


    };


    // <GEN_SHAPE_FUNCS_END>


    /**

     * @brief Element traits for 14-node quadratic pyramid (Pyramid14)

     *

     * Pyramid14 is a high-order 3D pyramidal element with:

     * - 5 corner nodes (4 base + 1 apex)

     * - 8 edge mid-nodes

     * - 1 base face center node

     *

     * Used for high-order finite element methods with pyramidal elements.

     */

    template <>


    struct ElementTraits<Pyramid14>

    {

        // ============================================================

        // Core Element Identification

        // ============================================================


        static constexpr ElemType elemType = Pyramid14;

        static constexpr int dim = 3;

        static constexpr int order = 2;

        static constexpr int numVertices = 5;

        static constexpr int numNodes = 14;

        static constexpr int numFaces = 5;

        static constexpr ParamSpace paramSpace = PyramidSpace;

        static constexpr t_real paramSpaceVol = 4.0 / 3.0;


        // ============================================================

        // Geometry Definition

        // ============================================================


        /**

         * @brief Standard coordinates of nodes in parametric space

         *

         * Nodes 0-4: vertices (same as Pyramid5)

         * Nodes 5-8: base edge midpoints

         * Nodes 9-12: lateral edge midpoints

         * Node 13: base face center

         */


        static constexpr std::array<t_real, 3 * 14> standardCoords = {

            // Vertices (0-4)

            -1, -1, 0,     1, -1, 0,     1,  1, 0,    -1,  1, 0,     0,  0, 1,

            // Base edge mids (5-8)

             0, -1, 0,     1,  0, 0,     0,  1, 0,    -1,  0, 0,

            // Lateral edge mids (9-12)

            -0.5, -0.5, 0.5,   0.5, -0.5, 0.5,   0.5, 0.5, 0.5,   -0.5, 0.5, 0.5,

            // Base face center (13)

             0,  0, 0};


        // ============================================================

        // Face/Edge Definitions

        // ============================================================


        /**

         * @brief Get the element type of a face

         * @param iFace Face index (0 is base, 1-4 are sides)

         * @return Quad9 for base, Tri6 for sides

         */


        static constexpr ElemType GetFaceType(t_index iFace)

        {

            return iFace < 1 ? Quad9 : Tri6;

        }


        /**

         * @brief Node indices for each face

         *

         * Base face has 9 nodes (4 vertices + 4 edge mids + 1 center)

         * Side faces have 6 nodes (3 vertices + 3 edge mids)

         */


        static constexpr std::array<std::array<t_index, 10>, 5> faceNodes = {{

            {0, 3, 2, 1, 8, 7, 6, 5, 13},     // Face 0: base (biquad)

            {0, 1, 4, 5, 10, 9},              // Face 1: side triangle

            {1, 2, 4, 6, 11, 10},             // Face 2: side triangle

            {2, 3, 4, 7, 12, 11},             // Face 3: side triangle

            {3, 0, 4, 8, 9, 12}}};            // Face 4: side triangle


        // ============================================================

        // 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 (12 sub-elements)

        static constexpr int numBisect = 12;


        /**

         * @brief Number of bisection variants (2 different diagonal choices)

         *

         * The base can be bisected using different internal diagonal patterns,

         * resulting in different sub-element configurations.

         */

        static constexpr int numBisectVariants = 2;


        /**

         * @brief Get the element type of a sub-element after bisection

         * @param i Sub-element index (first 4 are Pyramid5, remaining 8 are Tet4)

         * @return Pyramid5 for corner elements, Tet4 for internal elements

         */


        static constexpr ElemType GetBisectElemType(t_index i)

        {

            return i < 4 ? Pyramid5 : Tet4;

        }


        /**

         * @brief Node indices for each sub-element created by bisection

         *

         * 2 variants x 12 sub-elements = 24 entries total.

         * Each variant produces 4 corner pyramids and 8 internal tetrahedra.

         */


        static constexpr std::array<tBisectSub, 24> bisectElements = {{

            // Variant 0

            {0, 5, 13, 8, 9},

            {5, 1, 6, 13, 10},

            {8, 13, 7, 3, 12},

            {13, 6, 2, 7, 11},

            {12, 9, 8, 13},

            {9, 10, 5, 13},

            {10, 11, 6, 13},

            {11, 12, 7, 13},

            {9, 11, 12, 4},

            {9, 10, 11, 4},

            {9, 11, 10, 13},

            {9, 12, 11, 13},

            // Variant 1

            {0, 5, 13, 8, 9},

            {5, 1, 6, 13, 10},

            {8, 13, 7, 3, 12},

            {13, 6, 2, 7, 11},

            {12, 9, 8, 13},

            {9, 10, 5, 13},

            {10, 11, 6, 13},

            {11, 12, 7, 13},

            {10, 12, 9, 4},

            {10, 11, 12, 4},

            {10, 12, 11, 13},

            {10, 9, 12, 13}}};


        // ============================================================

        // VTK/Visualization Support

        // ============================================================


        /// @brief VTK cell type identifier (27 = VTK_TRIQUADRATIC_PYRAMID)

        static constexpr int vtkCellType = 27;


        /**

         * @brief VTK node ordering map

         *

         * VTK uses 13 nodes for quadratic pyramid:

         *   VTK nodes 0-4 = vertices 0-4

         *   VTK nodes 5-8 = base edge mids 5-8

         *   VTK nodes 9-12 = lateral edge mids 9-12

         * Note: Base face center node 13 is not included in VTK ordering

         */


        static constexpr std::array<int, 13> vtkNodeOrder = {

            0, 1, 2, 3, 4,       // Vertices

            5, 6, 7, 8,          // Base edges

            9, 10, 11, 12};      // Lateral edges


    };


} // namespace DNDS::Geom::Elem

Defines.hpp
Core type aliases, constants, and metaprogramming utilities for the DNDS framework.

ElemEnum.hpp

ElementTraitsBase.hpp

Geometric.hpp

DNDS::Geom::Elem
Definition Elements.cpp:4

DNDS::Geom::Elem::ElemType
ElemType
Definition ElemEnum.hpp:19

DNDS::Geom::Elem::Tri6
@ Tri6
Definition ElemEnum.hpp:25

DNDS::Geom::Elem::Pyramid14
@ Pyramid14
Definition ElemEnum.hpp:36

DNDS::Geom::Elem::Quad9
@ Quad9
Definition ElemEnum.hpp:27

DNDS::Geom::Elem::UnknownElem
@ UnknownElem
Definition ElemEnum.hpp:20

DNDS::Geom::Elem::Tet4
@ Tet4
Definition ElemEnum.hpp:29

DNDS::Geom::Elem::Pyramid5
@ Pyramid5
Definition ElemEnum.hpp:35

DNDS::Geom::Elem::ParamSpace
ParamSpace
Definition ElemEnum.hpp:42

DNDS::Geom::Elem::PyramidSpace
@ PyramidSpace
Definition ElemEnum.hpp:52

DNDS::Geom::t_index
int32_t t_index
Definition Geometric.hpp:6

DNDS::Geom::t_real
double t_real
Definition Geometric.hpp:8

DNDS::signP
constexpr real signP(real a)
"Signum, biased toward +1": treats 0 as positive.
Definition Defines.hpp:544

DNDS::Geom::Elem::ElementTraits< Pyramid14 >::GetBisectElemType
static constexpr ElemType GetBisectElemType(t_index i)
Get the element type of a sub-element after bisection.
Definition Pyramid14.hpp:765

DNDS::Geom::Elem::ElementTraits< Pyramid14 >::GetFaceType
static constexpr ElemType GetFaceType(t_index iFace)
Get the element type of a face.
Definition Pyramid14.hpp:717

DNDS::Geom::Elem::ElementTraits
Definition ElementTraitsBase.hpp:22

DNDS::Geom::Elem::ShapeFuncImpl< Pyramid14 >::Diff2
static void Diff2(const TPoint &p, TArray &&v)
Definition Pyramid14.hpp:189

DNDS::Geom::Elem::ShapeFuncImpl< Pyramid14 >::Diff0
static void Diff0(const TPoint &p, TArray &&v)
Definition Pyramid14.hpp:22

DNDS::Geom::Elem::ShapeFuncImpl< Pyramid14 >::Diff1
static void Diff1(const TPoint &p, TArray &&v)
Definition Pyramid14.hpp:71

DNDS::Geom::Elem::ShapeFuncImpl< Pyramid14 >::Diff3
static void Diff3(const TPoint &p, TArray &&v)
Definition Pyramid14.hpp:401

DNDS::Geom::Elem::ShapeFuncImpl
Definition Elements.hpp:153

v
Eigen::Matrix< real, 5, 1 > v
Definition test_ArrayDOF.cpp:468

order
double order
Definition test_ODE.cpp:257