DNDSR/doxygen/Hex27_8hpp_source.html

#pragma once

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

// Element: Hex27

// 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<Hex27>

    {

        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];

            t_real zt = p[2];

            const t_real _t0 = xi - 1;

            const t_real _t1 = et - 1;

            const t_real _t2 = et*xi;

            const t_real _t3 = _t1*_t2;

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

            const t_real _t5 = ((0.125))*_t4;

            const t_real _t6 = _t3*_t5;

            const t_real _t7 = xi + 1;

            const t_real _t8 = et + 1;

            const t_real _t9 = _t2*_t8;

            const t_real _t10 = _t5*_t9;

            const t_real _t11 = zt*(zt + 1);

            const t_real _t12 = ((0.125))*_t11;

            const t_real _t13 = _t12*_t3;

            const t_real _t14 = _t12*_t9;

            const t_real _t15 = ((xi) * (xi)) - 1;

            const t_real _t16 = _t15*et;

            const t_real _t17 = _t1*_t16;

            const t_real _t18 = ((0.25))*_t4;

            const t_real _t19 = ((et) * (et)) - 1;

            const t_real _t20 = _t19*xi;

            const t_real _t21 = _t18*_t20;

            const t_real _t22 = _t16*_t8;

            const t_real _t23 = ((0.25))*_t0;

            const t_real _t24 = ((zt) * (zt)) - 1;

            const t_real _t25 = _t24*_t3;

            const t_real _t26 = ((0.25))*_t7;

            const t_real _t27 = _t24*_t9;

            const t_real _t28 = ((0.25))*_t11;

            const t_real _t29 = _t11*_t20;

            const t_real _t30 = _t15*_t19;

            const t_real _t31 = ((0.5))*_t30;

            const t_real _t32 = ((0.5))*_t24;

            const t_real _t33 = _t20*_t32;

            v(0, 0) = _t0*_t6;

            v(0, 1) = _t6*_t7;

            v(0, 2) = _t10*_t7;

            v(0, 3) = _t0*_t10;

            v(0, 4) = _t0*_t13;

            v(0, 5) = _t13*_t7;

            v(0, 6) = _t14*_t7;

            v(0, 7) = _t0*_t14;

            v(0, 8) = -_t17*_t18;

            v(0, 9) = -_t21*_t7;

            v(0, 10) = -_t18*_t22;

            v(0, 11) = -_t0*_t21;

            v(0, 12) = -_t23*_t25;

            v(0, 13) = -_t25*_t26;

            v(0, 14) = -_t26*_t27;

            v(0, 15) = -_t23*_t27;

            v(0, 16) = -_t17*_t28;

            v(0, 17) = -_t26*_t29;

            v(0, 18) = -_t22*_t28;

            v(0, 19) = -_t23*_t29;

            v(0, 20) = _t31*_t4;

            v(0, 21) = _t17*_t32;

            v(0, 22) = _t33*_t7;

            v(0, 23) = _t22*_t32;

            v(0, 24) = _t0*_t33;

            v(0, 25) = _t11*_t31;

            v(0, 26) = -_t24*_t30;

        }


        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];

            t_real zt = p[2];

            const t_real _t0 = 2*xi;

            const t_real _t1 = _t0 - 1;

            const t_real _t2 = et*(et - 1);

            const t_real _t3 = zt*(zt - 1);

            const t_real _t4 = ((0.125))*_t3;

            const t_real _t5 = _t2*_t4;

            const t_real _t6 = _t0 + 1;

            const t_real _t7 = et + 1;

            const t_real _t8 = _t7*et;

            const t_real _t9 = _t4*_t8;

            const t_real _t10 = zt*(zt + 1);

            const t_real _t11 = ((0.125))*_t10;

            const t_real _t12 = _t11*_t2;

            const t_real _t13 = _t11*_t8;

            const t_real _t14 = ((0.5))*xi;

            const t_real _t15 = _t14*_t3;

            const t_real _t16 = -(0.25)*_t6;

            const t_real _t17 = ((et) * (et)) - 1;

            const t_real _t18 = _t17*_t3;

            const t_real _t19 = -(0.25)*_t1;

            const t_real _t20 = ((zt) * (zt)) - 1;

            const t_real _t21 = _t2*_t20;

            const t_real _t22 = _t20*_t8;

            const t_real _t23 = _t10*_t14;

            const t_real _t24 = _t10*_t17;

            const t_real _t25 = _t17*xi;

            const t_real _t26 = _t20*xi;

            const t_real _t27 = _t17*_t20;

            const t_real _t28 = ((0.5))*_t27;

            const t_real _t29 = _t26*et;

            const t_real _t30 = xi - 1;

            const t_real _t31 = 2*et;

            const t_real _t32 = _t31 - 1;

            const t_real _t33 = _t4*xi;

            const t_real _t34 = _t32*_t33;

            const t_real _t35 = xi + 1;

            const t_real _t36 = _t31 + 1;

            const t_real _t37 = _t33*_t36;

            const t_real _t38 = _t11*xi;

            const t_real _t39 = _t32*_t38;

            const t_real _t40 = _t36*_t38;

            const t_real _t41 = -(0.25)*_t32;

            const t_real _t42 = ((xi) * (xi)) - 1;

            const t_real _t43 = _t3*_t42;

            const t_real _t44 = _t15*et;

            const t_real _t45 = -(0.25)*_t36;

            const t_real _t46 = _t26*_t41;

            const t_real _t47 = _t26*_t45;

            const t_real _t48 = _t10*_t42;

            const t_real _t49 = _t23*et;

            const t_real _t50 = _t42*et;

            const t_real _t51 = _t20*_t42;

            const t_real _t52 = ((0.5))*_t51;

            const t_real _t53 = _t2*_t30;

            const t_real _t54 = 2*zt;

            const t_real _t55 = _t54 - 1;

            const t_real _t56 = ((0.125))*xi;

            const t_real _t57 = _t55*_t56;

            const t_real _t58 = _t35*_t57;

            const t_real _t59 = _t30*_t8;

            const t_real _t60 = _t54 + 1;

            const t_real _t61 = _t56*_t60;

            const t_real _t62 = _t35*_t61;

            const t_real _t63 = _t2*_t42;

            const t_real _t64 = -(0.25)*_t55;

            const t_real _t65 = _t25*_t64;

            const t_real _t66 = _t50*_t7;

            const t_real _t67 = _t14*zt;

            const t_real _t68 = _t35*_t67;

            const t_real _t69 = -(0.25)*_t60;

            const t_real _t70 = _t25*_t69;

            const t_real _t71 = _t17*_t42;

            const t_real _t72 = ((0.5))*_t71;

            const t_real _t73 = _t25*zt;

            v(0, 0) = _t1*_t5;

            v(0, 1) = _t5*_t6;

            v(0, 2) = _t6*_t9;

            v(0, 3) = _t1*_t9;

            v(0, 4) = _t1*_t12;

            v(0, 5) = _t12*_t6;

            v(0, 6) = _t13*_t6;

            v(0, 7) = _t1*_t13;

            v(0, 8) = -_t15*_t2;

            v(0, 9) = _t16*_t18;

            v(0, 10) = -_t15*_t8;

            v(0, 11) = _t18*_t19;

            v(0, 12) = _t19*_t21;

            v(0, 13) = _t16*_t21;

            v(0, 14) = _t16*_t22;

            v(0, 15) = _t19*_t22;

            v(0, 16) = -_t2*_t23;

            v(0, 17) = _t16*_t24;

            v(0, 18) = -_t23*_t8;

            v(0, 19) = _t19*_t24;

            v(0, 20) = _t25*_t3;

            v(0, 21) = _t2*_t26;

            v(0, 22) = _t28*_t6;

            v(0, 23) = _t29*_t7;

            v(0, 24) = _t1*_t28;

            v(0, 25) = _t10*_t25;

            v(0, 26) = -_t0*_t27;

            v(1, 0) = _t30*_t34;

            v(1, 1) = _t34*_t35;

            v(1, 2) = _t35*_t37;

            v(1, 3) = _t30*_t37;

            v(1, 4) = _t30*_t39;

            v(1, 5) = _t35*_t39;

            v(1, 6) = _t35*_t40;

            v(1, 7) = _t30*_t40;

            v(1, 8) = _t41*_t43;

            v(1, 9) = -_t35*_t44;

            v(1, 10) = _t43*_t45;

            v(1, 11) = -_t30*_t44;

            v(1, 12) = _t30*_t46;

            v(1, 13) = _t35*_t46;

            v(1, 14) = _t35*_t47;

            v(1, 15) = _t30*_t47;

            v(1, 16) = _t41*_t48;

            v(1, 17) = -_t35*_t49;

            v(1, 18) = _t45*_t48;

            v(1, 19) = -_t30*_t49;

            v(1, 20) = _t3*_t50;

            v(1, 21) = _t32*_t52;

            v(1, 22) = _t29*_t35;

            v(1, 23) = _t36*_t52;

            v(1, 24) = _t29*_t30;

            v(1, 25) = _t10*_t50;

            v(1, 26) = -_t31*_t51;

            v(2, 0) = _t53*_t57;

            v(2, 1) = _t2*_t58;

            v(2, 2) = _t58*_t8;

            v(2, 3) = _t57*_t59;

            v(2, 4) = _t53*_t61;

            v(2, 5) = _t2*_t62;

            v(2, 6) = _t62*_t8;

            v(2, 7) = _t59*_t61;

            v(2, 8) = _t63*_t64;

            v(2, 9) = _t35*_t65;

            v(2, 10) = _t64*_t66;

            v(2, 11) = _t30*_t65;

            v(2, 12) = -_t53*_t67;

            v(2, 13) = -_t2*_t68;

            v(2, 14) = -_t68*_t8;

            v(2, 15) = -_t59*_t67;

            v(2, 16) = _t63*_t69;

            v(2, 17) = _t35*_t70;

            v(2, 18) = _t66*_t69;

            v(2, 19) = _t30*_t70;

            v(2, 20) = _t55*_t72;

            v(2, 21) = _t63*zt;

            v(2, 22) = _t35*_t73;

            v(2, 23) = _t66*zt;

            v(2, 24) = _t30*_t73;

            v(2, 25) = _t60*_t72;

            v(2, 26) = -_t54*_t71;

        }


        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];

            t_real zt = p[2];

            const t_real _t0 = et - 1;

            const t_real _t1 = zt - 1;

            const t_real _t2 = _t0*_t1;

            const t_real _t3 = et*zt;

            const t_real _t4 = ((0.25))*_t3;

            const t_real _t5 = _t2*_t4;

            const t_real _t6 = et + 1;

            const t_real _t7 = _t1*_t6;

            const t_real _t8 = _t4*_t7;

            const t_real _t9 = zt + 1;

            const t_real _t10 = _t0*_t9;

            const t_real _t11 = _t10*_t4;

            const t_real _t12 = _t6*_t9;

            const t_real _t13 = _t12*_t4;

            const t_real _t14 = ((0.5))*_t3;

            const t_real _t15 = ((et) * (et)) - 1;

            const t_real _t16 = _t15*zt;

            const t_real _t17 = _t1*_t16;

            const t_real _t18 = -(0.5)*_t17;

            const t_real _t19 = ((zt) * (zt)) - 1;

            const t_real _t20 = _t19*et;

            const t_real _t21 = _t0*_t20;

            const t_real _t22 = -(0.5)*_t21;

            const t_real _t23 = _t20*_t6;

            const t_real _t24 = -(0.5)*_t23;

            const t_real _t25 = _t16*_t9;

            const t_real _t26 = -(0.5)*_t25;

            const t_real _t27 = _t15*_t19;

            const t_real _t28 = xi - 1;

            const t_real _t29 = _t1*_t28;

            const t_real _t30 = xi*zt;

            const t_real _t31 = ((0.25))*_t30;

            const t_real _t32 = _t29*_t31;

            const t_real _t33 = xi + 1;

            const t_real _t34 = _t1*_t33;

            const t_real _t35 = _t31*_t34;

            const t_real _t36 = _t28*_t9;

            const t_real _t37 = _t31*_t36;

            const t_real _t38 = _t33*_t9;

            const t_real _t39 = _t31*_t38;

            const t_real _t40 = ((xi) * (xi)) - 1;

            const t_real _t41 = _t40*zt;

            const t_real _t42 = _t1*_t41;

            const t_real _t43 = -(0.5)*_t42;

            const t_real _t44 = ((0.5))*_t30;

            const t_real _t45 = _t19*xi;

            const t_real _t46 = _t28*_t45;

            const t_real _t47 = -(0.5)*_t46;

            const t_real _t48 = _t33*_t45;

            const t_real _t49 = -(0.5)*_t48;

            const t_real _t50 = _t41*_t9;

            const t_real _t51 = -(0.5)*_t50;

            const t_real _t52 = _t19*_t40;

            const t_real _t53 = _t0*_t28;

            const t_real _t54 = et*xi;

            const t_real _t55 = ((0.25))*_t54;

            const t_real _t56 = _t53*_t55;

            const t_real _t57 = _t0*_t33;

            const t_real _t58 = _t55*_t57;

            const t_real _t59 = _t33*_t6;

            const t_real _t60 = _t55*_t59;

            const t_real _t61 = _t28*_t6;

            const t_real _t62 = _t55*_t61;

            const t_real _t63 = _t40*et;

            const t_real _t64 = _t0*_t63;

            const t_real _t65 = -(0.5)*_t64;

            const t_real _t66 = _t15*xi;

            const t_real _t67 = _t33*_t66;

            const t_real _t68 = -(0.5)*_t67;

            const t_real _t69 = _t6*_t63;

            const t_real _t70 = -(0.5)*_t69;

            const t_real _t71 = _t28*_t66;

            const t_real _t72 = -(0.5)*_t71;

            const t_real _t73 = ((0.5))*_t54;

            const t_real _t74 = _t15*_t40;

            const t_real _t75 = _t28*et;

            const t_real _t76 = _t0*xi + _t54;

            const t_real _t77 = _t53 + _t75 + _t76;

            const t_real _t78 = ((0.125))*zt;

            const t_real _t79 = _t1*_t78;

            const t_real _t80 = _t33*et;

            const t_real _t81 = _t57 + _t76 + _t80;

            const t_real _t82 = _t54 + _t6*xi;

            const t_real _t83 = _t59 + _t80 + _t82;

            const t_real _t84 = _t61 + _t75 + _t82;

            const t_real _t85 = _t78*_t9;

            const t_real _t86 = 2*et;

            const t_real _t87 = _t86 - 1;

            const t_real _t88 = -_t87;

            const t_real _t89 = _t1*_t44;

            const t_real _t90 = 2*xi;

            const t_real _t91 = _t90 + 1;

            const t_real _t92 = -_t91;

            const t_real _t93 = _t1*_t14;

            const t_real _t94 = _t86 + 1;

            const t_real _t95 = -_t94;

            const t_real _t96 = _t90 - 1;

            const t_real _t97 = -_t96;

            const t_real _t98 = ((0.25))*_t19;

            const t_real _t99 = _t44*_t9;

            const t_real _t100 = _t14*_t9;

            const t_real _t101 = 2*zt;

            const t_real _t102 = _t101*_t54;

            const t_real _t103 = _t0*zt;

            const t_real _t104 = _t1*et + _t3;

            const t_real _t105 = _t103 + _t104 + _t2;

            const t_real _t106 = ((0.125))*xi;

            const t_real _t107 = _t105*_t106;

            const t_real _t108 = _t6*zt;

            const t_real _t109 = _t104 + _t108 + _t7;

            const t_real _t110 = _t106*_t109;

            const t_real _t111 = _t3 + _t9*et;

            const t_real _t112 = _t10 + _t103 + _t111;

            const t_real _t113 = _t106*_t112;

            const t_real _t114 = _t108 + _t111 + _t12;

            const t_real _t115 = _t106*_t114;

            const t_real _t116 = ((0.25))*_t40;

            const t_real _t117 = _t101 - 1;

            const t_real _t118 = -_t117*_t73;

            const t_real _t119 = _t44*_t88;

            const t_real _t120 = _t44*_t95;

            const t_real _t121 = _t101 + 1;

            const t_real _t122 = -_t121*_t73;

            const t_real _t123 = _t28*zt;

            const t_real _t124 = _t1*xi + _t30;

            const t_real _t125 = _t123 + _t124 + _t29;

            const t_real _t126 = ((0.125))*et;

            const t_real _t127 = _t0*_t126;

            const t_real _t128 = _t33*zt;

            const t_real _t129 = _t124 + _t128 + _t34;

            const t_real _t130 = _t126*_t6;

            const t_real _t131 = _t30 + _t9*xi;

            const t_real _t132 = _t123 + _t131 + _t36;

            const t_real _t133 = _t128 + _t131 + _t38;

            const t_real _t134 = ((0.25))*_t15;

            const t_real _t135 = _t0*_t14;

            const t_real _t136 = _t14*_t6;

            const t_real _t137 = 2*_t54;

            v(0, 0) = _t5;

            v(0, 1) = _t5;

            v(0, 2) = _t8;

            v(0, 3) = _t8;

            v(0, 4) = _t11;

            v(0, 5) = _t11;

            v(0, 6) = _t13;

            v(0, 7) = _t13;

            v(0, 8) = -_t14*_t2;

            v(0, 9) = _t18;

            v(0, 10) = -_t14*_t7;

            v(0, 11) = _t18;

            v(0, 12) = _t22;

            v(0, 13) = _t22;

            v(0, 14) = _t24;

            v(0, 15) = _t24;

            v(0, 16) = -_t10*_t14;

            v(0, 17) = _t26;

            v(0, 18) = -_t12*_t14;

            v(0, 19) = _t26;

            v(0, 20) = _t17;

            v(0, 21) = _t21;

            v(0, 22) = _t27;

            v(0, 23) = _t23;

            v(0, 24) = _t27;

            v(0, 25) = _t25;

            v(0, 26) = -2*_t27;

            v(1, 0) = _t32;

            v(1, 1) = _t35;

            v(1, 2) = _t35;

            v(1, 3) = _t32;

            v(1, 4) = _t37;

            v(1, 5) = _t39;

            v(1, 6) = _t39;

            v(1, 7) = _t37;

            v(1, 8) = _t43;

            v(1, 9) = -_t34*_t44;

            v(1, 10) = _t43;

            v(1, 11) = -_t29*_t44;

            v(1, 12) = _t47;

            v(1, 13) = _t49;

            v(1, 14) = _t49;

            v(1, 15) = _t47;

            v(1, 16) = _t51;

            v(1, 17) = -_t38*_t44;

            v(1, 18) = _t51;

            v(1, 19) = -_t36*_t44;

            v(1, 20) = _t42;

            v(1, 21) = _t52;

            v(1, 22) = _t48;

            v(1, 23) = _t52;

            v(1, 24) = _t46;

            v(1, 25) = _t50;

            v(1, 26) = -2*_t52;

            v(2, 0) = _t56;

            v(2, 1) = _t58;

            v(2, 2) = _t60;

            v(2, 3) = _t62;

            v(2, 4) = _t56;

            v(2, 5) = _t58;

            v(2, 6) = _t60;

            v(2, 7) = _t62;

            v(2, 8) = _t65;

            v(2, 9) = _t68;

            v(2, 10) = _t70;

            v(2, 11) = _t72;

            v(2, 12) = -_t53*_t73;

            v(2, 13) = -_t57*_t73;

            v(2, 14) = -_t59*_t73;

            v(2, 15) = -_t61*_t73;

            v(2, 16) = _t65;

            v(2, 17) = _t68;

            v(2, 18) = _t70;

            v(2, 19) = _t72;

            v(2, 20) = _t74;

            v(2, 21) = _t64;

            v(2, 22) = _t67;

            v(2, 23) = _t69;

            v(2, 24) = _t71;

            v(2, 25) = _t74;

            v(2, 26) = -2*_t74;

            v(3, 0) = _t77*_t79;

            v(3, 1) = _t79*_t81;

            v(3, 2) = _t79*_t83;

            v(3, 3) = _t79*_t84;

            v(3, 4) = _t77*_t85;

            v(3, 5) = _t81*_t85;

            v(3, 6) = _t83*_t85;

            v(3, 7) = _t84*_t85;

            v(3, 8) = _t88*_t89;

            v(3, 9) = _t92*_t93;

            v(3, 10) = _t89*_t95;

            v(3, 11) = _t93*_t97;

            v(3, 12) = -_t77*_t98;

            v(3, 13) = -_t81*_t98;

            v(3, 14) = -_t83*_t98;

            v(3, 15) = -_t84*_t98;

            v(3, 16) = _t88*_t99;

            v(3, 17) = _t100*_t92;

            v(3, 18) = _t95*_t99;

            v(3, 19) = _t100*_t97;

            v(3, 20) = _t1*_t102;

            v(3, 21) = _t45*_t87;

            v(3, 22) = _t20*_t91;

            v(3, 23) = _t45*_t94;

            v(3, 24) = _t20*_t96;

            v(3, 25) = _t102*_t9;

            v(3, 26) = -4*_t19*_t54;

            v(4, 0) = _t107*_t28;

            v(4, 1) = _t107*_t33;

            v(4, 2) = _t110*_t33;

            v(4, 3) = _t110*_t28;

            v(4, 4) = _t113*_t28;

            v(4, 5) = _t113*_t33;

            v(4, 6) = _t115*_t33;

            v(4, 7) = _t115*_t28;

            v(4, 8) = -_t105*_t116;

            v(4, 9) = _t118*_t33;

            v(4, 10) = -_t109*_t116;

            v(4, 11) = _t118*_t28;

            v(4, 12) = _t119*_t28;

            v(4, 13) = _t119*_t33;

            v(4, 14) = _t120*_t33;

            v(4, 15) = _t120*_t28;

            v(4, 16) = -_t112*_t116;

            v(4, 17) = _t122*_t33;

            v(4, 18) = -_t114*_t116;

            v(4, 19) = _t122*_t28;

            v(4, 20) = _t117*_t63;

            v(4, 21) = _t41*_t87;

            v(4, 22) = _t102*_t33;

            v(4, 23) = _t41*_t94;

            v(4, 24) = _t102*_t28;

            v(4, 25) = _t121*_t63;

            v(4, 26) = -4*_t3*_t40;

            v(5, 0) = _t125*_t127;

            v(5, 1) = _t127*_t129;

            v(5, 2) = _t129*_t130;

            v(5, 3) = _t125*_t130;

            v(5, 4) = _t127*_t132;

            v(5, 5) = _t127*_t133;

            v(5, 6) = _t130*_t133;

            v(5, 7) = _t130*_t132;

            v(5, 8) = _t0*_t118;

            v(5, 9) = -_t129*_t134;

            v(5, 10) = _t118*_t6;

            v(5, 11) = -_t125*_t134;

            v(5, 12) = _t135*_t97;

            v(5, 13) = _t135*_t92;

            v(5, 14) = _t136*_t92;

            v(5, 15) = _t136*_t97;

            v(5, 16) = _t0*_t122;

            v(5, 17) = -_t133*_t134;

            v(5, 18) = _t122*_t6;

            v(5, 19) = -_t132*_t134;

            v(5, 20) = _t117*_t66;

            v(5, 21) = _t103*_t137;

            v(5, 22) = _t16*_t91;

            v(5, 23) = _t108*_t137;

            v(5, 24) = _t16*_t96;

            v(5, 25) = _t121*_t66;

            v(5, 26) = -4*_t15*_t30;

        }


        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];

            t_real zt = p[2];

            const t_real _t0 = 2*et;

            const t_real _t1 = _t0 - 1;

            const t_real _t2 = zt - 1;

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

            const t_real _t4 = _t2*_t3;

            const t_real _t5 = _t1*_t4;

            const t_real _t6 = _t0 + 1;

            const t_real _t7 = _t4*_t6;

            const t_real _t8 = zt + 1;

            const t_real _t9 = _t3*_t8;

            const t_real _t10 = _t1*_t9;

            const t_real _t11 = _t6*_t9;

            const t_real _t12 = -_t1;

            const t_real _t13 = ((0.5))*zt;

            const t_real _t14 = _t13*_t2;

            const t_real _t15 = -_t2;

            const t_real _t16 = et*zt;

            const t_real _t17 = _t15*_t16;

            const t_real _t18 = -_t6;

            const t_real _t19 = ((zt) * (zt)) - 1;

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

            const t_real _t21 = _t12*_t20;

            const t_real _t22 = _t18*_t20;

            const t_real _t23 = _t13*_t8;

            const t_real _t24 = -_t16*_t8;

            const t_real _t25 = _t0*zt;

            const t_real _t26 = _t0*_t19;

            const t_real _t27 = -4*_t19;

            const t_real _t28 = 2*xi;

            const t_real _t29 = _t28 - 1;

            const t_real _t30 = _t29*_t4;

            const t_real _t31 = _t28 + 1;

            const t_real _t32 = _t31*_t4;

            const t_real _t33 = _t29*_t9;

            const t_real _t34 = _t31*_t9;

            const t_real _t35 = xi*zt;

            const t_real _t36 = _t15*_t35;

            const t_real _t37 = -_t31;

            const t_real _t38 = -_t29;

            const t_real _t39 = _t20*_t38;

            const t_real _t40 = _t20*_t37;

            const t_real _t41 = -_t35*_t8;

            const t_real _t42 = _t28*zt;

            const t_real _t43 = _t19*_t28;

            const t_real _t44 = xi - 1;

            const t_real _t45 = 2*zt;

            const t_real _t46 = _t45 - 1;

            const t_real _t47 = ((0.25))*xi;

            const t_real _t48 = _t46*_t47;

            const t_real _t49 = _t44*_t48;

            const t_real _t50 = xi + 1;

            const t_real _t51 = _t48*_t50;

            const t_real _t52 = _t45 + 1;

            const t_real _t53 = _t47*_t52;

            const t_real _t54 = _t44*_t53;

            const t_real _t55 = _t50*_t53;

            const t_real _t56 = -_t46;

            const t_real _t57 = ((xi) * (xi)) - 1;

            const t_real _t58 = ((0.5))*_t57;

            const t_real _t59 = _t56*_t58;

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

            const t_real _t61 = _t56*_t60;

            const t_real _t62 = -_t44;

            const t_real _t63 = _t35*_t62;

            const t_real _t64 = -_t35*_t50;

            const t_real _t65 = -_t52;

            const t_real _t66 = _t58*_t65;

            const t_real _t67 = _t60*_t65;

            const t_real _t68 = _t45*_t57;

            const t_real _t69 = -4*_t57;

            const t_real _t70 = _t1*_t47;

            const t_real _t71 = _t44*_t70;

            const t_real _t72 = _t50*_t70;

            const t_real _t73 = _t47*_t6;

            const t_real _t74 = _t50*_t73;

            const t_real _t75 = _t44*_t73;

            const t_real _t76 = _t12*_t58;

            const t_real _t77 = et*xi;

            const t_real _t78 = -_t50*_t77;

            const t_real _t79 = _t18*_t58;

            const t_real _t80 = _t62*_t77;

            const t_real _t81 = _t12*_t60;

            const t_real _t82 = _t18*_t60;

            const t_real _t83 = _t0*_t57;

            const t_real _t84 = _t0*xi;

            const t_real _t85 = et - 1;

            const t_real _t86 = ((0.25))*et;

            const t_real _t87 = _t85*_t86;

            const t_real _t88 = _t29*_t87;

            const t_real _t89 = _t31*_t87;

            const t_real _t90 = et + 1;

            const t_real _t91 = _t86*_t90;

            const t_real _t92 = _t31*_t91;

            const t_real _t93 = _t29*_t91;

            const t_real _t94 = -_t85;

            const t_real _t95 = _t77*_t94;

            const t_real _t96 = ((et) * (et)) - 1;

            const t_real _t97 = ((0.5))*_t96;

            const t_real _t98 = _t37*_t97;

            const t_real _t99 = -_t77*_t90;

            const t_real _t100 = _t38*_t97;

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

            const t_real _t102 = _t101*_t85;

            const t_real _t103 = _t101*_t90;

            const t_real _t104 = _t28*_t96;

            const t_real _t105 = -4*_t96;

            const t_real _t106 = _t46*_t87;

            const t_real _t107 = _t46*_t91;

            const t_real _t108 = _t52*_t87;

            const t_real _t109 = _t52*_t91;

            const t_real _t110 = _t56*_t97;

            const t_real _t111 = _t16*_t94;

            const t_real _t112 = -_t16*_t90;

            const t_real _t113 = _t65*_t97;

            const t_real _t114 = _t45*_t96;

            const t_real _t115 = ((0.5))*_t77;

            const t_real _t116 = -_t115;

            const t_real _t117 = ((0.5))*_t35;

            const t_real _t118 = -_t117;

            const t_real _t119 = _t16*xi;

            const t_real _t120 = _t116 + _t118 + _t119 + _t47;

            const t_real _t121 = _t3 + (-0.125);

            const t_real _t122 = ((0.5))*_t16;

            const t_real _t123 = -_t122;

            const t_real _t124 = _t123 + _t86;

            const t_real _t125 = -_t86;

            const t_real _t126 = _t122 + _t125;

            const t_real _t127 = -_t3;

            const t_real _t128 = _t127 + (0.125);

            const t_real _t129 = _t119 - _t47;

            const t_real _t130 = _t116 + _t117 + _t129;

            const t_real _t131 = _t115 + _t118 + _t129;

            const t_real _t132 = _t3 + (0.125);

            const t_real _t133 = _t123 + _t125;

            const t_real _t134 = _t122 + _t86;

            const t_real _t135 = _t127 + (-0.125);

            const t_real _t136 = _t115 + _t117 + _t119 + _t47;

            const t_real _t137 = -_t0;

            const t_real _t138 = 4*_t16;

            const t_real _t139 = _t137 + _t138;

            const t_real _t140 = -_t45;

            const t_real _t141 = _t140 + 1;

            const t_real _t142 = -_t28;

            const t_real _t143 = 4*_t35;

            const t_real _t144 = _t142 + _t143;

            const t_real _t145 = 4*_t77;

            const t_real _t146 = _t142 + _t145;

            v(3, 0) = _t5;

            v(3, 1) = _t5;

            v(3, 2) = _t7;

            v(3, 3) = _t7;

            v(3, 4) = _t10;

            v(3, 5) = _t10;

            v(3, 6) = _t11;

            v(3, 7) = _t11;

            v(3, 8) = _t12*_t14;

            v(3, 9) = _t17;

            v(3, 10) = _t14*_t18;

            v(3, 11) = _t17;

            v(3, 12) = _t21;

            v(3, 13) = _t21;

            v(3, 14) = _t22;

            v(3, 15) = _t22;

            v(3, 16) = _t12*_t23;

            v(3, 17) = _t24;

            v(3, 18) = _t18*_t23;

            v(3, 19) = _t24;

            v(3, 20) = _t2*_t25;

            v(3, 21) = _t1*_t19;

            v(3, 22) = _t26;

            v(3, 23) = _t19*_t6;

            v(3, 24) = _t26;

            v(3, 25) = _t25*_t8;

            v(3, 26) = _t27*et;

            v(4, 0) = _t30;

            v(4, 1) = _t32;

            v(4, 2) = _t32;

            v(4, 3) = _t30;

            v(4, 4) = _t33;

            v(4, 5) = _t34;

            v(4, 6) = _t34;

            v(4, 7) = _t33;

            v(4, 8) = _t36;

            v(4, 9) = _t14*_t37;

            v(4, 10) = _t36;

            v(4, 11) = _t14*_t38;

            v(4, 12) = _t39;

            v(4, 13) = _t40;

            v(4, 14) = _t40;

            v(4, 15) = _t39;

            v(4, 16) = _t41;

            v(4, 17) = _t23*_t37;

            v(4, 18) = _t41;

            v(4, 19) = _t23*_t38;

            v(4, 20) = _t2*_t42;

            v(4, 21) = _t43;

            v(4, 22) = _t19*_t31;

            v(4, 23) = _t43;

            v(4, 24) = _t19*_t29;

            v(4, 25) = _t42*_t8;

            v(4, 26) = _t27*xi;

            v(5, 0) = _t49;

            v(5, 1) = _t51;

            v(5, 2) = _t51;

            v(5, 3) = _t49;

            v(5, 4) = _t54;

            v(5, 5) = _t55;

            v(5, 6) = _t55;

            v(5, 7) = _t54;

            v(5, 8) = _t59;

            v(5, 9) = _t50*_t61;

            v(5, 10) = _t59;

            v(5, 11) = _t44*_t61;

            v(5, 12) = _t63;

            v(5, 13) = _t64;

            v(5, 14) = _t64;

            v(5, 15) = _t63;

            v(5, 16) = _t66;

            v(5, 17) = _t50*_t67;

            v(5, 18) = _t66;

            v(5, 19) = _t44*_t67;

            v(5, 20) = _t46*_t57;

            v(5, 21) = _t68;

            v(5, 22) = _t42*_t50;

            v(5, 23) = _t68;

            v(5, 24) = _t42*_t44;

            v(5, 25) = _t52*_t57;

            v(5, 26) = _t69*zt;

            v(6, 0) = _t71;

            v(6, 1) = _t72;

            v(6, 2) = _t74;

            v(6, 3) = _t75;

            v(6, 4) = _t71;

            v(6, 5) = _t72;

            v(6, 6) = _t74;

            v(6, 7) = _t75;

            v(6, 8) = _t76;

            v(6, 9) = _t78;

            v(6, 10) = _t79;

            v(6, 11) = _t80;

            v(6, 12) = _t44*_t81;

            v(6, 13) = _t50*_t81;

            v(6, 14) = _t50*_t82;

            v(6, 15) = _t44*_t82;

            v(6, 16) = _t76;

            v(6, 17) = _t78;

            v(6, 18) = _t79;

            v(6, 19) = _t80;

            v(6, 20) = _t83;

            v(6, 21) = _t1*_t57;

            v(6, 22) = _t50*_t84;

            v(6, 23) = _t57*_t6;

            v(6, 24) = _t44*_t84;

            v(6, 25) = _t83;

            v(6, 26) = _t69*et;

            v(7, 0) = _t88;

            v(7, 1) = _t89;

            v(7, 2) = _t92;

            v(7, 3) = _t93;

            v(7, 4) = _t88;

            v(7, 5) = _t89;

            v(7, 6) = _t92;

            v(7, 7) = _t93;

            v(7, 8) = _t95;

            v(7, 9) = _t98;

            v(7, 10) = _t99;

            v(7, 11) = _t100;

            v(7, 12) = _t102*_t38;

            v(7, 13) = _t102*_t37;

            v(7, 14) = _t103*_t37;

            v(7, 15) = _t103*_t38;

            v(7, 16) = _t95;

            v(7, 17) = _t98;

            v(7, 18) = _t99;

            v(7, 19) = _t100;

            v(7, 20) = _t104;

            v(7, 21) = _t84*_t85;

            v(7, 22) = _t31*_t96;

            v(7, 23) = _t84*_t90;

            v(7, 24) = _t29*_t96;

            v(7, 25) = _t104;

            v(7, 26) = _t105*xi;

            v(8, 0) = _t106;

            v(8, 1) = _t106;

            v(8, 2) = _t107;

            v(8, 3) = _t107;

            v(8, 4) = _t108;

            v(8, 5) = _t108;

            v(8, 6) = _t109;

            v(8, 7) = _t109;

            v(8, 8) = _t102*_t56;

            v(8, 9) = _t110;

            v(8, 10) = _t103*_t56;

            v(8, 11) = _t110;

            v(8, 12) = _t111;

            v(8, 13) = _t111;

            v(8, 14) = _t112;

            v(8, 15) = _t112;

            v(8, 16) = _t102*_t65;

            v(8, 17) = _t113;

            v(8, 18) = _t103*_t65;

            v(8, 19) = _t113;

            v(8, 20) = _t46*_t96;

            v(8, 21) = _t25*_t85;

            v(8, 22) = _t114;

            v(8, 23) = _t25*_t90;

            v(8, 24) = _t114;

            v(8, 25) = _t52*_t96;

            v(8, 26) = _t105*zt;

            v(9, 0) = _t120 + _t121 + _t124;

            v(9, 1) = _t120 + _t126 + _t128;

            v(9, 2) = _t121 + _t126 + _t130;

            v(9, 3) = _t124 + _t128 + _t130;

            v(9, 4) = _t131 + _t132 + _t133;

            v(9, 5) = _t131 + _t134 + _t135;

            v(9, 6) = _t132 + _t134 + _t136;

            v(9, 7) = _t133 + _t135 + _t136;

            v(9, 8) = _t60*(-_t139 - _t141);

            v(9, 9) = _t101*(-_t144 - _t46);

            v(9, 10) = _t60*(-_t139 - _t46);

            v(9, 11) = _t101*(-_t141 - _t144);

            v(9, 12) = _t13*(-_t137 - _t146 - 1);

            v(9, 13) = _t13*(-_t1 - _t146);

            v(9, 14) = _t13*(-_t145 - _t28 - _t6);

            v(9, 15) = _t13*(-_t137 - _t145 - _t29);

            v(9, 16) = _t60*(-_t1 - _t138 - _t140);

            v(9, 17) = _t101*(-_t143 - _t31 - _t45);

            v(9, 18) = _t60*(-_t138 - _t45 - _t6);

            v(9, 19) = _t101*(-_t140 - _t143 - _t29);

            v(9, 20) = _t46*_t84;

            v(9, 21) = _t1*_t42;

            v(9, 22) = _t25*_t31;

            v(9, 23) = _t42*_t6;

            v(9, 24) = _t25*_t29;

            v(9, 25) = _t52*_t84;

            v(9, 26) = -8*_t119;

        }


    };


    // <GEN_SHAPE_FUNCS_END>


    /**

     * @brief Element traits for 27-node triquadratic hexahedron (Hex27)

     *

     * Hex27 is a high-order 3D hexahedral element with:

     * - 8 corner nodes (vertices)

     * - 12 edge mid-nodes

     * - 6 face center nodes

     * - 1 body center node

     *

     * Used for high-order finite element and spectral element methods.

     */

    template <>


    struct ElementTraits<Hex27>

    {

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

        // Core Element Identification

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


        static constexpr ElemType elemType = Hex27;

        static constexpr int dim = 3;

        static constexpr int order = 2;

        static constexpr int numVertices = 8;

        static constexpr int numNodes = 27;

        static constexpr int numFaces = 6;

        static constexpr ParamSpace paramSpace = HexSpace;

        static constexpr t_real paramSpaceVol = 8.0;


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

        // Geometry Definition

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


        /**

         * @brief Standard coordinates of nodes in parametric space

         *

         * Reference cube [-1,1]^3 with nodes:

         * Nodes 0-7: corners (same as Hex8)

         * Nodes 8-19: edge midpoints

         * Nodes 20-25: face centers

         * Node 26: body center

         */


        static constexpr std::array<t_real, 3 * 27> standardCoords = {

            // Corner nodes (0-7)

            -1, -1, -1,    1, -1, -1,    1,  1, -1,   -1,  1, -1,

            -1, -1,  1,    1, -1,  1,    1,  1,  1,   -1,  1,  1,

            // Edge midpoints (8-19)

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

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

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

            // Face centers (20-25)

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

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

            // Body center (26)

             0,  0,  0};


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

        // Face/Edge Definitions

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


        /**

         * @brief Get the element type of a face

         * @return Quad9 (all faces are 9-node biquadratic quads)

         */

        static constexpr ElemType GetFaceType(t_index /*iFace*/) { return Quad9; }


        /**

         * @brief Node indices for each face (biquadratic quad)

         *

         * Each face has 9 nodes: 4 vertices + 4 edge mids + 1 face center

         */


        static constexpr std::array<std::array<t_index, 10>, 6> faceNodes = {{

            {0, 3, 2, 1, 11, 10, 9, 8, 20},     // Face 0: bottom (z=-1)

            {0, 1, 5, 4, 8, 13, 16, 12, 21},    // Face 1: back (y=-1)

            {1, 2, 6, 5, 9, 14, 17, 13, 22},    // Face 2: right (x=+1)

            {2, 3, 7, 6, 10, 15, 18, 14, 23},   // Face 3: front (y=+1)

            {0, 4, 7, 3, 12, 19, 15, 11, 24},   // Face 4: left (x=-1)

            {4, 5, 6, 7, 16, 17, 18, 19, 25}}}; // Face 5: top (z=+1)


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

        // 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 (8 Hex8 elements)

        static constexpr int numBisect = 8;


        /// @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 Hex8 (all sub-elements are trilinear hexes)

         */

        static constexpr ElemType GetBisectElemType(t_index /*i*/) { return Hex8; }


        /**

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

         *

         * Bisecting creates 8 sub-hexes meeting at the body center node 26.

         * Each sub-hex uses corners, edge mids, face centers, and body center.

         */


        static constexpr std::array<tBisectSub, 8> bisectElements = {{

            {0, 8, 20, 11, 12, 21, 26, 24},     // Sub-hex: corner 0 octant

            {8, 1, 9, 20, 21, 13, 22, 26},     // Sub-hex: corner 1 octant

            {11, 20, 10, 3, 24, 26, 23, 15},   // Sub-hex: corner 3 octant

            {20, 9, 2, 10, 26, 22, 14, 23},    // Sub-hex: corner 2 octant

            {12, 21, 26, 24, 4, 16, 25, 19},   // Sub-hex: corner 4 octant

            {21, 13, 22, 26, 16, 5, 17, 25},   // Sub-hex: corner 5 octant

            {24, 26, 23, 15, 19, 25, 18, 7},   // Sub-hex: corner 7 octant

            {26, 22, 14, 23, 25, 17, 6, 18}}}; // Sub-hex: corner 6 octant


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

        // VTK/Visualization Support

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


        /// @brief VTK cell type identifier (25 = VTK_TRIQUADRATIC_HEXAHEDRON)

        static constexpr int vtkCellType = 25;


        /**

         * @brief VTK node ordering map

         *

         * VTK has non-trivial node reordering for Hex27:

         *   VTK nodes 0-7 = corner nodes 0-7

         *   VTK nodes 8-11 = bottom face edge mids 8-11

         *   VTK nodes 12-15 = top face edge mids 16-19

         *   VTK nodes 16-19 = vertical edge mids 12-15

         *   VTK nodes 20-25 = face centers 21-26 (reordered!)

         * Note: Only 20 nodes used by VTK (excludes some face centers)

         */


        static constexpr std::array<int, 20> vtkNodeOrder = {

            0, 1, 2, 3, 4, 5, 6, 7,       // Corners

            8, 9, 10, 11,                 // Bottom edges

            16, 17, 18, 19,               // Top edges (note: reordered)

            12, 13, 14, 15};              // Vertical edges


    };


} // namespace DNDS::Geom::Elem

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

DNDS_DEVICE_CALLABLE
#define DNDS_DEVICE_CALLABLE
Definition Defines.hpp:76

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::Hex27
@ Hex27
Definition ElemEnum.hpp:32

DNDS::Geom::Elem::Hex8
@ Hex8
Definition ElemEnum.hpp:31

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

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

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

DNDS::Geom::Elem::HexSpace
@ HexSpace
Definition ElemEnum.hpp:50

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

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

DNDS::Geom::Elem::ElementTraits< Hex27 >::GetBisectElemType
static constexpr ElemType GetBisectElemType(t_index)
Get the element type of a sub-element after bisection.
Definition Hex27.hpp:1009

DNDS::Geom::Elem::ElementTraits< Hex27 >::GetFaceType
static constexpr ElemType GetFaceType(t_index)
Get the element type of a face.
Definition Hex27.hpp:970

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

DNDS::Geom::Elem::ShapeFuncImpl< Hex27 >::Diff1
static DNDS_DEVICE_CALLABLE void Diff1(const TPoint &p, TArray &&v)
Definition Hex27.hpp:91

DNDS::Geom::Elem::ShapeFuncImpl< Hex27 >::Diff2
static DNDS_DEVICE_CALLABLE void Diff2(const TPoint &p, TArray &&v)
Definition Hex27.hpp:254

DNDS::Geom::Elem::ShapeFuncImpl< Hex27 >::Diff0
static DNDS_DEVICE_CALLABLE void Diff0(const TPoint &p, TArray &&v)
Definition Hex27.hpp:22

DNDS::Geom::Elem::ShapeFuncImpl< Hex27 >::Diff3
static DNDS_DEVICE_CALLABLE void Diff3(const TPoint &p, TArray &&v)
Definition Hex27.hpp:562

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