HexahedronTrilinear.m

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namespace fem{


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class HexahedronTrilinear
  :public fem.BaseFEM {
    public:

        HexahedronTrilinear(geo) {
            if nargin < 1
                geo = fem.geometry.Cube8Node;
            end
            this = this@fem.BaseFEM(geo);
            /* this.EdgeIndices = 1:8; */
        }


        function Nx = N(colvec<double> x) {
            Nx = [(1-x(1,:)).*(1-x(2,:)).*(1-x(3,:));... /*  1 */

                (1+x(1,:)).*(1-x(2,:)).*(1-x(3,:));...
                (1-x(1,:)).*(1+x(2,:)).*(1-x(3,:));... /*  3 */

                (1+x(1,:)).*(1+x(2,:)).*(1-x(3,:));...
                (1-x(1,:)).*(1-x(2,:)).*(1+x(3,:));... /*  5 */

                (1+x(1,:)).*(1-x(2,:)).*(1+x(3,:));...
                (1-x(1,:)).*(1+x(2,:)).*(1+x(3,:));... /*  7 */

                (1+x(1,:)).*(1+x(2,:)).*(1+x(3,:));]/8;
        }


        function dNx = gradN(colvec<double> x) {
            dNx = [-(1-x(2,:)).*(1-x(3,:)) -(1-x(1,:)).*(1-x(3,:)) -(1-x(1,:)).*(1-x(2,:));... /*  1 */

                (1-x(2,:)).*(1-x(3,:)) -(1+x(1,:)).*(1-x(3,:)) -(1+x(1,:)).*(1-x(2,:));...
                -(1+x(2,:)).*(1-x(3,:)) (1-x(1,:)).*(1-x(3,:)) -(1-x(1,:)).*(1+x(2,:));... /*  3 */

                (1+x(2,:)).*(1-x(3,:))  (1+x(1,:)).*(1-x(3,:)) -(1+x(1,:)).*(1+x(2,:));...
                -(1-x(2,:)).*(1+x(3,:)) -(1-x(1,:)).*(1+x(3,:)) (1-x(1,:)).*(1-x(2,:));... /*  5 */

                (1-x(2,:)).*(1+x(3,:)) -(1+x(1,:)).*(1+x(3,:)) (1+x(1,:)).*(1-x(2,:));...
                -(1+x(2,:)).*(1+x(3,:)) (1-x(1,:)).*(1+x(3,:)) (1-x(1,:)).*(1+x(2,:));... /*  7 */

                (1+x(2,:)).*(1+x(3,:))  (1+x(1,:)).*(1+x(3,:)) (1+x(1,:)).*(1+x(2,:))]/8;
        }

    
    public: /* ( Static ) */

        static function res = test_TrilinearBasisFun() {
            q = fem.HexahedronTrilinear;
            res = fem.BaseFEM.test_BasisFun(q);

            /*  test for correct basis function values on nodes */
            [X,Y,Z] = ndgrid(-1:2:1,-1:2:1,-1:2:1);
            p = [X(:) Y(:) Z(:)]^t;
            res = res && isequal(q.N(p),eye(8));
        }

    

};
}