C 代码 定义和评估有限元法 （FEM） 基函数 对于 M 维单纯形中的任何度数.rar

19 January 2020 11:30:35 AM FEM_BASIS_TEST: C version. Test the FEM_BASIS library. TEST01 FEM_BASIS_1D evaluates an arbitrary basis function over an interval. I J X L(I,J)(X) 2 1 0.666667 1 0 3 0 -0 1 2 0.333333 0 2 1 0.666667 1 3 0 1 0 TEST02 FEM_BASIS_2D evaluates an arbitrary triangular basis function. I J K X Y L(I,J,K)(X,Y) 1 0 2 0.333333 0 1 0 0 3 0 0 0 1 0 2 0.333333 0 1 2 0 1 0.666667 0 0 3 0 0 1 0 -0 0 1 2 0 0.333333 0 1 1 1 0.333333 0.333333 1.11022e-16 2 1 0 0.666667 0.333333 -1.66533e-16 0 2 1 0 0.666667 0 1 2 0 0.333333 0.666667 -1.66533e-16 0 3 0 0 1 -0 TEST03 FEM_BASIS_3D evaluates an arbitrary tetrahedral basis function. I J K L X Y Z L(I,J,K,L)(X,Y,Z) 1 0 2 1 0.25 0 0.5 1 0 0 0 4 0 0 0 -0 1 0 0 3 0.25 0 0 -0 2 0 0 2 0.5 0 0 -0 3 0 0 1 0.75 0 0 -0 4 0 0 0 1 0 0 -0 0 1 0 3 0 0.25 0 -0 1 1 0 2 0.25 0.25 0 -0 2 1 0 1 0.5 0.25 0 -0 3 1 0 0 0.75 0.25 0 -0 0 2 0 2 0 0.5 0 -0 1 2 0 1 0.25 0.5 0 -0 2 2 0 0 0.5 0.5 0 -0 0 3 0 1 0 0.75 0 -0 1 3 0 0 0.25 0.75 0 -0 0 4 0 0 0 1 0 -0 0 0 1 3 0 0 0.25 0 1 0 1 2 0.25 0 0.25 0 2 0 1 1 0.5 0 0.25 0 3 0 1 0 0.75 0 0.25 0 0 1 1 2 0 0.25 0.25 0 1 1 1 1 0.25 0.25 0.25 0 2 1 1 0 0.5 0.25 0.25 0 0 2 1 1 0 0.5 0.25 0 1 2 1 0 0.25 0.5 0.25 0 0 3 1 0 0 0.75 0.25 0 0 0 2 2 0 0 0.5 0 1 0 2 1 0.25 0 0.5 1 2 0 2 0 0.5 0 0.5 0 0 1 2 1 0 0.25 0.5 0 1 1 2 0 0.25 0.25 0.5 0 0 2 2 0 0 0.5 0.5 0 0 0 3 1 0 0 0.75 0 1 0 3 0 0.25 0 0.75 0 0 1 3 0 0 0.25 0.75 0 0 0 4 0 0 0 1 0 TEST04 FEM_BASIS_MD evaluates an arbitrary basis function over an M-dimensional simplex. I J X L(I,J)(X) 2 1 0.666667 1 0 3 0 -0 1 2 0.333333 0 2 1 0.666667 1 3 0 1 0 TEST05 FEM_BASIS_MD evaluates an arbitrary basis function over an M-dimensional simplex. I J K X Y L(I,J,K)(X,Y) 1 0 2 0.333333 0 1 0 0 3 0 0 0 1 0 2 0.333333 0 1 2 0 1 0.666667 0 0 3 0 0 1 0 -0 0 1 2 0 0.333333 0 1 1 1 0.333333 0.333333 0 2 1 0 0.666667 0.333333 -0 0 2 1 0 0.666667 0 1 2 0 0.333333 0.666667 -0 0 3 0 0 1 -0 TEST06 FEM_BASIS_MD evaluates an arbitrary basis function over an M-dimensional simplex. I J K L X Y Z L(I,J,K,L)(X,Y,Z) 1 0 2 1 0.25 0 0.5 1 0 0 0 4 0 0 0 -0 1 0 0 3 0.25 0 0 -0 2 0 0 2 0.5 0 0 -0 3 0 0 1 0.75 0 0 -0 4 0 0 0 1 0 0 -0 0 1 0 3 0 0.25 0 -0 1 1 0 2 0.25 0.25 0 -0 2 1 0 1 0.5 0.25 0 -0 3 1 0 0 0.75 0.25 0 -0 0 2 0 2 0 0.5 0 -0 1 2 0 1 0.25 0.5 0 -0 2 2 0 0 0.5 0.5 0 -0 0 3 0 1 0 0.75 0 -0 1 3 0 0 0.25 0.75 0 -0 0 4 0 0 0 1 0 -0 0 0 1 3 0 0 0.25 0 1 0 1 2 0.25 0 0.25 0 2 0 1 1 0.5 0 0.25 0 3 0 1 0 0.75 0 0.25 0 0 1 1 2 0 0.25 0.25 0 1 1 1 1 0.25 0.25 0.25 0 2 1 1 0 0.5 0.25 0.25 0 0 2 1 1 0 0.5 0.25 0 1 2 1 0 0.25 0.5 0.25 0 0 3 1 0 0 0.75 0.25 0 0 0 2 2 0 0 0.5 0 1 0 2 1 0.25 0 0.5 1 2 0 2 0 0.5 0 0.5 0 0 1 2 1 0 0.25 0.5 0 1 1 2 0 0.25 0.25 0.5 0 0 2 2 0 0 0.5 0.5 0 0 0 3 1 0 0 0.75 0 1 0 3 0 0.25 0 0.75 0 0 1 3 0 0 0.25 0.75 0 0 0 4 0 0 0 1 0 TEST07 FEM_BASIS_PRISM_TRIANGLE evaluates an arbitrary basis function over a right triangular prism. Here, we generate basis functions which can be up to degree 2 in X and Y, and up to degree 2 in Z. Choose a node N1, define the basis function associated with that node, and then evaluate it at all other nodes. I1 I2 I3 J1 J2 X Y Z B(X,Y,Z) 2 0 0 1 1 1 0 0.5 1 0 0 2 0 2 0 0 0 -0 0 0 2 1