fem2p mesh23

fem2p() def fem2p ( n  , ne  , x  , y  , knc  , p  , q  , f  , nb1  , ib  , bv  , nb2  , ks2  , alpha  , beta  , val  , rowptr  , colind  , rhs  , base  = 0  ) Assemble finite element matrix of Poisson equation (2D) in CSR sparse matrix format Purpose This routine assembles the finite element matrix of the generalized two dimensional Poisson equation as shown below. -div(p(x,y) grad u(x,y)) + q(x,y)u(x,y) = f(x,y) Dirichlet boundary condition: u(x,y) = g Natural boundary condition: p(x,y)*du/dn + α(k,l)*u(x,y) + β(k,l) = 0 Returns info (int) = 0: Successful exit. = i < 0: The (-i)-th argument is invalid or has an illegal value. = 11: Invalid element type in knc[]. = 12: Area of a triangular element is zero or negative. = 13: Invalid boundary element type in ks2[]. = 14: Invalid node number in ks2[]. = 16: Insufficient size of a[] and/or ja[]. = 17: Internal error occurred in assembling matrix. Parameters [in] n Number of nodes. (n > 0) [in] ne Number of elements. (ne > 0) [in] x Numpy ndarray (1-dimensional, float, n) x coordinates of the nodes. [in] y Numpy ndarray (1-dimensional, float, n) y coordinates of the nodes. [in] ldknc Leading dimension of the two dimensional array knc[]. (ldknc >= nn + 1, where nn is the number of nodes in the element) [in] knc Numpy ndarray (2-dimensional, int32, ldknc x ne) (ldknc = nn + 1 (where nn is the number of nodes in the element)) Connection matrix: knc[k, 0] is the type of element k, knc[k, 1], ..., knc[k, nn] point to the nodes of element k. The type of element value is as follows: = 2: 3-node triangle. = 3: 4-node quadrangle. = 10: 9-node second order quadrangle. [in] p Numpy ndarray (1-dimensional, float, n) Coefficient p(x, y) at each node. [in] q Numpy ndarray (1-dimensional, float, n) Coefficient q(x, y) at each node. [in] f Numpy ndarray (1-dimensional, float, n) Coefficient f(x, y) at each node. [in] nb1 Number of boundary nodes of the Dirichlet boundary condition. (nb1 >= 0) [in] ib Numpy ndarray (1-dimensional, int32, nb1) Node numbers of the boundary nodes of the Dirichlet boundary conditions. [in] bv Numpy ndarray (1-dimensional, float, nb1) Boundary value at each boundary node. [in] nb2 Number of boundary sides of the natural boundary conditions. (nb2 >= 0) [in] ks2 Numpy ndarray (2-dimensional, int32, ldks2 x nb2) (ldks2 = nns + 1 (where nn is the number of nodes in the boundary element)) Connection matrix of boundary sides: [k, 0] is the type of boundary element k, [k, 1], ..., [k, nns] point to the nodes of boundary element k of the natural boundary conditions. The type of element value is as follows: = 1: 2-node line element. = 2: 3-node second order line element. [in] alpha Numpy ndarray (2-dimensional, float, nns x nb2) Array alpha[ldalpha*lalpha] (lalpha >= nb2) Coefficient alpha of the natural boundary condition at the boundary node. [in] beta Numpy ndarray (2-dimensional, float, nns x nb2) Coefficient beta of the natural boundary condition at the boundary node. [out] val Numpy ndarray (1-dimensional, float, nnz) Assembled coefficient matrix of the finite element equation (values). (nnz is the number of nonzero elements) [out] rowptr Numpy ndarray (1-dimensional, int32, n + 1) Assembled coefficient matrix of the finite element equation (row pointers). [out] colind Numpy ndarray (1-dimensional, int32, nnz) Assembled coefficient matrix of the finite element equation (column indices). (nnz is the number of nonzero elements) [out] rhs Numpy ndarray (1-dimensional, float, n) Right-hand side vector of the finite element equation. element).