`123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657` ``````------------------------------------------------------------- SPARSKIT MODULE MATGEN ------------------------------------------------------------- The current directory MATGEN contains a few subroutines and drivers for generating sparse matrices. 1) 5-pt and 7-pt matrices on rectangular regions discretizing elliptic operators of the form: L u == delx( a delx u ) + dely ( b dely u) + delz ( c delz u ) + delx ( d u ) + dely (e u) + delz( f u ) + g u = h u with Boundary conditions, alpha del u / del n + beta u = gamma on a rectangular 1-D, 2-D or 3-D grid using centered difference scheme or upwind scheme. The functions a, b, ..., h are known through the subroutines afun, bfun, ..., hfun in the file functns.f. The alpha is a constant on each side of the rectanglar domain. the beta and the gamma are defined by the functions betfun and gamfun (see functns.f for examples). 2) block version of the finite difference matrices (several degrees of freedom per grid point. ) It only generates the matrix (without the right-hand-side), only Dirichlet Boundary conditions are used. 3) Finite element matrices for the convection-diffusion problem - Div ( K(x,y) Grad u ) + C(x,y) Grad u = f u = 0 on boundary (with Dirichlet boundary conditions). The matrix is returned assembled in compressed sparse row format. See genfeu for matrices in unassembled form. The user must provide the grid, (coordinates x, y and connectivity matrix ijk) as well as some information on the nodes (nodcode) and the material properties (the function K(x,y) above) in the form of a subroutine xyk. 4) Markov chain matrices arising from a random walk on a trangular grid. Useful for testing nonsymmetric eigenvalue codes. Has been suggested by G.W. Stewart in one of his papers. Used by Y. Saad in several papers as a test problem for nonsymmetric eigenvalue methods. 5) Matrices from the paper by Z. Zlatev, K. Schaumburg, and J. Wasniewski. (``A testing scheme for subroutines solving large linear problems.'' Computers and Chemistry, 5:91--100, 1981.) ---------------------------------------------------------------------- the items (1) and (2) are in directory FDIF, the item (3) is in directory FEM the items (4) and (5) are in directory MISC ``````