This generator computes a five-point central finite difference discretization of the two-dimensional variable-coefficient linear elliptic equation -(p u_x)_x -(q u_y)_y + r u_x + (r u)_x + s u_y + (s u)_y + t u = f, where p, q, r, s and t are the functions of x and y. The domain is the unit square (0,1)x(0,1), and the boundary condition are Dirichlet.

Although the code handles arbitrary p, q, r, s and t, it is set up initially with p = exp(-xy), Q = exp(xy), R = beta (x+y), S = gamma (x+y), and t = 1/(1+x+y). It is suggested to use values of beta and gamma between 0 and 250. The object is to estimate those eigenvalues with the largest real parts and to determine whether or not there are significant gaps in the spectrum.

Parameters:

• Source
• Matrix-vector multiply utility

Matrix Instances:

• PDE225 (real unsymmetric, 225 by 225, 1065 nonzeros) Parameters: NX=NY=15, BETA=20, GAMMA=0
• PDE900 (real unsymmetric, 900 by 900, 4380 nonzeros) Parameters: NX=NY=30, BETA=20, GAMMA=0
• PDE2961 (real unsymmetric, 2961 by 2961, 14585 nonzeros) Parameters: NX=47, NY=63, BETA=20, GAMMA=0

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Last change in this page: Wed Sep 22 13:37:29 US/Eastern 2004 [Comments: ]