Comparison of two-dimensional black box multigrid solvers for advection-diffussion equations

V. A. Bandy

University of Colorado at Denver

J. E. Dendy, Jr.

Group T-7, Los Alamos National Laboratory


We compare three black box multigrid codes for two-dimensional advection-diffusion equations in a logically rectangular domain. Two of the codes are black box multigrid codes for non-symmetric problems similar to BOXMG [jed-s,jed-n]; one uses standard coarsening in both the x- and y-directions while the other uses semi-coarsening in the y-direction only [jed-c]. The other black box multigrid solver is MGD9V [zeeuw], which uses sawtooth cycling and incomplete line LU factorization (ILLU) for the smoother.

This paper discusses several black box multigrid packages for solving problems that come from five or nine point discretizations of a second order partial differential advection-diffusion equation in a two-dimensional logically rectangular domain. We compare these black box solvers. Several numerical examples with isotropic, anisotropic, and discontinuous coefficents are presented.

The packages are all in FORTRAN 77, and the target computers are sequential, with vectorization for Cray supercomputers implemented so as not to interfere with execution on non-vectorizing computers.


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