Multigrid Smoothing for Symmetric Nine-Point Stencils

Irad Yavneh
Department of Computer Science
Technion
Haifa 32000
Israel

Abstract

Analytical formulae are obtained for the smoothing factors yielded by damped Jacobi relaxation and by red-black relaxation applied to symmetric nine-point stencil discretizations of elliptic partial differential operators in 2D. The results include point and line relaxation and full and partial coarsening. Several unusual results are implied by the formulae. Numerical results of multigrid cycles match the analytical predictions well.


Contributed November 27, 1996.