Stranger than Fiction: On smoothing symmetric nine-point operators.

Irad Yavneh

Department of Computer Science Technion - Israel Institute of Technology Haifa, 32000 Israel


Analytical formulae are derived 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.