Multigrid treatment of L-shape domain for boundary-value problems in two and three dimensions

The multigrid method is widely recognized as an efficient and rapidly convergent method to solve various partial differential equations. In many cases we are usually interested in the number of iterations. Moreover we are often interested in the applicability of the multigrid method to realistic problems. Our usual aims are to study an algorithm for solving a large linear system of equations which stems from the discretized partial differential equations. In this paper, we solve the linear PDE on the L-shape domain in two and three dimensions using the full multigrid (FMG) algorithm in which V(gamma(1), gamma(2)) cycles with suitable choices of alternating line relaxation, (in 2D) and alternating plane relaxation (in 3D), full weight residual restriction and linear interpolation. Numerical examples are given.