The parallel computation of solutions to electrostatic problems using multigrid techniques

The application of multigrid techniques to the computation of the static solutions of electromagnetic field problems governed by Laplace's equation is described. This technique is compared with the conventional successive over-relaxation (SOR) method for solving finite difference problems. In contrast to SOR, the number of iterations of multigrid needed to achieve convergence is largely independent of the grid size. It is shown that the relative performance of multigrid is excellent on large grids where the number of iterations of SOR needed to achieve convergence becomes prohibitively large. The technique is illustrated by applying a parallel implementation of multigrid to find a quasistatic solution of a boxed microstrip problem.