Efficient parallel implementation of a compact higher-order maxwell solver using spatial filtering

Abstract

This chapter describes the parallel implementation of a Maxwell equations solver on a cluster of heterogeneous workstations. The Maxwell solver, designated ANTHEM, computes the electromagnetic scattering by two-dimensional perfectly-conducting and dielectric bodies by solving Maxwell equations in frequency domain. The governing equations are derived by writing Maxwell equations in conservation-law form for scattered field quantities and then assuming a single-frequency incident wave. A pseudo-time variable is introduced, and the entire set of equations is driven to convergence by an explicit/point-implicit four-stage Runge-Kutta time-marching finite-volume scheme. Higher-order implicit spatial filtering is used in conjunction with a higher-order compact scheme for spatial discretization, to filter undesirable oscillations. Far-field boundary conditions are computed using the method of Giles and Shu. Results are compared with known analytic solutions and the method-of-moments. The results indicate that, although compact schemes satisfy the stringent requirements of an accurate electromagnetic computation, spatial filtering is important as it provides an excellent alternative to grid refinement at a fraction of the computational cost. Parallelization on heterogeneous workstations is accomplished by using PVM software for process control and communication. Excellent parallel efficiency is obtained, although it is somewhat dependent on the domain decomposition strategy.