Scalable Solutions to ]ntegral ILquation and Finite Itlcmcnt Simulations

When developing numerical methods, or applying them to the simulation and design of cnginccring components, it inevi(ab]y bccomcs necessary to examine the scaling of tlic rndhod with a problcm’s electrical size. The scaling results from the original mathematical development-for example, a dense system of equations in the solution of integral equations-as well as the specific numerical implementation. Scaling of the numerical implementation depends upon many factors–-for example, direct or iterative methods for solution of the linear system-–as well as the computer architecture used in the simulation. In this paper, scalability will be divided into two components; scalability of the numerical algorithm specifically on parallel computer systcm.s, and algorithm or sequential scalabi]it y. The sequential implementation and scaling is initial presented with the parallel inlplcmcntation following. “1’his progression is meant to illustrate the differences in using current parallel platforms from sequential machines, and the resulting savings. Time to solution (wall clock time) a]on~ with problc.m sim arc the kcy parameters plotted or tabulated. Sc~ucntial and parallel scalability of time harmonic surface integral equation forms and the frnitc clement solution to the pallial differential equations arc considered in detail.