Abstract-This paper presents a parallel implementation of a partial element equivalent circuit (PEEC) based electromagnetic modeling code. The parallelization is based on the GMM++ and ScaLAPACK packages. The parallel PEEC solver was successfully implemented and tested on several high performance computer systems. Large structures containing over 50 000 unknown current and voltage basis functions were successfully analyzed and memory, performance, and speedup results are presented. The numerical examples are both of orthogonal and nonorthogonal type with analysis in the time-and frequencydomain.
I. INTRODUCTIONThe partial element equivalent circuit (PEEC) method [1], [2] is widely used for solving mixed circuit and electromagnetic problems. The method gives a framework for creating electric equivalent circuit representations for threedimensional structures and calculating self and mutual inductances and capacitances. The resulting equivalent circuits can be solved in SPICE-like solvers or, for the full-wave case, by creating and solving the fully coupled circuit equations.As for all the methods within computational electromagnetics (CEM), the problem system size that can be solved is increasing with more efficient computer implementations [3] and more powerful computer systems. However, the desired problem sizes to be solved are also increasing and there is a clear gap between desired and possible problem size to be solved. Fast solutions for CEM problems have been treated for a long time, i.e. [4] where both differential and integral equation solvers were discussed. The next step after faster implementations are to improve the computing power running the algorithms. One solution is to use GRID computing on different levels. For example using a local area network of interconnected computers to speed up calculations or by porting the code to parallel architectures. Recent publications on the extension to parallel implementations are for example [5] where a nesting combination of the finite element domain decomposition method and the algebraic multigrid method is presented, [6] on the implicit FDTD method, and [7] for a parallel version of the numerical electromagnetics code (NEC).Until now, no parallel implementation on the PEEC method have been reported except for in [8] where a sequential code was parallelized for LANs using a freeware. In this paper, parallel implementations of the PEEC method is presented for supercomputers featuring different architectures using ScaLA-PACK [9]. Implementation issues and examples are presented for the time-and frequency-domain PEEC method. It is shown