Parallel computation of 3-D electromagnetic scattering using finite elements

Abstract

The finite element method (FEM) with local absorbing boundary conditions has been recently applied to compute electromagnetic scattering from large 3-D geometries. In this paper, we present details pertaining to code implementation and optimization. Various types of sparse matrix storage schemes are discussed and their performance is examined in terms of vectorization and net storage requirements. The system of linear equations is solved using a preconditioned biconjugate gradient (BCG) algorithm and a fairly detailed study of existing point and block preconditioners (diagonal and incomplete LU) is carried out. A modified ILU preconditioning scheme is also introducted which works better than the traditional version for our matrix systems. The parallelization of the iterative sparse solver and the matrix generation/assembly as implemented on the KSR1 multiprocessor is described and the interprocessor communication patterns are analysed in detail. Near-linear speed-up is obtained for both the iterative solver and the matrix generation/assembly phases. Results are presented for a problem having 224,476 unknowns and validated by comparison with measured data.