The development of a new preconditioner by modifying the simply sparse compression matrix to solve electromagnetic method of moments problems

Abstract

The aim of this research was to improve the matrix solution methods for SuperNEC MoM problems, which is an electromagnetic simulation software package used to model antennas, and develop a new preconditioner for the iterative method BICGSTAB(L). This was achieved by firstly implementing the ATLAS BLAS library optimised for a specific computer architecture. The ATLAS code primarily makes use of code generation to build and optimise applications. Comparisons show that the matrix solution times using LU decomposition optimised by ATLAS is improved by between 4.1 and 4.6 times, providing a good coding platform from which to compare other techniques. Secondly the BICGSTAB iterative solution method in SuperNEC was improved by making use of an alternative algorithm BICGSTAB(L). Systems of equations that converged slowly or not at all using BICGSTAB, converged more quickly when using BICGSTAB(L) with L set to 4, despite the high condition numbers in the coefficient matrices. Thirdly a domain decomposition method, Simply Sparse, was characterised. Investigations showed that Simply Sparse is a good compression technique for SuperNEC MoM matrices. The custom Simply Sparse solver also solves large matrix problems more quickly than LU decomposition and scales well with increased problem sizes. LU decomposition is still however quicker for problems smaller than 7000 unknowns as the overheads in compressing the coefficient matrices dominate the Simply Sparse method for small problems. Lastly a new preconditioner for BICGSTAB(L) was developed using a modified form of the Simply Sparse matrix. This was achieved by considering the Simply Sparse matrix to be equivalent to the full coefficient matrix [A] . The largest 1% to 2% of the Simply Sparse elements was selected to form the basis of the preconditioning matrix. These elements were further modified by multiplying them by a large constant i.e. 7 1×10 . The system of equations was then solved using BICGSTAB(L) with L set to 4. The new preconditioned BICGSTAB(L) algorithm is quicker than both LU decomposition and the custom Simply Sparse solution method for problems larger than 5000 unknowns.