EFFICIENT SOLUTION OF LINEAR SYSTEMS IN MICROWAVE NUMERICAL METHODS

Abstract

A common bottle-neck, limiting the performance of many electromagnetic numerical methods, is the solution of sparse linear systems. Until now, this task has been typically solved by using iterative sparse solvers, whose require heavy computational efforts, especially when the problem is not well conditioned. An alternative strategy is based on the use of banded solvers, which numerical complexity is quadratical with respect to the matrix bandwidth. Of course, these methods are efficient provided that the matrix bandwidth is sufficiently small. In this paper, a method (called WBRA) for the bandwith reduction of a sparse matrix is presented: it is here specifically customized to typical electromagnetic matrices. The approach is superior to all the previous algorithims, also with respect to commercial well-known packages, and is suitable also for non-symmetric problems. As demonstrated by results, the use of WBRA, in conjuction with common banded solvers, substantially improves (up to one order of magnitude) the solution times in several electromagnetic approaches, such as Mode-matching, FEM, and MoM analysis of microwave circuits. In conclusion, it is proved that the high efficiency and effectiveness of WBRA turns the stragety of bandwith reduction combined with a banded solver into the most profitable way of solving linear systems in electromagnetic numerical methods.