Matrix equilibration in method of moment solutions of surface integral equations

Abstract

Basic theory of matrix equilibration is presented, relating it to other techniques for decreasing the condition number of matrix equations obtained by the method of moments (MOM) applied to surface integral equations (SIEs). It is shown that matrix equilibration is a general technique that can be used for both (1) balancing field and source quantities in SIEs, which is used to decrease the condition number in the case of SIEs of mixed type and high contrast in material properties, and (2) scaling basis and test functions in MOM, which is used to decrease the condition number in the case of higher-order bases and patches of different sizes. In particular, it is demonstrated that a combination of such balancing and scaling can be performed using simple matrix equilibration based on magnitudes of diagonal elements and 2-norms of rows/columns of the MOM matrix.