Efficient preconditioning based on orthogonalization of method of moments equations

Efficient iterative solution of matrix equations, obtained by MoM/SIE (application of the Method of Moments to Surface Integral Equations) usually requires properly chosen preconditioning. Standard preconditioning methods are shown not to be very efficient in case of classic hierarchical higher order basis functions. On the other hand orthogonalization of such bases dramatically decreases the condition number of the MoM matrix. Having this in mind the preconditioning method based on simultaneous orthogonalization of rows and columns of the MoM matrix is proposed in this paper. The method is developed for symmetric matrices, such as those obtained by the Electric Field Integral Equation (EFIE) and the PMCHWT equation. Numerical results show that the condition number of the MoM matrix equation can be reduced by several orders of magnitude, and that number of iterations can be reduced a few times.