Asymptotic phase extraction as a preconditioning technique for mom

The most common preconditioners are of algebraic nature, based on sparse inverse approximations of the MoM matrix Z, like the incomplete LU decomposition (ILU). An improvement in the condition number can be also obtained directly in Z using appropriate basis functions, such as higher order basis functions, and multi-resolution techniques. The asymptotic phase integral equation method (AP-IE) is also a method to increase the range of applicability of MoM for high frequencies and smooth scatterers.