Multi-resolution approach to three-dimensional method-of-moments problems

Objectives, expectations and difficulties associated to the use of multi-resolution (MR) constructs in integral equation, method of moments (MoM) are reviewed and put in a contemporary perspective. A MR approach is presented that can be applied to any mesh without any constrain on the structure topology. The so-obtained MR basis positively affects the spectrum of the MoM matrix, affording an efficient (multiplicative) preconditioner. The reasons of this are explained in terms of the dual spatial-spectral resolution of the MR basis.