The Multi-resolution preconditioner

Abstract

The purpose of this chapter is to provide the main guidelines for an efficient implementation of the multi-resolution (MR) preconditioner for the electromagnetic (EM) analysis of perfect electric conductor (PEC) structures of arbitrary 3-D shape via the method of moments (MoM) applied to the electric field integral equation (EFIE) and to the combined field integral equation (CFIE). The chapter is structured in four main parts. First, the generation of the MR basis functions as a linear combination of the standard basis functions is described. Second, the generation of a multi-level set of meshes, starting from the usual mesh, is reported: the MR functions are defined on each level of the generated set of meshes. These two parts are essential to implement the proposed preconditioner. Then, the third part is dedicated to the insertion of the MR preconditioner into the solution algorithm, together with the description of some implementation tricks. Finally, numerical results, where the MR preconditioner is applied to complex realistic 3-D structures, are reported and commented. The expected property of the MR preconditioner is an improvement of the convergence rates of iterative solvers, with a limited computational cost for its generation and application. The proposed preconditioner can be applied to realistic structures with arbitrary topological complexity.