A novel MultiResolution Preconditioner Including Piecewise Homogeneous Dielectric Objects

Abstract

An extensive literature demonstrates the capabilities of the hierarchical quasi-Helmholtz decomposition multiresolution preconditioner both to address the breakdowns for the surface integral equations and to improve the convergence in multiscale problems, until now only applied to perfect electrical conductors. In this work we present a novel methodology based on this efficient preconditioner able to solve arbitrary complex geometries composed of piecewise homogeneous composite objects, that automatically satisfies the boundary conditions. To the authors’ knowledge, this is the first work where a multilevel quasi-Helmholtz decomposition is applied to objects with dielectric junctions without the need of a weak enforcement of the continuity or a number-of-unknown-reduction scheme. Numerical examples demonstrate the efficiency of the proposed approach for the solution of complex problems involving multiple materials (dielectric and conductors).