Hybrid Finite Element and Volume Integral Methods for Scattering Using Parametric Geometry

In this paper we address several topics relating to the development and implementation of volume integral and hybrid finite element methods for electromagnetic modeling. Comparisons with the finite elementboundary integral method are given in terms of accuracy and computing resources. We also discuss preconditioning, parallelization of the multilevel fast multipole method and propose higher-order basis for curvilinear quadrilaterals and volumetric basis functions for curvilinear hexahedra. The latter have the desirable property of vanishing divergence within the element but non-zero curl. In addition, a new domain decomposition is introduced for solving array problems involving involving several million degrees of freedom. Three orders of magnitude CPU reduction is demonstrated for such applications. keyword: Radar scattering, magnetic materials, volume integral equations, finite-element boundary-integral method, fast multipole method, parallelization, antenna radiation, preconditioning, curvilinear elements, higherorder basis functions.