Scattered Field Computation With an Extended Feti-Dpem2 Method

Abstract

Abstract-Due to the increasing number of applications in engineering design and optimization, more and more attention has been paid to full-wave simulations based on computational electromagnetics. In particular, the finite-element method (FEM) is well suited for problems involving inhomogeneous and arbitrary shaped objects. Unfortunately, solving large-scale electromagnetic problems with FEM may be time consuming. A numerical scheme, called the dual-primal finite element tearing and interconnecting method (FETI-DPEM2), distinguishes itself through the partioning on the computation domain into non-overlapping subdomains where incomplete solutions of the electrical field are evaluated independently. Next, all the subdomains are "glued" together using a modified Robin-type transmission condition along each common internal interface, apart from the corner points where a simple Neumann-type boundary condition is imposed. We propose an extension of the FETI-DPEM2 method where we impose a Robin type boundary conditions at each interface point, even at the corner points. We have implemented this Extended FETI-DPEM2 method in a bidimensional configuration while computing the field scattered by a set of heterogeneous, eventually anistropic, scatterers. The results presented here will assert the efficiency of the proposed method with respect to the classical FETI-DPEM2 method, whatever the mesh partition is arbitrary defined.

3-D Electromagnetic Scattering Computation in Free-Space With the FETI-FDP2 Method

“…In the framework of a 2-D configuration [21], we not only showed that the term W i↔j rc should not be neglected, but we also showed that the method can be further enhanced by imposing a Robin-type boundary condition everywhere. In that case, (20) should be kept as is.…”

“…In a previous work, performed in 2-D [21], we have extended the FETI-DPEM2 method by imposing everywhere, even on the corner nodes, more flexible Robin-type boundary conditions. The resulting interface problem is completely rewritten and acts as a new global coarse preconditioner.…”

“…Section II describes the considered 3-D free-space electromagnetic scattering configuration and the associated scattered field formulation. In Section III, following the notations introduced in [13] and [21], the mathematical formalisms of the different FETI-DPEM2 and FETI-FDP2 methods are described. The constructions of the full and reduced linear systems obtained for the various interfaces unknowns, either the corner edges or the inner interface edges, are detailed.…”

“…2) FETI-DPEM2 (b) Method: In a previous work, performed under a 2-D configuration [21], we showed that, in order to limit computational errors, the connection between the corner and interface DOFs must be kept. In other words, the term W i↔j rc should not be neglected during the "gluing" process.…”

“…Taking this into account, the resulting equation (22) is still valid [21], [26]. The only difference between the FETI-DPEM2 (a) and FETI-DPEM2 (b) methods relies on the definition of the matrix F λrEc , which now corresponds to…”