A Nonconformal Domain Decomposition Scheme for the Analysis of Multiscale Structures

Abstract

We present a Domain Decomposition (DD) framework for the analysis of impenetrable structures; it allows for the EFIE and CFIE, and for open, closed, and open-closed structures. The DD results in an effective preconditioner for large and complex problems exploiting iterative solution and fast factorizations. The domain decomposition employs specialized transmission conditions among the domains, and the use of discontinuous Galerkin (DG) allows conformal as well as nonconformal discretizations of domain boundaries; the nonconformal nature of the decomposition gives considerable flexibility in the meshing. The strategy is highly parallelizable, as all the operations involving the sub-domains can performed in parallel. The proposed scheme is implementation independent and can be easily merged with existing electromagnetic codes.

ADAPTIVE AND PARALLEL SURFACE INTEGRAL EQUATION SOLVERS FOR VERY LARGE-SCALE ELECTROMAGNETIC MODELING AND SIMULATION (Invited Paper)

“…Instead, one usually turns to preconditioned Krylov subspace iterative methods. When such iterative solutions are employed, the efficient and parallel computation of effective preconditioners poses an immense challenge [6,12,[36][37][38][39][40][41][42]. This work proposes a one-level non-overlapping additive Schwarz DD preconditioner [43] for the solution of the DG-BEM linear system equation, Ax = b.…”

A Domain Decomposition Scheme with an Efficient Multitrace Multiresolution Preconditioner for the Simulation of Complex Composite Problems

“…Surface integral equation (SIE) methods based on the method of moments (MoM) [1] constitute a powerful tool in computational electromagnetics (CEM), which has become indispensable for the simulation and engineering of a wide range of applications with interest to science and industry. In this context, domain decomposition methods (DDMs) have proven to be the cornerstone for the versatility and accuracy of the SIE methodology, especially when highly complex problems come into play [2][3][4][5][6].…”

A Domain-Decomposition-Based Surface Integral Equation Simulator for Characterizing EM Wave Propagation in Mine Environments

“…DD strateges have been widely used to augment traditional finite element [25][26][27] and integral equation [28][29][30] methods to solve large and/or multiscale EM problems (see [31] and references therein). While state-of-the-art DD-based methods often yield rapidly convergent solutions, they do not necessarily reduce the dimensionality of the EM problem being tackled.…”