A Discontinuous Galerkin Surface Integral Equation Method for Electromagnetic Wave Scattering From Nonpenetrable Targets

Abstract

We present a discontinuous Galerkin surface integral equation method, herein referred to as IEDG, for time harmonic electromagnetic wave scattering from nonpenetrable targets. The proposed IEDG algorithm allows the implementation of the combined field integral equation (CFIE) using square-integrable, , trial and test functions without any considerations of continuity requirements across element boundaries. Due to the local characteristics of basis functions, it is possible to employ nonconformal surface discretizations of the targets. Furthermore, it enables the possibility to mix different types of elements and employ different order of basis functions within the same discretization. Therefore, the proposed IEDG method is highly flexible to apply adaptation techniques. Numerical results are included to validate the accuracy and demonstrate the versatility of the proposed IEDG method. In addition, a complex large-scale simulation is conducted to illustrate the potential benefits offered by the proposed method for modeling multiscale electrically large targets.Index Terms-Discontinuous Galerkin method, electromagnetic scattering, integral equation method, Maxwell's equations.

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

“…In this way, the troublesome mesh generation task of complex, multi-scale targets can be facilitated dramatically. Initial work has been done to demonstrate the potential of DG-BEM in solving the EM wave scattering from PEC objects in [33]. We have shown that the DG-BEM provides the same order of accuracy and convergence behavior compared to that of the traditional Galerkin CFIE method, which uses standard H(div)-conforming boundary element spaces.…”

“…where the stabilization parameter [33] is chosen to be β = | logh|/10, whereh is the average element size over the entire discretization. The variational weak formulation of CFIE (5) using discontinuous Galerkin discretizations can be formally stated as:…”

Generalized Debye Sources-Based EFIE Solver on Subdivision Surfaces

“…The solution to the EFIE is typically effected by using method of moments (MoM) wherein surface current is represented by a set of vector basis functions, say the Rao-Wilton-Glisson basis functions [30] which are equivalent to the lowest order Raviart-Thomas functions [31]. Alternatives to this approach has been a topic of significant recent interest; these include using generalized method of moments (GMM) [32], [33], subdivision surfaces [27], discontinuous basis set [34] , and more recently, Debye sources [19]. All the aforementioned methods try to bring features into modeling electromagnetic scattering; but a common thread that ties GMM, MoM on subdivision surfaces, and Debye sources is the use of surface Helmholtz decomposition.…”

Automatic h-refinement through a-posteriori error estimation and discontinous Galerkin

“…The Discontinous Galerkin (DG) method overlays on a trial function space that is piecewise discontinuous, that is more general and gives flexibility in the definition of the domain. To obtain this, the Discontinuous Galerkin scheme introduces an interior penalty condition in the impedance matrix calculation in order to cancel out the charge accumulation on the mesh edges [4]. In this particular case the extension permits to use nonconforming triangular meshes instead of the usual conformal triangular meshes, that can be result of a localized refinement, as shown in fig.…”