Finite element methods for Maxwell's equations.

Surface-enhanced Raman scattering (SERS) has become a widely used spectroscopic technique for chemical identification, providing unbeaten sensitivity down to the single-molecule level. The amplification of the optical near field produced by collective electron excitations —plasmons— in nanostructured metal surfaces gives rise to a dramatic increase by many orders of magnitude in the Raman scattering intensities from neighboring molecules. This effect strongly depends on the detailed geometry and composition of the plasmon-supporting metallic structures. However, the search for optimized SERS substrates has largely relied on empirical data, due in part to the complexity of the structures, whose simulation becomes prohibitively demanding. In this work, we use state-of-the-art electromagnetic computation techniques to produce predictive simulations for a wide range of nanoparticle-based SERS substrates, including realistic configurations consisting of random arrangements of hundreds of nanoparticles with var...

Optimization of Nanoparticle-Based SERS Substrates through Large-Scale Realistic Simulations

We propose and study a nonoverlapping and nonconforming domain decomposition method for the integral-equation-based solution of large, complex electromagnetic (EM) scattering problems. The continuity of the electric surface current across the boundary between adjacent subdomains is enforced by a skew-symmetric interior penalty formulation. A nonoverlapping additive Schwarz preconditioner is designed and analyzed for the solution of the linear system of equations resulting from Galerkin boundary-element discretization. We show that the preconditioned system exhibits a uniformly confined eigenspectrum with respect to changing problem and discretization parameters. Numerical examples are presented to demonstrate the fast convergence of iterative solvers and the superior accuracy of the solutions obtained by our method. The proposed work can be viewed as an effective preconditioning scheme that reduces the condition number of very large systems of equations in challenging EM scattering problems. The strength and capability of the proposed method will be illustrated by means of several examples of practical interest.

Domain Decomposition Preconditioning for Surface Integral Equations in Solving Challenging Electromagnetic Scattering Problems

In this paper, we present our efforts in combating a challenging large multiscale electromagnetic scattering problem, viz. a plane-wave scattering from a mockup partially coated composite jet aircraft at X-band. We first summarize the application of the newly developed integral equation domain decomposition method (IE-DDM) to compute the plane-wave scattering from the jet aircraft, however with neither dielectrics nor lossy thin coatings. We proceed to compute the scattering from the aircraft with dielectrics and lossy thin coatings by employing two additional computational electromagnetics (CEM) techniques: a generalized combined field integral equation (G-CFIE) method to calculate electromagnetics (EM) scatterings from penetrable dielectric targets, and a hybrid finite elements and boundary elements method tailored specifically to address perfect electric conductor (PEC) targets partially coated with lossy thin materials.

Nonconformal Domain Decomposition Methods for Solving Large Multiscale Electromagnetic Scattering Problems

We present a domain decomposition (DD) framework for the analysis of impenetrable structures; it allows for the electric field integral equation (EFIE) and combined field integral equation (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 DD 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 subdomains can be performed in parallel. The proposed scheme is implementation independent and can be easily merged with existing electromagnetic codes.

A Nonconformal Domain Decomposition Scheme for the Analysis of Multiscale Structures

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.

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

We present a surface integral equation domain decomposition method (SIE-DDM) for time harmonic electromagnetic wave scattering from bounded composite targets. The proposed SIE-DDM starts by partitioning the composite object into homogeneous sub-regions with constant material properties. Each of the sub-regions is comprised of two sub-domains (the interior of the penetrable object, and the exterior free space), separated on the material interface. The interior and the exterior boundary value problems are coupled to each other through the Robin transmission conditions, which are prescribed on the material/domain interface. A generalized combined field integral equation is employed for both the interior and the exterior sub-domains. Convergence studies of the proposed SIE-DDM are included for both single homogeneous objects and composite penetrable objects. Furthermore, a complex large-scale simulation is conducted to demonstrate the capability of the proposed method to model multi-scale electrically large targets.

Computations of Electromagnetic Wave Scattering From Penetrable Composite Targets Using a Surface Integral Equation Method With Multiple Traces

We proposed herein a multisolver domain decomposition method (MS-DDM), and applied it to compute the isolations among multiple antennas mounted on a large air platform at X -band frequency. The fundamental strategy of the proposed MS-DDM is to decompose the entire computational domain into many subregions based on the local material properties and geometrical features. Subsequently, we employ the most suitable computational electromagnetic (CEM) technique for each of the subregions. Moreover, the coupling between well-separated subregions is implemented through Stratton-Chu representation formulas. However, for the touching interfaces between neighboring subregions, a Robin transmission condition is introduced to mitigate the troublesome self-integral terms with weak singular kernels. The proposed MS-DDM is, therefore, well suited for modeling multiple antennas conformally mounted on a large platform, where touching subregions are usually unavoidable. Furthermore, by using the proposed MS-DDM framework, multiple existing CEM solvers have been successfully integrated with few minor modifications.

Kheng-Hwee Lim

Papers

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

Computations of Electromagnetic Wave Scattering From Penetrable Composite Targets Using a Surface Integral Equation Method With Multiple Traces

Nonconformal Domain Decomposition Methods for Solving Large Multiscale Electromagnetic Scattering Problems

Multisolver Domain Decomposition Method for Modeling EMC Effects of Multiple Antennas on a Large Air Platform

A boundary integral equation domain decomposition method for electromagnetic scattering from large and deep cavities