M. A. Carr

Massively Parallel Fast Multipole Method Solutions of Large Electromagnetic Scattering Problems

We describe a massively parallel version of the single-level fast multipole method (FMM) that employs the fast Fourier transform (FFT) for the translation stage. The proposed FMM-FFT method alleviates the communication bottleneck and has a lower complexity, O(N4/3 log2/3 N), as compared to the conventional single level FMM which scales as O(N3/2), where N is the number of unknowns. Through numerical examples we demonstrate that the proposed parallel fast multipole method yields a faster solution time than its multilevel counterpart for very large problems in a distributed memory parallel setting.

Generalized volume-surface integral equation for modeling inhomogeneities within high contrast composite structures

Numerical solutions of volume integral equations with high contrast inhomogeneous materials require extremely fine discretization rates making their utility very limited. Given the application of such materials for antennas and metamaterials, it is extremely important to explore computationally efficient modeling methods. In this paper, we propose a novel volume integral equation technique where the domain is divided into different material regions each represented by a corresponding uniform background medium coupled with a variation, together representing the overall inhomogeneity. This perturbational approach enables us to use different Greens functions for each material region. Hence, the resulting volume-surface integral equation alleviates the necessity for higher discretizations within the higher contrast regions. With the incorporation of a junction resolution algorithm for the surface integral equations defined on domain boundaries, we show that the proposed volume-surface integral equation formulation can be generalized to model arbitrary composite structures incorporating conducting bodies as well as highly inhomogeneous material regions.

Watershed load balancing technique for distributed memory parallelization of fast multipole methods with near-field preconditioning

The fast multipole method (FMM) has demonstrated great potential for accelerating the solution of integral equation systems. However, FMMs reliance on iterative solution techniques, in conjunction with poorly conditioned systems resulting from typical electromagnetic problems, mandates the use of specialized preconditioning methods to improve convergence and reduce the overall solution time. Efficient parallelization and load balancing of the FMM algorithm and preconditioner is equally critical for reduction of solution time. The near-field preconditioner (NFP) (Carr, M. et al., IEEE Ant. Prop. Mag., 2004; Carr and Volakis, J.L., Proc. 2003 IEEE Int. Ant. Prop. Symp.) is one technique that is amenable parallelization. However the overlapping subdomain condition of the NFP presents a challenge for distributed memory parallelization. The paper describes a technique referred to as watershed load balancing (WLB) that employs image processing methods to form large, contiguous subdomains, reducing the total volume of overlap and therefore achieving improved parallelization efficiency while preserving the characteristics of the NFP.

Application of hierarchical basis functions to the generalized SIE for simulation of metamaterial antennas

Summary form only given. Antennas consisting of textured materials can lead to miniature, yet broadband, designs (Kiziltas, G., et al. IEEE Trans. Ant. Prop., vol.51, p.2732-43, 2003). These metamaterial antennas consist of very high contrast media with intricate texture detail. Due to the rapid variations within the textured substrates, accurate analysis of such structures requires a very fine sampling rate or the use of high order methods that have the ability to achieve the required resolution throughout the computational domain. Recently, a new class of higher order hierarchical basis functions have been proposed for curvilinear finite elements and applied to scattering by electrically large PEC structures (Jorgensen, E., et. al., IEEE Trans. Ant. Prop., vol.52, p.2985-95, 2004). We propose to use these bases in a generalized surface integral equation approach for analyzing complex structures consisting of intricate detail and which may incorporate high contrast textured materials. We also investigate (for an adaptive refinement) error indicators to aid us in the design of antennas containing complex materials.

Generalized VSIE formulation for arbitrary high contrast objects

High contrast materials can be found in many useful metamaterial applications. However, traditional VIE methods for high contrast inhomogeneous materials require extremely high field resolution where the sampling rate is inversely proportional to the material parameters. To overcome the sampling rate growth, this paper proposes a factorization technique allowing high contrast inhomogeneous materials to he represented by an equivalent uniform medium and a perturbation representing its inhomogeneity. The resulting VSIE alleviates, to a large degree, the necessity for higher discretizations within these material regions allowing for simulation of recently proposed complex media.