Daniel S. Weile

Genetic algorithm optimization applied to electromagnetics: a review

Genetic algorithms are on the rise in electromagnetics as design tools and problem solvers because of their versatility and ability to optimize in complex multimodal search spaces. This paper describes the basic genetic algorithm and recounts its history in the electromagnetics literature. Also, the application of advanced genetic operators to the field of electromagnetics is described, and design results are presented for a number of different applications.

A novel scheme for the solution of the time-domain integral equations of electromagnetics

A new method to numerically solve time-domain integral equations pertinent to electromagnetic surface scattering phenomena is presented. The method uses approximate prolate spheroidal wave functions and standard Rao-Wilton-Glisson basis functions to effect the temporal and spatial discretization of the integral equations, respectively. Because the temporal basis functions are noncausal, an extrapolation scheme is used to construct a system of equations that can be solved by marching on in time. Numerical results show that the proposed method is stable and that its solutions converge exponentially fast with the time-bandwidth product of the approximate prolate spheroidal wave functions to results from a frequency-domain method of moments solver that uses spatial basis functions and integration rules identical to those in the time-domain solver.

Genetic algorithm design of Pareto optimal broadband microwave absorbers

The concept of Pareto optimality is applied to the study of choice tradeoffs between reflectivity and thickness in the design of multilayer microwave absorbers. Absorbers composed of a given number of layers of absorbing materials selected from a predefined database of available materials are considered. Three types of Pareto genetic algorithms for absorber synthesis are introduced and compared to each other, as well as to methods operating with the weighted Tchebycheff method for Pareto optimization. The Pareto genetic algorithms are applied to construct Pareto fronts for microwave absorbers with five layers of materials selected from a representative database of available materials in the 0.2-2 GHz, 2-8 GHz, and 9-11 GHz bands.

A method for generating rational interpolant reduced order models of two-parameter linear systems☆

Abstract A model order reduction technique for systems depending on two parameters is developed. Given a large system model, the method generates the descriptor matrices of a system model of lower order that is a rational interpolant of the transfer function of the large system—the transfer functions have identical values and derivatives for a finite set of parameter values. The new technique is a generalization of recently developed algorithms for one-parameter systems that are based on projections onto Krylov subspaces defined by the descriptor matrices.

Application of a parallel particle swarm optimization scheme to the design of electromagnetic absorbers

The application of parallel (synchronous) particle swarm optimization (PSO) to electromagnetic absorber design is described. Synchronous PSO is a version of PSO that allows for parallelization and hence faster optimization. The velocity updating rule is empirically determined, and a simple approach is presented to improve its robustness. Absorbers designed with the PSO approach are compared with absorbers designed by genetic algorithms (GAs). Numerical results demonstrate that the PSO is able to deliver absorbers with comparable performance to GA-designed absorbers, with much less computational cost.

A Finite Difference Delay Modeling Approach to the Discretization of the Time Domain Integral Equations of Electromagnetics

A new method for solving the time-domain integral equations of electromagnetic scattering from conductors is introduced. This method, called finite difference delay modeling, appears to be completely stable and accurate when applied to arbitrary structures. The temporal discretization used is based on finite differences. Specifically, based on a mapping from the Laplace domain to the z-transform domain, first- and second-order unconditionally stable methods are derived. Spatial convergence is achieved using the higher-order divergence-conforming vector bases of Graglia et al. Low frequency instability problems are avoided with the loop-tree decomposition approach. Numerical results will illustrate the accuracy and stability of the technique.

Fast analysis of transient scattering in lossy media

The solution of time-domain integral equations pertinent to scattering from perfectly conducting objects residing in unbounded lossy media is considered. The computational cost of classical marching-on-in-time (MOT) schemes for the solution of such equations scales as O(N/sub t//sup 2/N/sub s//sup 2/), where N/sub t/ and N/sub s/ are the number of temporal and spatial unknowns, respectively. A fast Fourier transform (FFT)-based algorithm that reduces the computational complexity to O(N/sub t/N/sub s//sup 2/log/sup 2/N/sub t/) is introduced. When combined with spatial FFT algorithms, the proposed scheme further reduces the complexity of MOT-based integral equation solvers, for example to O(N/sub t/N/sub s/log(N/sub t/N/sub s/)logN/sub t/) if the objects are uniformly meshed. Numerical simulations that demonstrate the accuracy and efficiency of the algorithm are presented.

An accurate scheme for the solution of the time-domain Integral equations of electromagnetics using higher order vector bases and bandlimited extrapolation

Despite the numerous advances made in increasing the computational efficiency of time-domain integral equation (TDIE)-based solvers, the stability and accuracy of TDIE solvers remain problematic. This paper introduces a new numerical method for the accurate solution of TDIEs for scattering from arbitrary perfectly conducting surfaces. The work described in this paper uses the higher order divergence-conforming basis functions of Graglia et al. for spatial discretization and bandlimited interpolation functions for the temporal discretization of the relevant integral equations. Since the basis functions used for the temporal representation are noncausal, an extrapolation scheme is employed to recover the ability to solve the problem by marching on in time. Numerical results demonstrate that the proposed method is stable and that it exhibits superlinear convergence with regard to the spatial discretization and exponential convergence with respect to the temporal discretization.

A hierarchical FFT algorithm (HIL-FFT) for the fast analysis of transient electromagnetic scattering phenomena

A fast algorithm for accelerating the time-marching solution of time-domain integral equations pertinent to the analysis of free-space electromagnetic scattering from perfectly conducting, platelike and uniformly meshed structures is presented. The matrix-vector multiplications required by the time-marching scheme are accelerated by use of the fast Fourier transform (FFT). This acceleration is achieved in a multilevel fashion by hierarchically grouping sparse interactions to extract denser pieces that are efficiently evaluated by the FFT. The total computational cost and storage requirements of this algorithm scale as O(N/sub t/N/sub s/log/sup 2/ N/sub s/) and O(N/sup 1.5/), respectively, as opposed to O(N/sub t/N/sub s//sup 2/) and O(N/sub s//sup 2/) for classical time-marching methods (N/sub s/ and N/sub t/ denote the total number of spatial unknowns and time steps, respectively). Simulation results demonstrate the accuracy and efficiency of the algorithm.

A Fast Fourier Transform Accelerated Marching-on-in-Time Algorithm for Electromagnetic Analysis

A fast algorithm is presented for solving a time-domain electric field integral equation (EFIE) pertinent to the analysis of scattering from uniformly meshed, perfectly conducting structures. The marching-on-in-time (MOT) scheme that results from discretizing this EFIE is accelerated by using the fast Fourier transform to perform spatial convolutions. The computational cost and storage requirements of this algorithm scale as O(NtNs 1.5) and O(Ns 1.5), respectively, as opposed to O(NtNs 2) and O(Ns 2) for classical MOT methods. Simulation results demonstrate the accuracy and efficiency of the approach and suggestions for extending the technique are proffered.