Eric Michielssen

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.

Design of lightweight, broad-band microwave absorbers using genetic algorithms

A procedure for synthesizing multilayered radar absorbing coatings is presented. Given a predefined set of N/sub m/ available materials with frequency-dependent permittivities in /sub i/(f) and permeabilities mu /sub i/(f) (i=1,. . ., N/sub m/), the technique determines simultaneously the optimal material choice for each layer and its thickness. This optimal choice results in a screen which maximally absorbs TM and TE incident plane waves for a prescribed range of frequencies (f/sub 1/,f/sub 2/,. . ., f/sub N/f) and incident angles ( theta /sub 1/, theta /sub 2/,. . ., theta /sub N theta /). The synthesis technique is based on a genetic algorithm. The technique automatically places an upper bound on the total thickness of the coating, as well as the number of layers contained in it, which greatly simplifies manufacturing. In addition, the thickness or surface mass of the coating can be minimized simultaneously with the reflection coefficient. The algorithm was successfully applied to the synthesis of wideband absorbing coatings in the frequency ranges of 0.2-2 GHz and 2-8 GHz. >

A multilevel matrix decomposition algorithm for analyzing scattering from large structures

A multilevel algorithm is presented for analyzing scattering from electrically large surfaces. The algorithm accelerates the iterative solution of integral equations that arise in computational electromagnetics. The algorithm permits a fast matrix-vector multiplication by decomposing the traditional method of moment matrix into a large number of blocks, with each describing the interaction between distant scatterers. The multiplication of each block by a trial solution vector is executed using a multilevel scheme that resembles a fast Fourier transform (FFT) and that only relies on well-known algebraic techniques. The computational complexity and the memory requirements of the proposed algorithm are O(N log/sup 2/ N).

Fast solution methods in electromagnetics

Various methods for efficiently solving electromagnetic problems are presented. Electromagnetic scattering problems can be roughly classified into surface and volume problems, while fast methods are either differential or integral equation based. The resultant systems of linear equations are either solved directly or iteratively. A review of various differential equation solvers, their complexities, and memory requirements is given. The issues of grid dispersion and hybridization with integral equation solvers are discussed. Several fast integral equation solvers for surface and volume scatterers are presented. These solvers have reduced computational complexities and memory requirements.

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.

The plane-wave time-domain algorithm for the fast analysis of transient wave phenomena

This article describes a plane-wave time-domain (PWTD) algorithm that facilitates the fast evaluation of transient wave fields produced by surface scattering. The algorithm presented relies on a Whittaker-type expansion of transient fields in terms of propagating plane waves. The incorporation of the PWTD scheme into existing matching-on-in-time- (MOT-) based integral-equation solvers is elucidated. It is shown that the computational cost of performing a surface-scattering analysis, using two-level and multilevel PWTD-enhanced MOT schemes, scales as O(N/sub t/N/sub s//sup 1.5/ log N/sub s/) and O(N/sub t/N/sub s/log/sup 2/N/sub s/), respectively, when the surface source density is represented by N/sub s/ spatial and N/sub t/ temporal samples. Hence, the computational cost of the proposed algorithms scales much more favorably than that of classical MOT schemes, which scale as O(N/sub t/N/sub s//sup 2/). Therefore, PWTD-enhanced MOT schemes make possible the analysis of broadband scattering from structures of unprecedented dimensions.

Analysis of transient electromagnetic scattering from closed surfaces using a combined field integral equation

In the past, both the time-domain electric and magnetic field integral equations have been applied to the analysis of transient scattering from closed structures. Unfortunately, the solutions to both these equations are often corrupted by the presence of spurious interior cavity modes. In this article, a time-domain combined field integral equation is derived and shown to offer solutions devoid of any resonant components. It is anticipated that stable marching-on-in-time schemes for solving this combined field integral equation supplemented by fast transient evaluation schemes such as the plane wave time-domain algorithm will enable the analysis of scattering from electrically large closed bodies capable of supporting resonant modes.

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.

Time domain adaptive integral method for surface integral equations

An efficient marching-on-in-time (MOT) scheme is presented for solving electric, magnetic, and combined field integral equations pertinent to the analysis of transient electromagnetic scattering from perfectly conducting surfaces residing in an unbounded homogenous medium. The proposed scheme is the extension of the frequency-domain adaptive integral/pre-corrected fast-Fourier transform (FFT) method to the time domain. Fields on the scatterer that are produced by space-time sources residing on its surface are computed: 1) by locally projecting, for each time step, all sources onto a uniform auxiliary grid that encases the scatterer; 2) by computing everywhere on this grid the transient fields produced by the resulting auxiliary sources via global, multilevel/blocked, space-time FFTs; 3) by locally interpolating these fields back onto the scatterer surface. As this procedure is inaccurate when source and observer points reside close to each other; and 4) near fields are computed classically, albeit (pre-)corrected, for errors introduced through the use of global FFTs. The proposed scheme has a computational complexity and memory requirement of O(N/sub t/N/sub s/log/sup 2/N/sub s/) and O(N/sub s//sup 3/2/) when applied to quasiplanar structures, and of O(N/sub t/N/sub s//sup 3/2/log/sup 2/N/sub s/) and O(N/sub s//sup 2/) when used to analyze scattering from general surfaces. Here, N/sub s/ and N/sub t/ denote the number of spatial and temporal degrees of freedom of the surface current density. These computational cost and memory requirements are contrasted to those of classical MOT solvers, which scale as O(N/sub t/N/sub s//sup 2/) and O(N/sub s//sup 2/), respectively. A parallel implementation of the scheme on a distributed-memory computer cluster that uses the message-passing interface is described. Simulation results demonstrate the accuracy, efficiency, and the parallel performance of the implementation.

Fast analysis of transient electromagnetic scattering phenomena using the multilevel plane wave time domain algorithm

The computational complexity of classical marching-on-in-time (MOT) methods for solving time domain integral equations (TDIEs) pertinent to the analysis of transient scattering phenomena involving perfectly conducting targets grows as O(N/sub t/N/sub s//sup 2/) (N/sub t/ and N/sub s/ denote the number of temporal and spatial degrees of freedom (DOF) of the electric current on the target). This scaling law impedes the application of these schemes to the analysis of large-scale scattering phenomena. The recently developed plane wave time domain (PWTD) algorithm permits the rapid evaluation of transient wave fields generated by temporally bandlimited sources and hence the acceleration of marching on in time based TDIE solvers. Previously, we described a two-level PWTD enhanced TDIE solver for analyzing electromagnetic scattering from perfectly conducting targets; the computational complexity of this algorithm scales as O(N/sub t/N/sub s//sup 1.5/logN/sub s/). Here, a multilevel PWTD scheme for rapidly evaluating electric fields due to temporally bandlimited electric current sources is described. In addition, a multilevel PWTD enhanced TDIE solver for analyzing electromagnetic scattering from perfectly conducting scatterers using O(N/sub t/N/sub s/log/sup 2/N/sub s/) CPU resources is outlined. Last, the accuracy and CPU/memory efficiency of this solver are demonstrated by analyzing transient scattering from electrically large bodies.