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Title: THE COMPUTATION OF LINEAR DISPERSIVE ELECTROMAGNETIC WAVES
Abstract: Numerical solutions of the equations describing electromagnetic pulse propagation in geometrically complex Debye-dispersive dielectrics are used in the development of safety standards for human exposure to non-ionizing radiation. Debye dispersion is a relaxation process, a phenomenon which occurs when the underlying material is forced into non-equilibrium due to the passing waves. This relaxation is typically stiff in applications, and the system of equations is then singularly perturbed. Such systems are notoriously expensive to solve with standard numerical methods. We review previous work related to the numerical solution of such problems, and consider a representative numerical scheme in order to elucidate the nature of the challenge posed to Computational Electromagnetics by the stiffness. Further. an analysis of the stiffness leads us to propose a scheme that seems "natural" for the problem at hand. [Vol. 11, No. 1 (1996), pp 8-16, Special issue on Applied Mathematics: Meeting the challenges presented by computational electromagnetics]
Author(s): Peter G. Petropoulos
File Type: Journal Paper
Issue:Volume: 11      Number: 1      Year: 1996
Download Link:Click here to download PDF     File Size: 708 KB

Title: CALCULATION OF ELECTROMAGNETIC SCATTERING VIA VARIATIONS AND ANALYTIC CONTINUATION
Abstract: In this paper we review a numerical method we introduced recently for the solution of problems of electromagnetic scattering. Based on variations of the boundaries of the scatterers and analytic continuation, our approach yields algorithms which are applicable to a wide variety of scattering configurations. We discuss some recent applications of this method to scattering by diffraction gratings and by large two-dimensional bounded bodies, and we present results of new applications to three-dimensional gratings containing corners and edges. In many cases of practical interest our algorithms give nu- merical results which are several orders of magnitude more accurate than those given by classical methods. [Vol. 11, No. 1 (1996), pp 17- 31, Special issue on Applied Mathematics: Meeting the challenges presented by computational electromagnetics]
Author(s): Oscar P. Bruno, Fernando Reitich
File Type: Journal Paper
Issue:Volume: 11      Number: 1      Year: 1996
Download Link:Click here to download PDF     File Size: 1314 KB

Title: ERROR CONTROL IN NUMERICAL SOLUTIONS OF BOUNDARY INTEGRAL EQUATIONS
Abstract: A method of estimating the error committed in numerical solutions of integral equations is presented. It is shown how the error can be computed in spaces other than L^2, why this is reasonable and sometimes necessary. The appropriate function spaces are also shown to lead to bounded condition numbers even for first kind equations. [Vol. 11, No. 1 (1996), pp 32-36, Special issue on Applied Mathematics: Meeting the challenges presented by computational electromagnetics]
Author(s): G . C . HSIAO, R. E . R. E . KLEINMAN
File Type: Journal Paper
Issue:Volume: 11      Number: 1      Year: 1996
Download Link:Click here to download PDF     File Size: 386 KB

Title: SUB-GRIDDING FDTD SCHEMES
Abstract: Local meshing or sub-gridding has been advocated by a number of authors as a way of increasing the spatial resolution of the finite difference time domain method (FDTD). In this paper we show how to use supraconvergence to analyze the error in a simple sub-gridding strategy in two dimensions. We also analyze the spurious reflection that occurs at an interface between two grids for the standard FDTD scheme, for simple subgridding method and for another subgridding scheme employing linear interpolation. The overall order of convergence of the reflection coefficients is the same for all the methods, but the linear scheme has a lower amplitude spurious transmitted mode compared to the simple subgridding scheme.
Author(s): Peter Monk
File Type: Journal Paper
Issue:Volume: 11      Number: 1      Year: 1996
Download Link:Click here to download PDF     File Size: 700 KB

Title: CALCULATIONS IN MATHEMATICA ON LOW-FREQUENCY DIFFRACTION BY A CIRCULAR DISK
Abstract: This paper is devoted to the symbolic calculation of the scattering coefficient in diffraction by a circular disk, by the use of Mathematica. Three diffraction problems are considered: scalar diffraction by an acoustically soft disk, scalar diffraction by an acoustically hard disk, and electromagnetic diffraction by a perfectly conducting disk. In the low-frequency approximation, the solutions of these problems are in the form of expansions in powers of ka, where a is the radius of the disk and k is the wave number. The emphasis is on the low-frequency expansion for the scattering coefficient, of which several terms are determined exactly with the help of Mathematica. [Vol. 11, No. 1 (1996), pp 47-56, Special issue on Applied Mathematics: Meeting the challenges presented by computational electromagnetics]
Author(s): J. Boersma, M. J. H. Anthonissen
File Type: Journal Paper
Issue:Volume: 11      Number: 1      Year: 1996
Download Link:Click here to download PDF     File Size: 597 KB

Title: SCATTERING BY LARGE STRUCTURES WITH PERIODIC SURFACES: A PROTOTYPE PROBLEM
Abstract: A hybrid method which uses both numerical and asymptotic techniques is described and applied to the scattering of an electromagnetic wave off a large corrugated circular cylinder. The radius of the cylinder is large compared to the wavelength of the incident radiation, but the corrugation height and period are of the same order as the wavelength. This problem is a prototype of a more general situation where the surface of a target is covered with a periodic coating. The method of attack essentially blends boundary layer theory, which describes the local scattering behavior of the surface, and the theory of geometrical optics which gives a global description of the scattering. Although the hybrid method is only developed here for this simple model, its applicability for other targets is clear. [Vol. 11, No. 1 (1996), pp 57-62, Special issue on Applied Mathematics: Meeting the challenges presented by computational electromagnetics]
Author(s): G.A. Kriegsmann
File Type: Journal Paper
Issue:Volume: 11      Number: 1      Year: 1996
Download Link:Click here to download PDF     File Size: 428 KB

Title: MONO-STATIC RCS COMPUTATION WITH A BLOCK GMRES ITERATIVE SOLVER
Abstract: We present a new method of computing mono-static radar cross sections using a preconditioned Block GMRES iterative algorithm. The convergence properties of this algorithm are analyzed using RCS error, equation residual error and solution error. It is found that this method is nearly an order of magnitude faster than direct methods (LINPACK) for realistic method of moment problems. [Vol. 11, No. 1 (1996), pp 63-69, Special issue on Applied Mathematics: Meeting the challenges presented by computational electromagnetics]
Author(s): William E. Boyse, Andrew A. Seidl
File Type: Journal Paper
Issue:Volume: 11      Number: 1      Year: 1996
Download Link:Click here to download PDF     File Size: 617 KB

Title: MODERN KRYLOV SUBSPACE METHODS IN ELECTROMAGNETIC FIELD COMPUTATION USING THE FINITE INTEGRATION THEORY
Abstract: A theoretical basis for numerical electromagnetics, the so-called Finite Integration Theory, is described. Based upon Maxwell's equations in their integral form, it results in a set of matrix equations, each of which is a discrete analogue of its original analytical equation. Applications of this discretization process are described here in the context of the numerical simulation of electroquasistatic problems and of time-harmonic field computations including a new type of waveguide boundary condition, which is presented here for the first time. In both fields the process of mathematical modelling and discretization yields large systems of complex linear equations which have to be solved numerically. For this task several modern Krylov subspace methods are presented such as BiCG, CGS and their more recent stabilized variants CGS2, BiCGSTAB(I) and TFQMR. They are applied in connection with efficient preconditioning methods. The applicability of these modern methods is shown for a number of examples for both problem types. [Vol. 11, No. 1 (1996), pp 70-84, Special issue on Applied Mathematics: Meeting the challenges presented by computational electromagnetics]
Author(s): Markus Clemens, Rolf Schuhmann, Ursula van Rienen, Thomas Weiland
File Type: Journal Paper
Issue:Volume: 11      Number: 1      Year: 1996
Download Link:Click here to download PDF     File Size: 1195 KB

Title: CALCULATION OF ASSOCIATED LEGENDRE POLYNOMIALS WITH NON-INTEGER DEGREE
Abstract: The exact eigenfunction solution for the electromagnetic scattering from a perfectly conducting cone (or any other sectoral body of revolution with a tip) requires the solution in the form of spherical harmonics. The solution for the variation of these harmonics is the associated Legendre polynomial. The boundary conditions for the cone generate associated Legendre polynomials with non-integer degree found for a specific cone angle. This paper will discuss the derivation used to calculate the associated Legendre polynomial, the determination of the eigenvalues, the incomplete normalization integral, and a validation technique. [Vol. 11, No. 1 (1996), pp 85-89, Special issue on Applied Mathematics: Meeting the challenges presented by computational electromagnetics]
Author(s): Keith D. Trott
File Type: Journal Paper
Issue:Volume: 11      Number: 1      Year: 1996
Download Link:Click here to download PDF     File Size: 602 KB

Title: FINITE DIFFERENCE METHODS FOR THE NONLINEAR EQUATIONS OF PERTURBED GEOMETRICAL OPTICS
Abstract: Finite difference methods are developed to solve the nonlinear partial differential equations approximating solutions of the Helmholtz equation in high frequency regime. Numerical methods are developed for solving the geometrical optics approximation, the classical asymptotic expansion, and a new perturbed geometrical optics system. We propose a perturbed geometrical optics system to recover diffraction phenomena that are lost in geometrical optics approximations. We discuss techniques we have developed for recovering multivalued solutions and we present numerical examples computed with finite difference approximations of the above systems. [Vol. 11, No. 1 (1996), pp 90-98, Special issue on Applied Mathematics: Meeting the challenges presented by computational electromagnetics]
Author(s): E. Fatemi, B. Engquist, and S. Osher
File Type: Journal Paper
Issue:Volume: 11      Number: 1      Year: 1996
Download Link:Click here to download PDF     File Size: 661 KB