Applied

Numerical analysis for electromagnetic integral equations by Karl F Warnick

By Karl F Warnick

Numerical simulation is key to electric engineers operating in antenna layout, instant communications, optical structures, and a bunch of alternative parts. This new applications-focused e-book presents engineers with state of the art tools for predicting simulation accuracy, worked-out effects for dozens of real-world difficulties, the newest accuracy-improving options, and exact tips for all parameters required to optimize numerical simulations. Bridging the space among summary educational remedies and useful engineering wishes, this well timed paintings introduces a variety of floor necessary equation formulations, techniques to discretizing the crucial equations, and measures of answer accuracy. All advised, this definitive source is vital for all engineers and software program builders operating with computational simulation instruments in electromagnetics and wave propagation.

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Chapter 2 Surface Integral Equation Formulations and the Method of Moments For conducting or dielectric bodies, Maxwell’s equations and the boundary conditions on the electromagnetic fields at the surface of the scatterer can be cast into an equivalent system of surface integral equations. These equations are based on integral operators that relate an unknown, equivalent current on the surface of the body to the fields scattered in response to a given incident field. We consider only perfectly electrically conducting (PEC) scatterers, although the results of this book could be readily extended to surface integral formulations for homogeneous dielectric objects.

24) Numerical Analysis for Electromagnetic Integral Equations 44 which is a sinc function raised to a power determined by the polynomial order of the testing function. 24) is zero and the Fourier series coefficients are all equal to one. 25) is a squared sinc function. Since this class of low-order basis functions are convolutions of the pulse function in real space, it is to be expected that the Fourier series coefficients are products of sinc functions. 17) that the spectral error depends on the product T−q Fq.

For smooth scatterers, if no sources lie on the scatterer surface, then the surface current is bounded and hence is square integrable. In this case, the L2 error of the numerical current solution ˆJ with respect to the exact current J is in principle a meaningful error measure, which could be used to assess the accuracy of a numerical method. 49) which has the advantage of being dimensionless. 51) n=1 where Jn is the surface current density vector evaluated at the nth node point of the surface mesh.

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