TAILIEUCHUNG - Wavelets trong Electromagnetics và mô hình thiết bị P4

Wavelets in Boundary Integral Equations Numerical treatment of integral equations can be found in classic books [1, 2]. In this chapter the integral equations obtained from field analysis of electromagnetic wave scattering, radiating, and guiding problems are solved by the wavelet expansion method [3–7]. The integral equations are converted into a system of linear algebraic equations. The subsectional bases, namely the pulses or piecewise sinusoidal (PWS) modes, are replaced by a set of orthogonal wavelets. In the numerical example we demonstrate that while the PWS basis yields a full matrix, the wavelet expansion results in a nearly diagonal or nearly block-diagonal. | Wavelets in Electromagnetics and Device Modeling. George W. Pan Copyright 2003 John Wiley Sons Inc. ISBN 0-471-41901-X CHAPTER FOUR Wavelets in Boundary Integral Equations Numerical treatment of integral equations can be found in classic books 1 2 . In this chapter the integral equations obtained from field analysis of electromagnetic wave scattering radiating and guiding problems are solved by the wavelet expansion method 3-7 . The integral equations are converted into a system of linear algebraic equations. The subsectional bases namely the pulses or piecewise sinusoidal PWS modes are replaced by a set of orthogonal wavelets. In the numerical example we demonstrate that while the PWS basis yields a full matrix the wavelet expansion results in a nearly diagonal or nearly block-diagonal matrix both approaches result in very close answers. However as the geometry of the problem becomes more complicated and consequently the resulting matrix size increases greatly the advantages of having a nearly diagonal matrix over a full matrix will become more profound. WAVELETS IN ELECTROMAGNETICS Galerkin s method is a zero residual method if the basis functions are orthogonal and complete and thus Galerkin s method with orthogonal basis functions is generally more accurate and rapidly convergent. Two types of orthogonal basis functions are frequently utilized for electromagnetic field computation. Mode expansion method or mode-matching method has often been applied to solve problems due to various discontinuities in waveguides finlines and microstrip lines. Generally this technique is useful when the geometry of the structure can be identified as consisting of two or more regions which each belongings to a separable coordinate system. The basic idea in the mode expansion procedure is to expand the unknown fields in the individual regions in terms of their respective normal modes. In fact the mode expansion method is identical to Galerkin s method which uses the normal mode

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