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PIER PIER B PIER C PIER M PIER Letters
2010-11-03
Semi-Analytical Solutions of 2-d Homogeneous Helmholtz Equation by the Method of Connected Local Fields
By
Hung-Wen Chang,

    Prof. Hung-Wen Chang

    Department of Photonics

    National Sun Yat-sen University

    Taiwan, ROC

    Homepage

Sin-Yuan Mu

    Dr. Sin-Yuan Mu

    Institute of Electro-optical Engineering and Department of Photonics

    National Sun Yat-sen University

    Taiwan

    Homepage

Progress In Electromagnetics Research, Vol. 109, 399-424, 2010
doi:10.2528/PIER10092807
Abstract
The frequency-domain finite-difference (FD-FD) methods have been successfully used to obtain numerical solutions of two-dimensional (2-D) Helmholtz equation. The standard second-order accurate FD-FD scheme is known to produce unwanted numerical spatial and temporal dispersions when the sampling is inadequate. Recently compact higher-order accurate FD-FD methods have been proposed to reduce the spatial sampling density. We present a semi-analytical solution of 2-D homogeneous Helmholtz equation by connecting overlapping square patches of local fields where each patch is expanded in a set of Fourier-Bessel (FB) series. These local FB coefficients are related to total eight points, four on the sides and four on the corners, on the square patch. The local field expansion (LFE) analysis leads to an improved, compact FD-like, nine-point stencil for the 2-D homogeneous Helmholtz equation. We show that LFE formulation possesses superior numerical properties of being low dispersive and nearly isotropic because this method of connecting local fields merely ties these overlapping EM field patches already satisfy the Helmholtz equation.
Citation
Hung-Wen Chang, and Sin-Yuan Mu, "Semi-Analytical Solutions of 2-d Homogeneous Helmholtz Equation by the Method of Connected Local Fields," Progress In Electromagnetics Research, Vol. 109, 399-424, 2010.
doi:10.2528/PIER10092807
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