volume | PIER Journals

Abstract

The method of connected local fields (CLF), developed for computing numerical solutions of the two-dimensional (2-D) Helmholtz equation, is capable of advancing existing frequency-domain finite-difference (FD-FD) methods by reducing the spatial sampling density nearly to the theoretical limit of two points per wavelength. In this paper, we show that the core theory of CLF is the result of applying the uniqueness theorem to local EM waves. Furthermore, the mathematical process for computing the local field expansion (LFE) coefficients from eight adjacent points on a square is similar to that in the theory of discrete Fourier transform. We also present a theoretical analysis of both the local and global errors in the theory of connected local fields and provide closed-form expressions for these errors.

1. Chang, H.-W. and S.-Y. 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

2. Chang, H.-W. and S.-Y. Mu, "Novel nine-point FD coefficients for the two-dimensional Helmholtz equation," Cross Strait Tri-Regional Radio Science and Wireless Technology Conference, Hanan, China, 2010.

3. Chang, H.-W. and S.-Y. Mu, "Frequency dependent FD-like coefficients for 2-D Helmholtz equation derived from local Fourier-Bessel series," The 6th International Conference on Photonics and Applications, ICPA-6 2010, HaNoi, Vietnam, 2010.

4. Chang, H.-W. and S.-Y. Mu, "Dispersion analysis of Fourier-Bessel series derived FD coefficients for two-dimensional Helmholtz equation," The 6th International Conference on Photonics and Applications, ICPA-6 2010, HaNoi, Vietnam, 2010.

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6. Jung, B. H. and T. K. Sarkar, "Solving time domain Helmholtz wave equation with MOD-FDM," Progress In Electromagnetics Research, Vol. 79, 339-352, 2008.
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7. Chang, H.-W., W.-C. Cheng, and S.-M. Lu, "Layer-mode transparent boundary condition for the hybrid FD-FD method," Progress In Electromagnetics Research, Vol. 94, 175-195, 2009.
doi:10.2528/PIER09061606

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doi:10.2528/PIER09111502

9. Chang, H.-W. and Y.-H. Wu, "Analysis of perpendicular crossing dielectric waveguides with various typical index contrasts and intersection profiles," Progress In Electromagnetics Research, Vol. 108, 323-341, 2010.
doi:10.2528/PIER10081008

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15. Zhu, C.-H., Q. H. Liu, Y. Shen, and L. Liu, "A high accuracy conformal method for evaluating the discontinuous Fourier transform," Progress In Electromagnetics Research, Vol. 109, 425-440, 2010.
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18. Chang, H.-W., Y.-H. Wu, and W.-C. Cheng, "Hybrid FD-FD analysis of crossing waveguides by both the plus and the cross structural Symmetry," Progress In Electromagnetics Research, Vol. 103, 217-240, 2010.
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Dr. Sin-Yuan Mu

Prof. Hung-Wen Chang