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Progress In Electromagnetics Research  ISSN: 10704698, EISSN: 15598985 
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THEORETICAL FOUNDATION FOR THE METHOD OF CONNECTED LOCAL FIELDSBy S.Y. Mu and H.W. ChangAbstract: The method of connected local fields (CLF), developed for computing numerical solutions of the twodimensional (2D) Helmholtz equation, is capable of advancing existing frequencydomain finitedifference (FDFD) 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 closedform expressions for these errors.
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