Compact 2D stencils for inhomogeneous Helmholtz equation based on method of connected local fields

Chang, Hung‐Wen; Mu, Sin-Yuan

doi:10.1109/compem.2015.7052610

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Local Plane Wave Expansion (Lpwe) Formulation1

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2015

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“…In our previous work [6,7], semi-analytic FD-like formulae LFE-9 and LFE-27 were derived for homogeneous Helmholtz equation by expanding the local field as a truncated Fourier-Bessel series for the 2-D case and a truncated spherical Fourier-Bessel series for the 3-D case. For cells containing an arbitrarily oriented dielectric interface we chose [25] to represent the local fields as a linear combination of select sets of plane wave solutions. The combined plane wave solutions automatically satisfy interface conditions given by Eqs.…”

Section: Local Plane Wave Expansion (Lpwe) Formulationmentioning

confidence: 99%

Two-Dimensional Compact Fd-Like Stencils With High-Order Accuracy for Helmholtz Equation With a Planar Dielectric Interface

Chang

Mu²

2015

PIER B

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We derive and compare several finite-difference frequency-domain (FD-FD) stencils for points on or near a planar dielectric interface. They are based on interface conditions or from modifying Helmholtz equation. We present a highly accurate formulation based on local plane wave expansion (LPWE). LPWE-based compact stencil is an extension of the analytically obtained LFE-9 stencil as used by the method of connected local fields [6]. We report that merely using five points per wavelength spatial sampling, LPWE coefficients achieve better than 0.01% local error near a planar interface. We numerically determine that we have fourth to eighth-order accuracy in the local errors for LPWE stencils.

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Section: Local Plane Wave Expansion (Lpwe) Formulationmentioning

confidence: 99%