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 [Chang and Mu, PIER 109, 399 (2010)]. 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.
"Two-Dimensional Compact FD-Like Stencils with High-Order Accuracy for Helmholtz Equation with a Planar Dielectric Interface," Progress In Electromagnetics Research B,
Vol. 64, 15-27, 2015. doi:10.2528/PIERB15081801
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