We present a highly accurate frequency-domain finite-difference algorithm for computing mode field solutions of microwave waveguides with regular and reentrant corners. Based on FBS (Fourier-Bessel series)-derived 3-by-3 compact coefficients, our method allows for a flexible layout of the 2-D uniform grids so that distance from the waveguide boundaries to the adjacent unknowns can be arbitrary. Fourth to sixth-order convergent rates of the proposed coefficients are verified by resonance-frequency error analysis for rectangular microwave waveguides for both TE/TM polarizations. We also study the first four Neumann/Dirichlet eigenvalues of the L-shaped MW-WGs calculated by the flexible scheme, and the Neumann results are reported for the first time. Although our results achieve sixth-order accuracy for analytic modes, the order of accuracy is about one and a third for both fundamental TE and TM modes due to singularity around the reentrant corner.
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