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Fast transform based preconditioners for 2D finite-difference frequency-domain. Waveguides and periodic structures. (English) Zbl 1143.78010
Summary: The fields scattered by dielectric objects placed inside parallel-plate waveguides and periodic structures in two dimensions may efficiently be computed via a finite-difference frequency-domain (FDFD) method. This involves large, sparse linear systems of equations that may be solved using preconditioned Krylov subspace methods. Our preconditioners involve fast discrete trigonometric transforms and are based on a physical approximation. Simulations show significant gain in terms of computation time and iteration count in comparison with results obtained with preconditioners based on incomplete LU (ILU) factorization. Moreover, with the new preconditioners, the required number of iterations is independent of the grid size.
78M20 Finite difference methods applied to problems in optics and electromagnetic theory
78A50 Antennas, waveguides in optics and electromagnetic theory
78A45 Diffraction, scattering
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
Full Text: DOI
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