Fast transform based preconditioners for 2D finite-difference frequency-domain - Waveguides and periodic structures

Authors:
A. Chabory;B. P. de Hon;W. H. A. Schilders;A. G. Tijhuis
Affiliations:
Department of Electrical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;Department of Electrical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;Department of Electrical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
Venue:
Journal of Computational Physics
Year:
2008

Citing 6
Cited 0

Conjugate Gradient Methods for Toeplitz Systems

SIAM Review
Efficient iterative solution of the three-dimensional Helmholtz equation

Journal of Computational Physics
A Domain Decomposition Method for the Helmholtz Equation in a Multilayer Domain

SIAM Journal on Scientific Computing
Iterative Solution of the Helmholtz Equation by a Second-Order Method

SIAM Journal on Matrix Analysis and Applications
A Multigrid Method Enhanced by Krylov Subspace Iteration for Discrete Helmholtz Equations

SIAM Journal on Scientific Computing
A Novel Multigrid Based Preconditioner For Heterogeneous Helmholtz Problems

SIAM Journal on Scientific Computing

Quantified Score

Hi-index	31.45

Visualization

Abstract

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.