Conjugate Gradient Methods for Toeplitz Systems
SIAM Review
Preconditioning of Block Toeplitz Matrices by Sine Transforms
SIAM Journal on Scientific Computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
A Fast Algorithm for the Electromagnetic Scattering from a Large Cavity
SIAM Journal on Scientific Computing
Iterative Methods for Toeplitz Systems (Numerical Mathematics and Scientific Computation)
Iterative Methods for Toeplitz Systems (Numerical Mathematics and Scientific Computation)
Applied Numerical Mathematics
Compact optimal quadratic spline collocation methods for the Helmholtz equation
Journal of Computational Physics
Numerical solution of electromagnetic scattering from a large partly covered cavity
Journal of Computational and Applied Mathematics
Journal of Computational Physics
GMRES with adaptively deflated restarting and its performance on an electromagnetic cavity problem
Applied Numerical Mathematics
A composite preconditioner for the electromagnetic scattering from a large cavity
Journal of Computational Physics
Cosine transform based preconditioners for total variation deblurring
IEEE Transactions on Image Processing
Scattering signals of monochromatic light incident on a rectangular microchannel
Computers & Mathematics with Applications
Journal of Computational Physics
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In this paper, on the basis of the optimal sine transform based approximation we propose a new preconditioner for the interface system arising in the fast Helmholtz solver [G. Bao, W. Sun, A fast algorithm for the electromagnetic scattering from a large cavity, SIAM J. Sci. Comput. 27 (2005) 553-574 (electronic)] for the electromagnetic scattering from a large cavity with layered media. We show that the spectrum of the preconditioned matrix is clustered around 1 if the preconditioner is not nearly singular. Numerical results show that the number of iterations of an preconditioned iterative method for the interface system is independent of the mesh size and the wavenumber. The computational cost of the fast method proposed in this paper for calculating the radar cross section, which is very important in electromagnetism, by means of fast Fourier transforms, is O(N^2) on an NxN uniform partition of the unit square for the source free case.