GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Scientific and Statistical Computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A Fast Algorithm for the Electromagnetic Scattering from a Large Cavity
SIAM Journal on Scientific Computing
Applied Numerical 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
A new preconditioner for the interface system arising in a fast Helmholtz solver
Computers & Mathematics with Applications
Hi-index | 7.30 |
The paper focuses on the numerical study of electromagnetic scattering from two-dimensional (2D) large partly covered cavities, which is described by the Helmholtz equation with a nonlocal boundary condition on the aperture. The classical five-point finite difference method is applied for the discretization of the Helmholtz equation and a linear approximation is used for the nonlocal boundary condition. We prove the existence and uniqueness of the numerical solution when the medium in the cavity is y-direction layered or the number of the mesh points on the aperture is large enough. The fast algorithm proposed in Bao and Sun (2005) [2] for open cavity models is extended to solving the partly covered cavity problem with (vertically) layered media. A preconditioned Krylov subspace method is proposed to solve the partly covered cavity problem with a general medium, in which a layered medium model is used as a preconditioner of the general model. Numerical results for several types of partly covered cavities with different wave numbers are reported and compared with those by ILU-type preconditioning algorithms. Our numerical experiments show that the proposed preconditioning algorithm is more efficient for partly covered cavity problems, particularly with large wave numbers.