GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
CGS, a fast Lanczos-type solver for nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Scientific and Statistical Computing
Conjugate Gradient Methods for Toeplitz Systems
SIAM Review
A domain decomposition method for the Helmholtz equation and related optimal control problems
Journal of Computational Physics
Iterative methods for solving linear systems
Iterative methods for solving linear systems
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
A Multigrid Method Enhanced by Krylov Subspace Iteration for Discrete Helmholtz Equations
SIAM Journal on Scientific Computing
Separation-of-variables as a preconditioner for an iterative Helmholtz solver
Applied Numerical Mathematics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
On a class of preconditioners for solving the Helmholtz equation
Applied Numerical Mathematics
A Fast Algorithm for the Electromagnetic Scattering from a Large Cavity
SIAM Journal on Scientific Computing
A Novel Multigrid Based Preconditioner For Heterogeneous Helmholtz Problems
SIAM Journal on Scientific Computing
A fast iterative solver for scattering by elastic objects in layered media
Applied Numerical Mathematics
A parallel multigrid-based preconditioner for the 3D heterogeneous high-frequency Helmholtz equation
Journal of Computational Physics
Fast Directional Multilevel Algorithms for Oscillatory Kernels
SIAM Journal on Scientific Computing
Applied Numerical Mathematics
An Introduction to Iterative Toeplitz Solvers (Fundamentals of Algorithms)
An Introduction to Iterative Toeplitz Solvers (Fundamentals of Algorithms)
A domain decomposition solver for acoustic scattering by elastic objects in layered media
Journal of Computational Physics
A Fast Direct Solver for a Class of Elliptic Partial Differential Equations
Journal of Scientific Computing
Applied Numerical Mathematics
Preconditioning Helmholtz linear systems
Applied Numerical Mathematics
Compact optimal quadratic spline collocation methods for the Helmholtz equation
Journal of Computational Physics
A fast method for the solution of 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
A new preconditioner for the interface system arising in a fast Helmholtz solver
Computers & Mathematics with Applications
A two-dimensional Helmhotlz equation solution for the multiple cavity scattering problem
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.46 |
In this paper, we propose a composite preconditioner for the electromagnetic scattering from a large cavity. The electromagnetic cavity problem is described by the Helmholtz equation with a nonlocal boundary condition on the aperture of the cavity and Dirichlet (or Neumann) boundary conditions on the walls of the cavity. The preconditioner proposed here combines the optimal sine transform based approximation with a layered medium model. Using fast Fourier transforms, the computational cost of every iteration is O(N^2logN) on an NxN uniform partition of the unit square. Numerical results for a model problem show that the new preconditioner is more efficient than those recently considered in the literature. For the cavity with a small portion of non-layered media, we propose a sparse preconditioned conjugate orthogonal conjugate gradient solver combined with the new preconditioner. Numerical results for a model problem are reported to demonstrate the efficiency of the sparse solver.