We consider high order finite difference approximations to the Helmholtz equation in an exterior domain. We include a simplified absorbing boundary condition to approximate the Sommerfeld radiation condition. This yields a large, but sparse, complex system, which is not self-adjoint and not positive definite. We discretize the equation with a compact fourth or sixth order accurate scheme. We solve this large system of linear equations with a Krylov subspace iterative method. Since the method converges slowly, a preconditioner is introduced, which is a Helmholtz equation but with a modified complex wavenumber. This is discretized by a second or fourth order compact scheme. The system is solved by BICGSTAB with multigrid used for the precondi...
This paper studies and analyzes a preconditioned Krylov solver for Helmholtz problems that are formu...
The development of efficient solution algorithms for Poisson's equation on domains allowing for...
In this paper, third and fourth order compact finite difference schemes are proposed for solving Hel...
The numerical solution of the Helmholtz equation subject to nonlocal radiation boundary conditions i...
The Helmholtz equation is the simplest possible model for the wave propagation. Perhaps this is the ...
The Helmholtz equation is the simplest possible model for the wave propagation. Perhaps this is the ...
Some preconditioners for the iterative solution of Helmholtz's equation discretized with spectral Le...
In this thesis we propose methods for preconditioning Krylov subspace methods for solving the integr...
In this paper we generalize and improve a recently developed domain decomposition preconditioner for...
An iterative solution method, in the form of a preconditioner for a Krylov subspace method, is prese...
Wave propagation is described by the wave equation, or in the time-periodic case, by the Helmholtz e...
An iterative solution method, in the form of a preconditioner for a Krylov subspace method, is prese...
Wave propagation is described by the wave equation, or in the time-periodic case, by the Helmholtz e...
Wave propagation is described by the wave equation, or in the time-periodic case, by the Helmholtz e...
We examine preconditioners for the discrete indefinite Helmholtz equation on a three-dimensional bo...
This paper studies and analyzes a preconditioned Krylov solver for Helmholtz problems that are formu...
The development of efficient solution algorithms for Poisson's equation on domains allowing for...
In this paper, third and fourth order compact finite difference schemes are proposed for solving Hel...
The numerical solution of the Helmholtz equation subject to nonlocal radiation boundary conditions i...
The Helmholtz equation is the simplest possible model for the wave propagation. Perhaps this is the ...
The Helmholtz equation is the simplest possible model for the wave propagation. Perhaps this is the ...
Some preconditioners for the iterative solution of Helmholtz's equation discretized with spectral Le...
In this thesis we propose methods for preconditioning Krylov subspace methods for solving the integr...
In this paper we generalize and improve a recently developed domain decomposition preconditioner for...
An iterative solution method, in the form of a preconditioner for a Krylov subspace method, is prese...
Wave propagation is described by the wave equation, or in the time-periodic case, by the Helmholtz e...
An iterative solution method, in the form of a preconditioner for a Krylov subspace method, is prese...
Wave propagation is described by the wave equation, or in the time-periodic case, by the Helmholtz e...
Wave propagation is described by the wave equation, or in the time-periodic case, by the Helmholtz e...
We examine preconditioners for the discrete indefinite Helmholtz equation on a three-dimensional bo...
This paper studies and analyzes a preconditioned Krylov solver for Helmholtz problems that are formu...
The development of efficient solution algorithms for Poisson's equation on domains allowing for...
In this paper, third and fourth order compact finite difference schemes are proposed for solving Hel...