Some domain decomposition algorithms for elliptic problems
Iterative methods for large linear systems
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Iterative methods for solving linear systems
Iterative methods for solving linear systems
Optimized Schwarz Methods without Overlap for the Helmholtz Equation
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
SIAM Journal on Numerical Analysis
An analysis of the BEM-FEM non-overlapping domain decomposition method for a scattering problem
Journal of Computational and Applied Mathematics
Applied Numerical Mathematics
A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation
Journal of Computational Physics
Matrix Probing and its Conditioning
SIAM Journal on Numerical Analysis
The Optimized Schwarz Method with a Coarse Grid Correction
SIAM Journal on Scientific Computing
A rapidly converging domain decomposition method for the Helmholtz equation
Journal of Computational Physics
Hi-index | 31.45 |
This paper presents a preconditioner for non-overlapping Schwarz methods applied to the Helmholtz problem. Starting from a simple analytic example, we show how such a preconditioner can be designed by approximating the inverse of the iteration operator for a layered partitioning of the domain. The preconditioner works by propagating information globally by concurrently sweeping in both directions over the subdomains, and can be interpreted as a coarse grid for the domain decomposition method. The resulting algorithm is shown to converge very fast, independently of the number of subdomains and frequency. The preconditioner has the advantage that, like the original Schwarz algorithm, it can be implemented as a matrix-free routine, with no additional preprocessing.