Domain decomposition preconditioning for high-frequency Helmholtz problems with absorption

Domain decomposition preconditioning for high-frequency Helmholtz problems with absorption

In this paper we give new results on domain decomposition preconditioners for GMRES when computing piecewise-linear finite-element approximations of the Helmholtz equation −∆u − (k2 + iε)u = f , with absorption parameter ε ∈ R. Multigrid approximations of this equation with ε 6= 0 are commonly used as preconditioners for the pure Helmholtz case (ε = 0). However a rigorous theory for such (so-ca...

Feti-h: a Scalable Domain Decomposition Method for High Frequency Exterior Helmholtz Problems

Domain decomposition preconditioning for elliptic problems with jumps in coefficients

In this paper, we propose an effective iterative preconditioning method to solve elliptic problems with jumps in coefficients. The algorithm is based on the additive Schwarz method (ASM). First, we consider a domain decomposition method without ‘cross points’ on interfaces between subdomains and the second is the ‘cross points’ case. In both cases the main computational cost is an implementatio...

Hierarchical matrix techniques for low- and high-frequency Helmholtz problems

In this paper, we discuss the application of hierarchical matrix techniques to the solution of Helmholtz problems with large wave number κ in two dimensions. We consider the Brakhage-Werner integral formulation of the problem, discretised by the Galerkin boundary element method. The dense n×n Galerkin matrix arising from this approach is represented by a sum of an H-matrix and an H2-matrix, two...

Preconditioning for Domain Decomposition through Function Approximation

A new approach was presented in [11] for construcling preconditioners through a function approximation for the domain decomposi~ion-basedpreconditioned conjugate gradient method. This work extends the approach to more general cases where grids may be nonuniform; elliptic operatoI'B may have variable coefficients (but are separable and self-adjoint); and geometric domains may be nonrectangular. ...