5 papers
Theory of two-level Schwarz preconditioners with piecewise-polynomial coarse spaces for the high-frequency Helmholtz equation
Ivan G. Graham, Euan A. Spence
We analyse the classic two-level additive Schwarz domain-decomposition GMRES preconditioner for finite-element discretisations of the Helmholtz equation with large wavenumber ,…
Spectral coarse spaces based on indefinite operators: the -GenEO method
Théophile Chaumont-Frelet, Victorita Dolean, Mark Fry +2
GenEO (`Generalised Eigenvalue problems on the Overlap') is a method for constructing coarse spaces used in the preconditioning of iterative solvers for discrete PDEs. This method…
Massively parallel Schwarz methods for the high frequency Helmholtz equation
Yan Xie, Shihua Gong, Ivan G. Graham +2
We investigate the parallel one-level overlapping Schwarz method for solving finite element discretization of high-frequency Helmholtz equations. The resulting linear systems are l…
Quasi-Monte Carlo methods for uncertainty quantification of wave propagation and scattering problems modelled by the Helmholtz equation
Ivan G. Graham, Frances Y. Kuo, Dirk Nuyens +2
We analyse and implement a quasi-Monte Carlo (QMC) finite element method (FEM) for the forward problem of uncertainty quantification (UQ) for the Helmholtz equation with random coe…
Schwarz methods with PMLs for Helmholtz problems: fast convergence at high frequency
Jeffrey Galkowski, Shihua Gong, Ivan G. Graham +2
We discuss parallel (additive) and sequential (multiplicative) variants of overlapping Schwarz methods for the Helmholtz equation in , with large real wavenumber and…