3 citations · 3 across the 10 of their papers we have counts for
10 papers
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…
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 ,…
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…
Schwarz preconditioner with -GenEO coarse space for the indefinite Helmholtz problem
Victorita Dolean, Mark Fry, Ivan G. Graham +1
GenEO (`Generalised Eigenvalue problems on the Overlap') is a method from the family of spectral coarse spaces that can efficiently rely on local eigensolves in order to build a ro…
Convergence of overlapping domain decomposition methods with PML transmission conditions applied to nontrapping Helmholtz problems
Jeffrey Galkowski, Shihua Gong, Ivan G. Graham +2
We study overlapping Schwarz methods for the Helmholtz equation posed in any dimension with large, real wavenumber and smooth variable wave speed. The radiation condition is approx…
Optimising seismic imaging design parameters via bilevel learning
Shaunagh Downing, Silvia Gazzola, Ivan G. Graham +1
Full Waveform Inversion (FWI) is a standard algorithm in seismic imaging. Its implementation requires the a priori choice of a number of "design parameters", such as the positions…
Analysis of a Helmholtz preconditioning problem motivated by uncertainty quantification
Ivan G. Graham, Owen R. Pembery, Euan A. Spence
This paper analyses the following question: let , be the Galerkin matrices corresponding to finite-element discretisations of the exterior Dirichlet problem…
Recent Results on Domain Decomposition Preconditioning for the High-frequency Helmholtz Equation using Absorption
I. G. Graham, E. A. Spence, E. Vainikko
In this paper we present an overview of recent progress on the development and analysis of domain decomposition preconditioners for discretised Helmholtz problems, where the precon…