49 citations · 96 across the 20 of their papers we have counts for
24 papers
A Filon-Clenshaw-Curtis-Smolyak rule for multi-dimensional oscillatory integrals with application to a UQ problem for the Helmholtz equation
Zhizhang Wu, Ivan G. Graham, Dingjiong Ma +1
In this paper, we combine the Smolyak technique for multi-dimensional interpolation with the Filon-Clenshaw-Curtis (FCC) rule for one-dimensional oscillatory integration, to obtain…
Convergence of Restricted Additive Schwarz with impedance transmission conditions for discretised Helmholtz problems
Shihua Gong, Ivan G. Graham, Euan A. Spence
The Restricted Additive Schwarz method with impedance transmission conditions, also known as the Optimised Restricted Additive Schwarz (ORAS) method, is a simple overlapping one-le…
Overlapping Schwarz methods with GenEO coarse spaces for indefinite and non-self-adjoint problems
Niall Bootland, Victorita Dolean, Ivan G. Graham +2
GenEO (`Generalised Eigenvalue problems on the Overlap') is a method for computing an operator-dependent spectral coarse space to be combined with local solves on subdomains to for…
Convergence of parallel overlapping domain decomposition methods for the Helmholtz equation
Shihua Gong, Martin J. Gander, Ivan G. Graham +2
We analyse parallel overlapping Schwarz domain decomposition methods for the Helmholtz equation, where the subdomain problems satisfy first-order absorbing (impedance) transmission…
GenEO coarse spaces for heterogeneous indefinite elliptic problems
Niall Bootland, Victorita Dolean, Ivan G. Graham +2
Motivated by recent work on coarse spaces for Helmholtz problems, we provide in this paper a comparative study on the use of spectral coarse spaces of GenEO type for heterogeneous…
A variational interpretation of Restricted Additive Schwarz with impedance transmission condition for the Helmholtz problem
Shihua Gong, Martin J. Gander, Ivan G. Graham +1
In this paper we revisit the Restricted Additive Schwarz method for solving discretized Helmholtz problems, using impedance boundary conditions on subdomains (sometimes called ORAS…