5 papers
Multigrid preconditioners for the hybridized Discontinuous Galerkin discretisation of the shallow water equations
Jack D. Betteridge, Thomas H. Gibson, Ivan G. Graham +1
Numerical climate- and weather-prediction requires the fast solution of the equations of fluid dynamics. Discontinuous Galerkin (DG) discretisations have several advantageous prope…
Domain decomposition preconditioners for high-order discretisations of the heterogeneous Helmholtz equation
Shihua Gong, Ivan G. Graham, Euan A. Spence
We consider one-level additive Schwarz domain decomposition preconditioners for the Helmholtz equation with variable coefficients (modelling wave propagation in heterogeneous media…
Unified Analysis of Periodization-Based Sampling Methods for Matérn Covariances
Markus Bachmayr, Ivan G. Graham, Van Kien Nguyen +1
The periodization of a stationary Gaussian random field on a sufficiently large torus comprising the spatial domain of interest is the basis of various efficient computational meth…
Full Error Analysis and Uncertainty Quantification for the Heterogeneous Transport Equation in Slab Geometry
Ivan G. Graham, Matthew J. Parkinson, Robert Scheichl
We present an analysis of multilevel Monte Carlo techniques for the forward problem of uncertainty quantification for the radiative transport equation, when the coefficients ({\em…
Domain Decomposition with local impedance conditions for the Helmholtz equation with absorption
I. G. Graham, E. A. Spence, J. Zou
We consider one-level additive Schwarz preconditioners for a family of Helmholtz problems with absorption and increasing wavenumber . These problems are discretized using the Ga…