49 citations · 96 across the 20 of their papers we have counts for
6 papers · 2 filters
Domain decomposition preconditioning for the high-frequency time-harmonic Maxwell equations with absorption
Marcella Bonazzoli, Victorita Dolean, Ivan G. Graham +2
This paper rigorously analyses preconditioners for the time-harmonic Maxwell equations with absorption, where the PDE is discretised using curl-conforming finite-element methods of…
Circulant embedding with QMC -- analysis for elliptic PDE with lognormal coefficients
Ivan G. Graham, Frances Y. Kuo, Dirk Nuyens +2
In a previous paper (J. Comp. Phys. 230 (2011), 3668--3694), the authors proposed a new practical method for computing expected values of functionals of solutions for certain class…
Analysis of circulant embedding methods for sampling stationary random fields
Ivan G. Graham, Frances Y. Kuo, Dirk Nuyens +2
In this paper we prove, under mild conditions, that the positive definiteness of the circulant matrix appearing in the circulant embedding method is always guaranteed, provided the…
Two-level preconditioners for the Helmholtz equation
Marcella Bonazzoli, Victorita Dolean, Ivan Graham +2
In this paper we compare numerically two different coarse space definitions for two-level domain decomposition preconditioners for the Helmholtz equation, both in two and three dim…
A two-level domain-decomposition preconditioner for the time-harmonic Maxwell's equations
Marcella Bonazzoli, Victorita Dolean, Ivan Graham +2
The construction of fast iterative solvers for the indefinite time-harmonic Maxwell's system at mid- to high-frequency is a problem of great current interest. Some of the difficult…
Modern Monte Carlo Variants for Uncertainty Quantification in Neutron Transport
Ivan G. Graham, Matthew J. Parkinson, Robert Scheichl
We describe modern variants of Monte Carlo methods for Uncertainty Quantification (UQ) of the Neutron Transport Equation, when it is approximated by the discrete ordinates method w…