256 citations · 934 across the 55 of their papers we have counts for
7 papers · 1 filter
PCPATCH: software for the topological construction of multigrid relaxation methods
Patrick E. Farrell, Matthew G. Knepley, Lawrence Mitchell +1
Effective relaxation methods are necessary for good multigrid convergence. For many equations, standard Jacobi and Gauß-Seidel are inadequate, and more sophisticated space decompos…
Bifurcation analysis of stationary solutions of two-dimensional coupled Gross-Pitaevskii equations using deflated continuation
E. G Charalampidis, N. Boullé, P. E. Farrell +1
Recently, a novel bifurcation technique known as the deflated continuation method (DCM) was applied to the single-component nonlinear Schrödinger (NLS) equation with a parabolic tr…
Complexity bounds on supermesh construction for quasi-uniform meshes
M. Croci, P. E. Farrell
Projecting fields between different meshes commonly arises in computational physics. This operation requires a supermesh construction and its computational cost is proportional to…
Multilevel quasi Monte Carlo methods for elliptic PDEs with random field coefficients via fast white noise sampling
M. Croci, M. B. Giles, P. E. Farrell
When solving partial differential equations with random fields as coefficients the efficient sampling of random field realisations can be challenging. In this paper we focus on the…
A local Fourier analysis of additive Vanka relaxation for the Stokes equations
Patrick E. Farrell, Yunhui He, Scott P. MacLachlan
Multigrid methods are popular solution algorithms for many discretized PDEs, either as standalone iterative solvers or as preconditioners, due to their high efficiency. However, th…
Deflation for semismooth equations
Patrick E. Farrell, Matteo Croci, Thomas M. Surowiec
Variational inequalities can in general support distinct solutions. In this paper we study an algorithm for computing distinct solutions of a variational inequality, without varyin…