256 citations · 934 across the 55 of their papers we have counts for
5 papers · 1 filter
Analysis of Carrier's problem
S. J. Chapman, P. E. Farrell
A computational and asymptotic analysis of the solutions of Carrier's problem is presented. The computations reveal a striking and beautiful bifurcation diagram, with an infinite s…
Geometric MCMC for Infinite-Dimensional Inverse Problems
Alexandros Beskos, Mark Girolami, Shiwei Lan +2
Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are charact…
A preconditioner for the Ohta--Kawasaki equation
Patrick E. Farrell, John W. Pearson
We propose a new preconditioner for the Ohta--Kawasaki equation, a nonlocal Cahn--Hilliard equation that describes the evolution of diblock copolymer melts. We devise a computable…
The computation of disconnected bifurcation diagrams
Patrick E. Farrell, Casper H. L. Beentjes, Ásgeir Birkisson
Arclength continuation and branch switching are enormously successful algorithms for the computation of bifurcation diagrams. Nevertheless, their combination suffers from three sig…
A Deflation Technique for Detecting Multiple Liquid Crystal Equilibrium States
J. H. Adler, D. B. Emerson, P. E. Farrell +1
Multiple equilibrium states arise in many physical systems, including various types of liquid crystal structures. Having the ability to reliably compute such states enables more ac…