256 citations · 934 across the 55 of their papers we have counts for
10 papers · 1 filter
Finite element appoximation and augmented Lagrangian preconditioning for anisothermal implicitly-constituted non-Newtonian flow
Patrick Farrell, Pablo Alexei Gazca Orozco, Endre Süli
We devise 3-field and 4-field finite element approximations of a system describing the steady state of an incompressible heat-conducting fluid with implicit non-Newtonian rheology.…
Irksome: Automating Runge--Kutta time-stepping for finite element methods
Patrick E. Farrell, Robert C. Kirby, Jorge Marchena-Menendez
While implicit Runge--Kutta methods possess high order accuracy and important stability properties, implementation difficulties and the high expense of solving the coupled algebrai…
Monolithic Multigrid for Magnetohydrodynamics
J. H. Adler, T. Benson, E. C. Cyr +3
The magnetohydrodynamics (MHD) equations model a wide range of plasma physics applications and are characterized by a nonlinear system of partial differential equations that strong…
Augmented saddle point formulation of the steady-state Stefan--Maxwell diffusion problem
Alexander Van-Brunt, Patrick E. Farrell, Charles W. Monroe
We investigate structure-preserving finite element discretizations of the steady-state Stefan--Maxwell diffusion problem which governs diffusion within a phase consisting of multip…
An augmented Lagrangian preconditioner for implicitly-constituted non-Newtonian incompressible flow
P. E. Farrell, P. A. Gazca-Orozco
We propose an augmented Lagrangian preconditioner for a three-field stress-velocity-pressure discretization of stationary non-Newtonian incompressible flow with an implicit constit…
Computing multiple solutions of topology optimization problems
Ioannis P. A. Papadopoulos, Patrick E. Farrell, Thomas M. Surowiec
Topology optimization problems often support multiple local minima due to a lack of convexity. Typically, gradient-based techniques combined with continuation in model parameters a…