Simulating cardiac electrophysiology using anisotropic mesh adaptivity. - James Southern; Gerard J. Gorman; M. D. Piggott; Patrick E. Farrell; Miguel O. Bernabeu; Joe Pitt-Francis (J. Comput. Sci., 2010)

Anisotropic mesh adaptivity for cardiac electrophysiology. - James Southern; Gerard J. Gorman; M. D. Piggott; Patrick E. Farrell; Miguel O. Bernabeu; Joe Pitt-Francis (ICCS, 2010)

The addition of fields on different meshes. - Patrick E. Farrell (J. Comput. Phys., 2011)

A framework for the automation of generalised stability theory - Patrick E. Farrell; Colin J. Cotter; Simon W. Funke (CoRR, 2012)

Directional integration on unstructured meshes via supermesh construction. - James R. Maddison; Patrick E. Farrell (J. Comput. Phys., 2012)

Parallel anisotropic mesh adaptivity with dynamic load balancing for cardiac electrophysiology. - James Southern; Gerard J. Gorman; M. D. Piggott; Patrick E. Farrell (J. Comput. Sci., 2012)

Hybrid OpenMP/MPI Anisotropic Mesh Smoothing. - Gerard J. Gorman; James Southern; Patrick E. Farrell; M. D. Piggott; Georgios Rokos; Paul H. J. Kelly (ICCS, 2012)

A framework for automated PDE-constrained optimisation - Simon W. Funke; Patrick E. Farrell (CoRR, 2013)

Tidal turbine array optimisation using the adjoint approach - Simon W. Funke; Patrick E. Farrell; M. D. Piggott (CoRR, 2013)

Automated Derivation of the Adjoint of High-Level Transient Finite Element Programs. - Patrick E. Farrell; David A. Ham; Simon W. Funke; Marie E. Rognes (SIAM J. Sci. Comput., 2013)

A Framework for the Automation of Generalized Stability Theory. - Patrick E. Farrell; Colin J. Cotter; Simon W. Funke (SIAM J. Sci. Comput., 2014)

Deflation Techniques for Finding Distinct Solutions of Nonlinear Partial Differential Equations. - Patrick E. Farrell; Á. Birkisson; Simon W. Funke (SIAM J. Sci. Comput., 2015)

The Number of Distinct Eigenvalues of a Matrix After Perturbation. - Patrick E. Farrell (SIAM J. Matrix Anal. Appl., 2016)

Geometric MCMC for infinite-dimensional inverse problems. - Alexandros Beskos; Mark A. Girolami; Shiwei Lan; Patrick E. Farrell; Andrew M. Stuart (J. Comput. Phys., 2017)

cbcbeat: an adjoint-enabled framework for computational cardiac electrophysiology. - Marie E. Rognes; Patrick E. Farrell; Simon W. Funke; Johan E. Hake; Mary M. Maleckar (J. Open Source Softw., 2017)

Analysis of Carrier's Problem. - S. J. Chapman; Patrick E. Farrell (SIAM J. Appl. Math., 2017)

A Preconditioner for the Ohta-Kawasaki Equation. - Patrick E. Farrell; John W. Pearson (SIAM J. Matrix Anal. Appl., 2017)

Combining Deflation and Nested Iteration for Computing Multiple Solutions of Nonlinear Variational Problems. - J. H. Adler; David B. Emerson; Patrick E. Farrell; Scott P. MacLachlan (SIAM J. Sci. Comput., 2017)

Computing stationary solutions of the two-dimensional Gross-Pitaevskii equation with deflated continuation. - Efstathios G. Charalampidis; P. G. Kevrekidis; Patrick E. Farrell (Commun. Nonlinear Sci. Numer. Simul., 2018)

Efficient White Noise Sampling and Coupling for Multilevel Monte Carlo with Nonnested Meshes. - Matteo Croci; Michael B. Giles; Marie E. Rognes; Patrick E. Farrell (SIAM/ASA J. Uncertain. Quantification, 2018)

Higher-Order Moving Mesh Methods for PDE-Constrained Shape Optimization. - Alberto Paganini; Florian Wechsung; Patrick E. Farrell (SIAM J. Sci. Comput., 2018)

Automated Adjoints of Coupled PDE-ODE Systems. - Patrick E. Farrell; Johan E. Hake; Simon W. Funke; Marie E. Rognes (SIAM J. Sci. Comput., 2019)

An Augmented Lagrangian Preconditioner for the 3D Stationary Incompressible Navier-Stokes Equations at High Reynolds Number. - Patrick E. Farrell; Lawrence Mitchell; Florian Wechsung (SIAM J. Sci. Comput., 2019)

Bifurcation analysis of stationary solutions of two-dimensional coupled Gross-Pitaevskii equations using deflated continuation. - Efstathios G. Charalampidis; Nicolas Boullé; Patrick E. Farrell; Panayotis G. Kevrekidis (Commun. Nonlinear Sci. Numer. Simul., 2020)

Robust multigrid methods for nearly incompressible elasticity using macro elements. - Patrick E. Farrell; Lawrence Mitchell; L. Ridgway Scott; Florian Wechsung (CoRR, 2020)

Augmented Lagrangian preconditioners for the Oseen-Frank model of cholesteric liquid crystals. - Jingmin Xia; Patrick E. Farrell; Florian Wechsung (CoRR, 2020)

A Reynolds-robust preconditioner for the Reynolds-robust Scott-Vogelius discretization of the stationary incompressible Navier-Stokes equations. - Patrick E. Farrell; Lawrence Mitchell; L. Ridgway Scott; Florian Wechsung (CoRR, 2020)

Deflation-based Identification of Nonlinear Excitations of the 3D Gross-Pitaevskii equation. - Nicolas Boullé; Efstathios G. Charalampidis; Patrick E. Farrell; Panayotis G. Kevrekidis (CoRR, 2020)

Augmented saddle point formulation of the steady-state Stefan-Maxwell diffusion problem. - Alexander Van-Brunt; Patrick E. Farrell; Charles W. Monroe (CoRR, 2020)

Monolithic Multigrid for Magnetohydrodynamics. - J. H. Adler; Thomas R. Benson; Eric C. Cyr; Patrick E. Farrell; Scott P. MacLachlan; Ray S. Tuminaro (CoRR, 2020)

Finite element appoximation and augmented Lagrangian preconditioning for anisothermal implicitly-constituted non-Newtonian flow. - Patrick E. Farrell; Pablo Alexei Gazca-Orozco; Endre Süli (CoRR, 2020)

Complexity bounds on supermesh construction for quasi-uniform meshes. - Matteo Croci; Patrick E. Farrell (J. Comput. Phys., 2020)

Deflation for semismooth equations. - Patrick E. Farrell; Matteo Croci; Thomas M. Surowiec (Optim. Methods Softw., 2020)

Numerical Analysis of Unsteady Implicitly Constituted Incompressible Fluids: 3-Field Formulation. - Patrick E. Farrell; Pablo Alexei Gazca-Orozco; Endre Süli (SIAM J. Numer. Anal., 2020)

An Augmented Lagrangian Preconditioner for Implicitly Constituted Non-Newtonian Incompressible Flow. - Patrick E. Farrell; Pablo Alexei Gazca-Orozco (SIAM J. Sci. Comput., 2020)

Accurate numerical simulation of electrodiffusion and water movement in brain tissue. - Ada J. Ellingsrud; Nicolas Boullé; Patrick E. Farrell; Marie E. Rognes (CoRR, 2021)

Bifurcation analysis of two-dimensional Rayleigh-Bénard convection using deflation. - Nicolas Boullé; Vassilios Dallas; Patrick E. Farrell (CoRR, 2021)

Code generation for productive portable scalable finite element simulation in Firedrake. - Jack D. Betteridge; Patrick E. Farrell; David A. Ham (CoRR, 2021)

A new mixed finite-element method for the biharmonic problem. - Patrick E. Farrell; Abdalaziz Hamdan; Scott P. MacLachlan (CoRR, 2021)

A scalable and robust preconditioner for high-order FEM based on the fast diagonalization method. - Pablo D. Brubeck; Patrick E. Farrell (CoRR, 2021)

Variational and numerical analysis of a Q-tensor model for smectic-A liquid crystals. - Jingmin Xia; Patrick E. Farrell (CoRR, 2021)

Transformations for Piola-mapped elements. - Francis Aznaran; Robert C. Kirby; Patrick E. Farrell (CoRR, 2021)

Numerical approximation of viscous contact problems applied to glacial sliding. - Gonzalo Gonzalez de Diego; Patrick E. Farrell; Ian J. Hewitt (CoRR, 2021)

Code Generation for Productive, Portable, and Scalable Finite Element Simulation in Firedrake. - Jack D. Betteridge; Patrick E. Farrell; David A. Ham (Comput. Sci. Eng., 2021)

A local Fourier analysis of additive Vanka relaxation for the Stokes equations. - Patrick E. Farrell; Yunhui He; Scott P. MacLachlan (Numer. Linear Algebra Appl., 2021)

Monolithic Multigrid Methods for Magnetohydrodynamics. - James H. Adler; Thomas R. Benson; Eric C. Cyr; Patrick E. Farrell; Scott P. MacLachlan; Ray S. Tuminaro (SIAM J. Sci. Comput., 2021)

Multilevel Quasi Monte Carlo Methods for Elliptic PDEs with Random Field Coefficients via Fast White Noise Sampling. - Matteo Croci; Michael B. Giles; Patrick E. Farrell (SIAM J. Sci. Comput., 2021)

Computing Multiple Solutions of Topology Optimization Problems. - Ioannis P. A. Papadopoulos; Patrick E. Farrell; Thomas M. Surowiec (SIAM J. Sci. Comput., 2021)

Irksome: Automating Runge-Kutta Time-stepping for Finite Element Methods. - Patrick E. Farrell; Robert C. Kirby; Jorge Marchena-Menendez (ACM Trans. Math. Softw., 2021)

PCPATCH: Software for the Topological Construction of Multigrid Relaxation Methods. - Patrick E. Farrell; Matthew G. Knepley; Lawrence Mitchell; Florian Wechsung (ACM Trans. Math. Softw., 2021)

A new mixed finite-element method for H2 elliptic problems. - Patrick E. Farrell; Abdalaziz Hamdan; Scott P. MacLachlan (Comput. Math. Appl., 2022)

Optimal control of Hopf bifurcations. - Nicolas Boullé; Patrick E. Farrell; Marie E. Rognes (CoRR, 2022)

Finite-element discretization of the smectic density equation. - Patrick E. Farrell; Abdalaziz Hamdan; Scott P. MacLachlan (CoRR, 2022)

Two-Component 3D Atomic Bose-Einstein Condensates Support Complex Stable Patterns. - Nicolas Boullé; I. Newell; Patrick E. Farrell; Panayotis G. Kevrekidis (CoRR, 2022)

Finite element methods for multicomponent convection-diffusion. - Francis R. A. Aznaran; Patrick E. Farrell; Charles W. Monroe; Alexander J. Van-Brunt (CoRR, 2022)

Finite element approximation and preconditioning for anisothermal flow of implicitly-constituted non-Newtonian fluids. - Patrick E. Farrell; Pablo Alexei Gazca-Orozco; Endre Süli (Math. Comput., 2022)

One-Dimensional Ferronematics in a Channel: Order Reconstruction, Bifurcations, and Multistability. - James Dalby; Patrick E. Farrell; Apala Majumdar; Jingmin Xia (SIAM J. Appl. Math., 2022)

Control of Bifurcation Structures using Shape Optimization. - Nicolas Boullé; Patrick E. Farrell; Alberto Paganini (SIAM J. Sci. Comput., 2022)

A Scalable and Robust Vertex-Star Relaxation for High-Order FEM. - Pablo D. Brubeck; Patrick E. Farrell (SIAM J. Sci. Comput., 2022)

An Augmented Lagrangian Preconditioner for the Magnetohydrodynamics Equations at High Reynolds and Coupling Numbers. - Fabian Laakmann; Patrick E. Farrell; Lawrence Mitchell (SIAM J. Sci. Comput., 2022)

On the Finite Element Approximation of a Semicoercive Stokes Variational Inequality Arising in Glaciology. - Gonzalo Gonzalez de Diego; Patrick E. Farrell; Ian J. Hewitt (SIAM J. Numer. Anal., 2023)

Monolithic multigrid for implicit Runge-Kutta discretizations of incompressible fluid flow. - Razan Abu-Labdeh; Scott P. MacLachlan; Patrick E. Farrell (J. Comput. Phys., 2023)

Optimization of Hopf Bifurcation Points. - Nicolas Boullé; Patrick E. Farrell; Marie E. Rognes (SIAM J. Sci. Comput., 2023)

Preconditioners for Computing Multiple Solutions in Three-Dimensional Fluid Topology Optimization. - Ioannis P. A. Papadopoulos; Patrick E. Farrell (SIAM J. Sci. Comput., 2023)

Structure-preserving and helicity-conserving finite element approximations and preconditioning for the Hall MHD equations. - Fabian Laakmann; Kaibo Hu; Patrick E. Farrell (J. Comput. Phys., 2023)

High-order conservative and accurately dissipative numerical integrators via auxiliary variables. - Boris D. Andrews; Patrick E. Farrell (CoRR, 2024)

An augmented Lagrangian preconditioner for the control of the Navier-Stokes equations. - Santolo Leveque; Michele Benzi; Patrick E. Farrell (CoRR, 2024)

High-order finite element methods for three-dimensional multicomponent convection-diffusion. - Aaron Baier-Reinio; Patrick E. Farrell (CoRR, 2024)

Kinetic Derivation of an Inviscid Compressible Leslie-Ericksen Equation for Rarified Calamitic Gases. - Patrick E. Farrell; Giovanni Russo; Umberto Zerbinati (Multiscale Model. Simul., 2024)

Multigrid Solvers for the de Rham Complex with Optimal Complexity in Polynomial Degree. - Pablo D. Brubeck; Patrick E. Farrell (SIAM J. Sci. Comput., 2024)

A Full Approximation Scheme Multilevel Method for Nonlinear Variational Inequalities. - Ed Bueler; Patrick E. Farrell (SIAM J. Sci. Comput., 2024)

Two Conjectures on the Stokes Complex in Three Dimensions on Freudenthal Meshes. - Patrick E. Farrell; Lawrence Mitchell; L. Ridgway Scott (SIAM J. Sci. Comput., 2024)

ngsPETSc: A coupling between NETGEN/NGSolve and PETSc. - Jack D. Betteridge; Patrick E. Farrell; Matthias Hochsteger; Christopher Lackner; Joachim Schöberl; Stefano Zampini; Umberto Zerbinati (J. Open Source Softw., 2024)

Topology-preserving discretization for the magneto-frictional equations arising in the Parker conjecture. - Mingdong He; Patrick E. Farrell; Kaibo Hu; Boris D. Andrews (CoRR, 2025)

The latent variable proximal point algorithm for variational problems with inequality constraints. - Jørgen S. Dokken; Patrick E. Farrell; Brendan Keith; Ioannis P. A. Papadopoulos; Thomas M. Surowiec (CoRR, 2025)

Analysis and numerical analysis of the Helmholtz-Korteweg equation. - Patrick E. Farrell; Tim van Beeck; Umberto Zerbinati (CoRR, 2025)

Fast solvers for the high-order FEM simplicial de Rham complex. - Pablo D. Brubeck; Patrick E. Farrell; Robert C. Kirby; Charles Parker (CoRR, 2025)