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Automated Galerkin time stepping in Irksome
Boris D. Andrews, Pablo Brubeck, Patrick E. Farrell +2
As the study of temporal and spatial discretization schemes continues to advance, recent work has focused on the use of Galerkin-in-time discretization schemes that enable broader…
Automated Runge-Kutta-Nyström time stepping for finite element methods in Irksome
Robert C. Kirby, Scott P. MacLachlan, Pablo D. Brubeck
Irksome is a library based on the Unified Form Language (UFL) that automates the application of Runge-Kutta time-stepping methods for finite element spatial discretizations of part…
Improving patch selection for monolithic multigrid solvers for high-order {T}aylor-{H}ood discretizations
Amin Rafiei, Scott MacLachlan
Numerical simulation of incompressible fluid flows has been an active topic of research in Scientific Computing for many years, with many contributions to both discretizations and…
Achieving - and -robust monolithic multigrid solvers for the Stokes equations
Amin Rafiei, Scott MacLachlan
The numerical analysis of higher-order mixed finite-element discretizations for saddle-point problems, such as the Stokes equations, has been well-studied in recent years. While th…
Monolithic Multigrid Preconditioners for High-Order Discretizations of Stokes Equations
Alexey Voronin, Graham Harper, Scott MacLachlan +2
This work introduces and assesses the efficiency of a monolithic MG multigrid framework designed for high-order discretizations of stationary Stokes systems using Taylor-Hood a…
Space-time waveform relaxation multigrid for Navier-Stokes
James Jackaman, Scott MacLachlan
Space-time finite-element discretizations are well-developed in many areas of science and engineering, but much work remains within the development of specialized solvers for the r…
Extending Irksome: improvements in automated Runge--Kutta time stepping for finite element methods
Robert C. Kirby, Scott P. MacLachlan
Irksome is a library based on the Unified Form Language (UFL) that enables automated generation of Runge--Kutta methods for time-stepping finite element spatial discretizations of…
Exploiting mesh structure to improve multigrid performance for saddle point problems
Lukas Spies, Luke Olson, Scott MacLachlan
In recent years, solvers for finite-element discretizations of linear or linearized saddle-point problems, like the Stokes and Oseen equations, have become well established. There…