13 citations · 17 across the 4 of their papers we have counts for
8 papers · 1 filter
Local Fourier analysis of Balancing Domain Decomposition by Constraints algorithms
Jed Brown, Yunhui He, Scott MacLachlan
Local Fourier analysis is a commonly used tool for the analysis of multigrid and other multilevel algorithms, providing both insight into observed convergence rates and predictive…
Multigrid Reduction in Time for non-linear hyperbolic equations
Federico Danieli, Scott MacLachlan
Time-parallel algorithms seek greater concurrency by decomposing the temporal domain of a Partial Differential Equation (PDE), providing possibilities for accelerating the computat…
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…
Optimizing multigrid reduction-in-time (MGRIT) and Parareal coarse-grid operators for linear advection
Hans De Sterck, Robert D. Falgout, Stephanie Friedhoff +2
Parallel-in-time methods, such as multigrid reduction-in-time (MGRIT) and Parareal, provide an attractive option for increasing concurrency when simulating time-dependent PDEs in m…
First-order system least squares finite-elements for singularly perturbed reaction-diffusion equations
James H. Adler, Scott MacLachlan, Niall Madden
We propose a new first-order-system least squares (FOSLS) finite-element discretization for singularly perturbed reaction-diffusion equations. Solutions to such problems feature la…
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…