Publications (15)
Coupled Multirate Infinitesimal GARK Schemes for Stiff Systems with Multiple Time Scales
Steven Roberts, Arash Sarshar, Adrian Sandu
Traditional time discretization methods use a single timestep for the entire system of interest and can perform poorly when the dynamics of the system exhibits a wide range of time…
Design of High-Order Decoupled Multirate GARK Schemes
Arash Sarshar, Steven Roberts, Adrian Sandu
Multirate time integration methods apply different step sizes to resolve different components of the system based on the local activity levels. This local selection of step sizes a…
Implicit multirate GARK methods
Steven Roberts, John Loffeld, Arash Sarshar +2
This work considers multirate generalized-structure additively partitioned Runge-Kutta (MrGARK) methods for solving stiff systems of ordinary differential equations (ODEs) with mul…
Parallel implicit-explicit general linear methods
Steven Roberts, Arash Sarshar, Adrian Sandu
High-order discretizations of partial differential equations (PDEs) necessitate high-order time integration schemes capable of handling both stiff and nonstiff operators in an effi…
Explicit Runge Kutta Methods that Alleviate Order Reduction
Abhijit Biswas, David I. Ketcheson, Steven Roberts +2
Explicit Runge--Kutta (RK) methods are susceptible to a reduction in the observed order of convergence when applied to initial-boundary value problem with time-dependent boundary c…
Linearly implicit GARK schemes
Adrian Sandu, Michael Günther, Steven Roberts
Systems driven by multiple physical processes are central to many areas of science and engineering. Time discretization of multiphysics systems is challenging, since different proc…