21 citations · 79 across the 12 of their papers we have counts for
7 papers · 1 filter
A unified formulation of splitting-based implicit time integration schemes
Severiano González-Pinto, Domingo Hernández-Abreu, Maria S. Pérez-Rodríguez +3
Splitting-based time integration approaches such as fractional steps, alternating direction implicit, operator splitting, and locally one-dimensional methods partition the system o…
A fast time-stepping strategy for dynamical systems equipped with a surrogate model
Steven Roberts, Andrey A Popov, Arash Sarshar +1
Simulation of complex dynamical systems arising in many applications is computationally challenging due to their size and complexity. Model order reduction, machine learning, and o…
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…
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…
Alternating Directions Implicit Integration in a General Linear Method Framework
Arash Sarshar, Steven Roberts, Adrian Sandu
Alternating Directions Implicit (ADI) integration is an operator splitting approach to solve parabolic and elliptic partial differential equations in multiple dimensions based on s…
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…