21 citations · 84 across the 13 of their papers we have counts for
13 papers
New Time Integrators and Capabilities in SUNDIALS Versions 6.2.0-7.4.0
Steven B. Roberts, Mustafa Ağgül, Daniel R. Reynolds +3
SUNDIALS is a well-established numerical library that provides robust and efficient time integrators and nonlinear solvers. This paper overviews several significant improvements an…
Moment-based adaptive time integration for thermal radiation transport
Ben S. Southworth, Steven Walton, Steven B. Roberts +1
In this paper we develop a framework for moment-based adaptive time integration of deterministic multifrequency thermal radiation transpot (TRT). We generalize our recent semi-impl…
Leveraging Mixed Precision in Exponential Time Integration Methods
Cody J. Balos, Steven Roberts, David J. Gardner
The machine learning explosion has created a prominent trend in modern computer hardware towards low precision floating-point operations. In response, there have been growing effor…
Implicit-Explicit Multirate Infinitesimal Stage-Restart Methods
Alex C. Fish, Daniel R. Reynolds, Steven B. Roberts
Implicit-Explicit (IMEX) methods are flexible numerical time integration methods which solve an initial-value problem (IVP) that is partitioned into stiff and nonstiff processes wi…
Eliminating Order Reduction on Linear, Time-Dependent ODEs with GARK Methods
Steven Roberts, Adrian Sandu
When applied to stiff, linear differential equations with time-dependent forcing, Runge-Kutta methods can exhibit convergence rates lower than predicted by the classical order cond…
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…
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…
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…
ODE Test Problems: a MATLAB suite of initial value problems
Steven Roberts, Andrey A. Popov, Adrian Sandu
ODE Test Problems (OTP) is an object-oriented MATLAB package offering a broad range of initial value problems which can be used to test numerical methods such as time integration m…
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…