10 citations · 13 across the 9 of their papers we have counts for
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Multirate Runge-Kutta for Nonlinearly Partitioned Systems
Tommaso Buvoli, Brian K. Tran, Ben S. Southworth
Multirate integration is an increasingly relevant tool that enables scientists to simulate multiphysics systems. Existing multirate methods are designed for equations whose fast an…
Order Conditions for Nonlinearly Partitioned Runge-Kutta Methods
Brian K. Tran, Ben S. Southworth, Tommaso Buvoli
Recently a new class of nonlinearly partitioned Runge--Kutta (NPRK) methods was proposed for nonlinearly partitioned systems of autonomous ordinary differential equations, $y' = F(…
A New Class of Runge-Kutta Methods for Nonlinearly Partitioned Systems
Tommaso Buvoli, Ben S. Southworth
This work introduces a new class of Runge-Kutta methods for solving nonlinearly partitioned initial value problems. These new methods, named nonlinearly partitioned Runge-Kutta (NP…
One-sweep moment-based semi-implicit-explicit integration for gray thermal radiation transport
Ben S. Southworth, Samuel S. Olivier, HyeongKae Park +1
Thermal radiation transport (TRT) is a time dependent, high dimensional partial integro-differential equation. In practical applications such as inertial confinement fusion, TRT is…
Exponential Runge-Kutta Parareal for Non-Diffusive Equations
Tommaso Buvoli, Michael L. Minion
Parareal is a well-known parallel-in-time algorithm that combines a coarse and fine propagator within a parallel iteration. It allows for large-scale parallelism that leads to sign…
Additive Polynomial Time Integrators, Part I: Framework and Fully-Implicit-Explicit (FIMEX) Collocation Methods
Tommaso Buvoli, Ben S. Southworth
In this paper we generalize the polynomial time integration framework to additively partitioned initial value problems. The framework we present is general and enables the construc…
On the Stability of Exponential Integrators for Non-Diffusive Equations
Tommaso Buvoli, Michael L. Minion
Exponential integrators are a well-known class of time integration methods that have been the subject of many studies and developments in the past two decades. Surprisingly, there…
Constructing Polynomial Block Methods
Tommaso Buvoli
The recently introduced polynomial time integration framework proposes a novel way to construct time integrators for solving systems of first-order ordinary differential equation b…
IMEX Runge-Kutta Parareal for Non-Diffusive Equations
Tommaso Buvoli, Michael L. Minion
Parareal is a widely studied parallel-in-time method that can achieve meaningful speedup on certain problems. However, it is well known that the method typically performs poorly on…
Exponential Polynomial Block Methods
Tommaso Buvoli
In this paper we extend the polynomial time integration framework to include exponential integration for both partitioned and unpartitioned initial value problems. We then demonstr…
A Class of Exponential Integrators Based on Spectral Deferred Correction
Tommaso Buvoli
We introduce a new class of arbitrary-order exponential time differencing methods based on spectral deferred correction (ETDSDC) and describe a simple procedure for initializing th…