Applications of time parallelization
BW Ong, JB Schroder - Computing and Visualization in Science, 2020 - Springer
This review article serves to summarize the many advances in time-parallel computations
since the excellent review article by Gander,“50 years of Time Parallel Integration”(Gander …
since the excellent review article by Gander,“50 years of Time Parallel Integration”(Gander …
A unified analysis framework for iterative parallel-in-time algorithms
Parallel-in-time integration has been the focus of intensive research efforts over the past two
decades due to the advent of massively parallel computer architectures and the scaling …
decades due to the advent of massively parallel computer architectures and the scaling …
A direct time parallel solver by diagonalization for the wave equation
With the advent of very large scale parallel computers, it has become more and more
important to also use the time direction for parallelization when solving evolution problems …
important to also use the time direction for parallelization when solving evolution problems …
Multilevel convergence analysis of multigrid-reduction-in-time
A Hessenthaler, BS Southworth, D Nordsletten… - SIAM Journal on …, 2020 - SIAM
This paper presents a multilevel convergence framework for multigrid-reduction-in-time
(MGRIT) as a generalization of previous two-grid estimates. The framework provides a priori …
(MGRIT) as a generalization of previous two-grid estimates. The framework provides a priori …
Interweaving PFASST and parallel multigrid
The parallel full approximation scheme in space and time (PFASST) introduced by Emmett
and Minion in 2012 is an iterative strategy for the temporal parallelization of ODEs and …
and Minion in 2012 is an iterative strategy for the temporal parallelization of ODEs and …
Multiple shooting shadowing for sensitivity analysis of chaotic dynamical systems
PJ Blonigan, Q Wang - Journal of Computational Physics, 2018 - Elsevier
Sensitivity analysis methods are important tools for research and design with simulations.
Many important simulations exhibit chaotic dynamics, including scale-resolving turbulent …
Many important simulations exhibit chaotic dynamics, including scale-resolving turbulent …
A superlinear convergence estimate for the parareal Schwarz waveform relaxation algorithm
MJ Gander, YL Jiang, B Song - SIAM Journal on Scientific Computing, 2019 - SIAM
The parareal Schwarz waveform relaxation algorithm is a new space-time parallel algorithm
for the solution of evolution partial differential equations. It is based on a decomposition of …
for the solution of evolution partial differential equations. It is based on a decomposition of …
Multigrid interpretations of the parareal algorithm leading to an overlapping variant and MGRIT
The parareal algorithm is by construction a two level method, and there are several ways to
interpret the parareal algorithm to obtain multilevel versions. We first review the three main …
interpret the parareal algorithm to obtain multilevel versions. We first review the three main …
Low-rank Parareal: a low-rank parallel-in-time integrator
In this work, the Parareal algorithm is applied to evolution problems that admit good low-
rank approximations and for which the dynamical low-rank approximation (DLRA) can be …
rank approximations and for which the dynamical low-rank approximation (DLRA) can be …
Time-periodic steady-state solution of fluid-structure interaction and cardiac flow problems through multigrid-reduction-in-time
A Hessenthaler, RD Falgout, JB Schroder… - Computer Methods in …, 2022 - Elsevier
In this paper, a time-periodic MGRIT algorithm is proposed as a means to reduce the time-to-
solution of numerical algorithms by exploiting the time periodicity inherent to many …
solution of numerical algorithms by exploiting the time periodicity inherent to many …