Analysis of the Parareal Time-Parallel Time-Integration Method
By Martin J. Gander, Stefan Vandewalle. SIAM Journal on Scientific Computing, 2007
487 citations recorded by the source corpus.
Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/6bdaefe7927bae15c17f83486680dd9f510843df
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Mechanics
- Christine Tobler
- Tony Lelièvre
- Frédéric Legoll
- Giovanni Samaey
- Jacob B. Schroder
- Daniel B. Szyld
- Roman Andreev
- Marcus V. Sarkis
In Computational Theory and Mathematics
- Christine Tobler
- Roman Andreev
- Tony Lelièvre
- Frédéric Legoll
- Giovanni Samaey
- Marcus V. Sarkis
- Christian E. Schaerer
- Xiuhong Du
In Numerical Analysis
- Christine Tobler
- Tony Lelièvre
- Giovanni Samaey
- Frédéric Legoll
- Marcus V. Sarkis
- Christian E. Schaerer
- Xiuhong Du
- Jacob B. Schroder
Citations in the corpus
- Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model (2014, background): “This algorithm is studied and shows stability and convergence results [8, 9, 10, 11, 12] particularly for diffusion system and others.”
- Parallel time integration with multigrid (2013, methodology): “The parareal in time method, introduced by Lions, Maday, and Turinici in [25], can be interpreted as a two-level multigrid method [16], even though the leading idea came from a spatial domain decomposition approach.”
- Multilevel preconditioning and low‐rank tensor iteration for space–time simultaneous discretizations of parabolic PDEs (2015, background): “While convergence can be routinely established for time-stepping methods (and the derived methods mentioned in [2]), optimality seems to be exclusive to space–time methods.”
- Implicit Parallel Time Integrators (2011, unknown): “the recent parareal algorithm [8–10, 21, 22].”
- A Micro-Macro Parareal Algorithm: Application to Singularly Perturbed Ordinary Differential Equations (2012, methodology): “We refer to [14] for a reformulation in a more general setting that relates the parareal strategy to earlier time-parallel algorithms, such as multiple shooting (see e.g. [21, 33]) or multigrid waveform relaxation (see e.g. [27, 36]) approaches.”
- INEXACT AND TRUNCATED PARAREAL-INTIME KRYLOV SUBSPACE METHODS FOR PARABOLIC OPTIMAL CONTROL PROBLEMS (2012, methodology): “2984256075 holds when the backward Euler scheme is applied to both time step steps τ and ∆T ; see [10, 21, 22] on how to establish convergence rate for parareal methods.”