A parareal in time procedure for the control of partial differential equations

By Yvon Maday, Gabriel Turinici. 2002

164 citations recorded by the source corpus.

Subfields: Computational Mechanics, Control and Systems Engineering, Numerical Analysis

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

1. G. Em Karniadakis
2. Xuhui Meng
3. Dongkun Zhang
4. Zhen Li
5. Tony Lelièvre
6. Giovanni Samaey
7. Frédéric Legoll
8. Paris Perdikaris

In Control and Systems Engineering

1. Xuhui Meng
2. G. Em Karniadakis
3. Tony Lelièvre
4. Dongkun Zhang
5. Zhen Li
6. Giovanni Samaey
7. Frédéric Legoll
8. Maizar Raissi

In Numerical Analysis

1. G. Em Karniadakis
2. Zhen Li
3. Tony Lelièvre
4. Dongkun Zhang
5. Giovanni Samaey
6. Frédéric Legoll
7. Xuhui Meng
8. Beth A. Wingate

Citations in the corpus

• PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs (2019, methodology): “…physics-informed neural network (PPINN) to split one long-time problem into many independent short-time problems supervised by an inexpensive / fast coarse-grained (CG) solver, which is inspired by the original parareal algorithm [18] and a more recent supervised parallel-in-time algorithm [19].”
• A Micro-Macro Parareal Algorithm: Application to Singularly Perturbed Ordinary Differential Equations (2012, methodology): “The algorithm has been further analyzed in [30, 31].”
• Implicit Parallel Time Integrators (2011, unknown): “the recent parareal algorithm [8–10, 21, 22].”
• Analysis of the Parareal Time-Parallel Time-Integration Method (2007, unknown): “The algorithm has been further analyzed in [20, 21], and its stability is investigated in [28, 2].”