15 citations · 16 across the 6 of their papers we have counts for
6 papers · 1 filter
Linear Convergence of Parareal Algorithm for Semilinear Parabolic Equations
Guanglian Li, Qingle Lin, Shu-lin Wu +1
Long-time simulations of evolution equations present substantial computational challenges due to the inherently sequential nature of conventional time-stepping schemes. The pararea…
Parareal algorithm via Chebyshev-Gauss spectral collocation method
Quan Zhou, Yicheng Liu, Shu-Lin Wu
We present the Parareal-CG algorithm for time-dependent differential equations in this work. The algorithm is a parallel in time iteration algorithm utilizes Chebyshev-Gauss spectr…
A well-conditioned direct PinT algorithm for first-and second-order evolutionary equations
Jun Liu, Xiang-Sheng Wang, Shu-Lin Wu +1
In this paper, we propose a direct parallel-in-time (PinT) algorithm for time-dependent problems with first- or second-order derivative. We use a second-order boundary value method…
Parallel-in-time preconditioners for the Sinc-Nyström method
Jun Liu, Shu-Lin Wu
The Sinc-Nyström method is a high-order numerical method based on Sinc basis functions for discretizing evolutionary differential equations in time. But in this method we have to s…
Stability implies robust convergence of a class of preconditioned parallel-in-time iterative algorithms
Shu-Lin Wu, Tao Zhou, Zhi Zhou
Solving evolutionary equations in a parallel-in-time manner is an attractive topic and many algorithms are proposed in recent two decades. The algorithm based on the block -circ…
ParaDiag: parallel-in-time algorithms based on the diagonalization technique
Martin J. Gander, Jun Liu, Shu-Lin Wu +2
In 2008, Maday and Ronquist introduced an interesting new approach for the direct parallel-in-time (PinT) solution of time-dependent PDEs. The idea is to diagonalize the time stepp…