Related papers: A micro/macro parallel-in-time (parareal) algorith…
A weighted version of the parareal method for parallel-in-time computation of time dependent problems is presented. Linear stability analysis for a scalar weighing strategy shows that the new scheme may enjoy favorable stability properties…
With the advent of supercomputers, multi-processor environments and parallel-in-time (PinT) algorithms offer ways to solve initial value problems for ordinary and partial differential equations (ODEs and PDEs) over long time intervals, a…
We propose a parareal based time parallelization scheme in the phase-space for the particle-in-Fourier (PIF) discretization of the Vlasov-Poisson system used in kinetic plasma simulations. We use PIF with a coarse tolerance for the…
We propose a new parallel-in-time algorithm for solving optimal control problems constrained by discretized partial differential equations. Our approach, which is based on a deeper understanding of ParaExp, considers an overlapping…
We consider a new class of Parareal algorithms, which use ideas from localized reduced basis methods to construct the coarse solver from spectral approximations of the transfer operators mapping initial values for a given time interval to…
The time parallel solution of optimality systems arising in PDE constraint optimization could be achieved by simply applying any time parallel algorithm, such as Parareal, to solve the forward and backward evolution problems arising in the…
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 spectral collocation method for fine propagator F and backward…
The Parareal parallel-in-time integration method often performs poorly when applied to hyperbolic partial differential equations. This effect is even more pronounced when the coarse propagator uses a reduced spatial resolution. However,…
We propose three semi-decoupled algorithms for efficiently solving a four-field thermoporoelastic model. The first two algorithms adopt a sequential strategy: at the initial time step, all variables are computed simultaneously using a…
Nonlinear regression is a useful statistical tool, relating observed data and a nonlinear function of unknown parameters. When the parameter-dependent nonlinear function is computationally intensive, a straightforward regression analysis by…
Parareal algorithms are studied for semilinear parabolic stochastic partial differential equations. These algorithms proceed as two-level integrators, with fine and coarse schemes, and have been designed to achieve a `parallel in real time'…
The parareal in time algorithm allows to perform parallel simulations of time dependent problems. This algorithm has been implemented on many types of time dependent problems with some success. Recent contributions have allowed to extend…
In this papers, we couple the parareal algorithm with projection methods of the trajectory on a specific manifold, defined by the preservation of some conserved quantities of the differential equations. First, projection methods are…
In view of the existing limitations of sequential computing, parallelization has emerged as an alternative in order to improve the speedup of numerical simulations. In the framework of evolutionary problems, space-time parallel methods…
Recently, the ParaOpt algorithm was proposed as an extension of the time-parallel Parareal method to optimal control. ParaOpt uses quasi-Newton steps that each require solving a system of matching conditions iteratively. The…
In this paper we accomplish the development of the fast rank-adaptive solver for tensor-structured symmetric positive definite linear systems in higher dimensions. In [arXiv:1301.6068] this problem is approached by alternating minimization…
The aim of this paper is to analyze the robust convergence of a class of parareal algorithms for solving parabolic problems. The coarse propagator is fixed to the backward Euler method and the fine propagator is a high-order single step…
High-temperature superconductors (HTS) have the potential to enable magnetic fields beyond the current limits of low-temperature superconductors in applications like accelerator magnets. However, the design of HTS-based magnets requires…
We present the Wavelet-based Edge Multiscale Parareal (WEMP) Algorithm, recently proposed in [Li and Hu, {\it J. Comput. Phys.}, 2021], for efficiently solving subdiffusion equations with heterogeneous coefficients in long time. This…
We numerically investigate an adaptive version of the parareal algorithm in the context of molecular dynamics. This adaptive variant has been originally introduced in [F. Legoll, T. Lelievre and U. Sharma, SISC 2022]. We focus here on test…