English
Related papers

Related papers: Efficient coarse correction for parallel time-step…

200 papers

Parareal is a well-known parallel-in-time algorithm that combines a coarse and fine propagator within a parallel iteration. It allows for large-scale parallelism that leads to significantly reduced computational time compared to serial…

Numerical Analysis · Mathematics 2023-11-07 Tommaso Buvoli , Michael L. Minion

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…

Numerical Analysis · Mathematics 2025-08-13 Martin J. Gander , Mario Ohlberger , Stephan Rave

This paper focuses on efficient steady-state computations of induction machines. In particular, the periodic Parareal algorithm with initial-value coarse problem (PP-IC) is considered for acceleration of classical time-stepping simulations…

Computational Engineering, Finance, and Science · Computer Science 2020-02-19 Denys Bast , Iryna Kulchytska-Ruchka , Sebastian Schöps , Oliver Rain

The Cox proportional hazards model stands as a widely-used semi-parametric approach for survival analysis in medical research and many other fields. Numerous extensions of the Cox model have further expanded its versatility. Statistical…

Computation · Statistics 2023-10-26 Jianxiao Yang , Martijn J. Schuemie , Marc A. Suchard

Solving multiscale diffusion problems is often computationally expensive due to the spatial and temporal discretization challenges arising from high-contrast coefficients. To address this issue, a partially explicit temporal splitting…

Numerical Analysis · Mathematics 2026-02-26 Yating Wang , Zhengya Yang , Wing Tat Leung

We present a convergence analysis of the parallel-in-time integration method known as the Parareal algorithm for degenerate differential-algebraic systems arising from quasi-static Biot models, which govern coupled flow and deformation in…

Numerical Analysis · Mathematics 2026-01-22 Iñigo Jimenez-Ciga , Francisco Gaspar , Kundan Kumar , Florin A. Radu

In this paper, we are concerned with the micro-macro Parareal algorithm for the simulation of initial-value problems. In this algorithm, a coarse (fast) solver is applied sequentially over the time domain, and a fine (time-consuming) solver…

Numerical Analysis · Mathematics 2025-10-29 Ignace Bossuyt , Stefan Vandewalle , Giovanni Samaey

In this work, we propose a novel framework for accelerating the parareal algorithm, in which the coarse propagator is formulated as a two-step method and optimized with respect to the convergence factor.} We derive a rigorous error estimate…

Numerical Analysis · Mathematics 2026-05-19 Guanglian Li , Qingle Lin , Kai Zhang , Zhi Zhou

In this paper we combine the Parareal parallel-in-time method together with spatial parallelization and investigate this space-time parallel scheme by means of solving the three-dimensional incompressible Navier-Stokes equations.…

Computational Engineering, Finance, and Science · Computer Science 2017-05-18 Roberto Croce , Daniel Ruprecht , Rolf Krause

Sequential numerical methods for integrating initial value problems (IVPs) can be prohibitively expensive when high numerical accuracy is required over the entire interval of integration. One remedy is to integrate in a parallel fashion,…

Numerical Analysis · Mathematics 2022-09-26 Kamran Pentland , Massimiliano Tamborrino , T. J. Sullivan , James Buchanan , L. C. Appel

Asynchronous iterations are more and more investigated for both scaling and fault-resilience purpose on high performance computing platforms. While so far, they have been exclusively applied within space domain decomposition frameworks,…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-10-22 Frederic Magoules , Guillaume Gbikpi-Benissan

We introduce a new strategy for coupling the parallel in time (parareal) iterative methodology with multiscale integrators. Following the parareal framework, the algorithm computes a low-cost approximation of all slow variables in the…

Numerical Analysis · Mathematics 2015-11-19 Gil Ariel , Seong Jun Kim , Richard Tsai

We present a space-time multiscale method for a parabolic model problem with an underlying coefficient that may be highly oscillatory with respect to both the spatial and the temporal variables. The method is based on the framework of the…

Numerical Analysis · Mathematics 2021-12-13 Per Ljung , Roland Maier , Axel Målqvist

Analyses of individual atherosclerotic plaques are mostly descriptive, relying -- for example -- on histological classification by spectral analysis of ultrasound waves or staining and observing particular cellular components. Such passive…

Tissues and Organs · Quantitative Biology 2019-11-26 Navid Mohammad Mirzaei , Pak-Wing Fok , William S. Weintraub

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…

Numerical Analysis · Mathematics 2018-02-09 Gil Ariel , Hieu Nguyen , Richard Tsai

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…

Numerical Analysis · Mathematics 2025-06-17 Sriramkrishnan Muralikrishnan , Robert Speck

The fusion research facility ITER is currently being assembled to demonstrate that fusion can be used for industrial energy production, while several other programmes across the world are also moving forward, such as EU-DEMO, CFETR, SPARC…

This paper proposes a general formulation for temporal parallelisation of dynamic programming for optimal control problems. We derive the elements and associative operators to be able to use parallel scans to solve these problems with…

Optimization and Control · Mathematics 2022-01-25 Simo Särkkä , Ángel F. García-Fernández

In this work the parallel-in-time algorithm Parareal was applied to the ocean-circulation and sea-ice model FESOM2 developed by the Alfred-Wegener Institut (AWI). The climate model provides one time integration method and hence, the coarse…

Numerical Analysis · Mathematics 2022-08-17 Benedict Philippi , Thomas Slawig

The applicability of the Parareal parallel-in-time integration scheme for the solution of a linear, two-dimensional hyperbolic acoustic-advection system, which is often used as a test case for integration schemes for numerical weather…

Computational Engineering, Finance, and Science · Computer Science 2015-10-09 Daniel Ruprecht , Rolf Krause