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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

We propose a deep learning approach for wave propagation in media with multiscale wave speed, using a second-order linear wave equation model. We use neural networks to enhance the accuracy of a given inaccurate coarse solver, which…

Numerical Analysis · Mathematics 2022-05-05 Hieu Nguyen , Richard Tsai

In this paper, we propose a model order reduction based adaptive parareal method for time-dependent partial differential equations. By using the data obtained by the fine propagator in each iteration of the plain parareal method together…

Numerical Analysis · Mathematics 2026-01-19 Xiaoying Dai , Miao Hu , Shuwei Shen

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,…

Numerical Analysis · Mathematics 2025-10-13 Judith Angel , Sebastian Götschel , Daniel Ruprecht

Iterative parallel-in-time algorithms like Parareal can extend scaling beyond the saturation of purely spatial parallelization when solving initial value problems. However, they require the user to build coarse models to handle the…

Numerical Analysis · Mathematics 2025-06-24 Abdul Qadir Ibrahim , Sebastian Götschel , Daniel Ruprecht

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

The Parareal algorithm is used to solve time-dependent problems considering multiple solvers that may work in parallel. The key feature is a initial rough approximation of the solution that is iteratively refined by the parallel solvers. We…

Systems and Control · Computer Science 2014-02-18 Loïc Michel

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 a variety of scientific and engineering domains, the need for high-fidelity and efficient solutions for high-frequency wave propagation holds great significance. Recent advances in wave modeling use sufficiently accurate fine solver…

Analysis of PDEs · Mathematics 2025-09-17 Luis Kaiser , Richard Tsai , Christian Klingenberg

The paper derives and analyses the (semi-)discrete dispersion relation of the Parareal parallel-in-time integration method. It investigates Parareal's wave propagation characteristics with the aim to better understand what causes the well…

Numerical Analysis · Mathematics 2018-07-02 Daniel Ruprecht

We propose new sequential sorting operations by adapting techniques and methods used for designing parallel sorting algorithms. Although the norm is to parallelize a sequential algorithm to improve performance, we adapt a contrarian…

Data Structures and Algorithms · Computer Science 2016-09-01 Alexandros V Gerbessiotis

In this work, the Parareal algorithm is applied to evolution problems that admit good low-rank approximations and for which the dynamical low-rank approximation (DLRA) can be used as time stepper. Many discrete integrators for DLRA have…

Numerical Analysis · Mathematics 2022-09-14 Benjamin Carrel , Martin J. Gander , Bart Vandereycken

This paper presents a highly-parallelizable parallel-in-time algorithm for efficient solution of nonlinear time-periodic problems. It is based on the time-periodic extension of the Parareal method, known to accelerate sequential…

Numerical Analysis · Mathematics 2020-07-08 Iryna Kulchytska-Ruchka , Sebastian Schöps

While recent advances in deep learning have shown promising efficiency gains in solving time-dependent partial differential equations (PDEs), matching the accuracy of conventional numerical solvers still remains a challenge. One strategy to…

Numerical Analysis · Mathematics 2025-11-26 Yuwei Geng , Junqi Yin , Eric C. Cyr , Guannan Zhang , Lili Ju

We present a method for fast and accurate physics-based predictions during non-prehensile manipulation planning and control. Given an initial state and a sequence of controls, the problem of predicting the resulting sequence of states is a…

Robotics · Computer Science 2022-03-02 Wisdom C. Agboh , Daniel Ruprecht , Mehmet R. Dogar

In this paper, we investigate the strong convergence analysis of parareal algorithms for stochastic Maxwell equations with the damping term driven by additive noise. The proposed parareal algorithms proceed as two-level temporal…

Numerical Analysis · Mathematics 2024-08-20 Liying Zhang , Qi Zhang

In this paper we develop optimal algorithms in the binary-forking model for a variety of fundamental problems, including sorting, semisorting, list ranking, tree contraction, range minima, and ordered set union, intersection and difference.…

Data Structures and Algorithms · Computer Science 2020-06-26 Guy E. Blelloch , Jeremy T. Fineman , Yan Gu , Yihan Sun

This paper investigates the parareal algorithms for solving the stochastic Maxwell equations driven by multiplicative noise, focusing on their convergence, computational efficiency and numerical performance. The algorithms use the…

Numerical Analysis · Mathematics 2025-02-05 Liying Zhang , Qi Zhang , Lihai Ji

The parareal in time algorithm allows to efficiently use parallel computing for the simulation of time-dependent problems. It is based on a decomposition of the time interval into subintervals, and on a predictor-corrector strategy, where…

Numerical Analysis · Mathematics 2010-11-30 X. Dai , C. Le Bris , F. Legoll , Y. Maday

We propose a probabilistic model for the parallel execution of Las Vegas algorithms, i.e., randomized algorithms whose runtime might vary from one execution to another, even with the same input. This model aims at predicting the parallel…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-06-24 Charlotte Truchet , Florian Richoux , Philippe Codognet