Related papers: A stable parareal-like method for the second order…
The parareal algorithm is a powerful parallel-in-time integration method that accelerates the numerical solution of evolution equations by iteratively combining a fine propagator and a coarse propagator. Although the convergence of the…
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…
Applying parallel-in-time algorithms to multiscale Hamiltonian systems to obtain stable long time simulations is very challenging. In this paper, we present novel data-driven methods aimed at improving the standard parareal algorithm…
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…
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…
The parareal algorithm is known to allow for a significant reduction in wall clock time for accurate numerical solutions by parallelising across the time dimension. We present and test a micro-macro version of parareal, in which the fine…
The parareal algorithm represents an important class of parallel-in-time algorithms for solving evolution equations and has been widely applied in practice. To achieve effective speedup, the choice of the coarse propagator in the algorithm…
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…
We introduce a micro-macro parareal algorithm for the time-parallel integration of multiscale-in-time systems. The algorithm first computes a cheap, but inaccurate, solution using a coarse propagator (simulating an approximate slow…
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…
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…
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…
Multi-scale wave propagation problems are computationally costly to solve by traditional techniques because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and…
We present the application of a micro/macro parareal algorithm for a 1-D energy balance climate model with discontinuous and non-monotone coefficients and forcing terms. The micro/macro parareal method uses a coarse propagator, based on a…
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…
In order to make the numerical simulation of atherosclerotic plaque growth feasible, a temporal homogenization approach is employed. The resulting macro-scale problem for the plaque growth can be further accelerated by using parallel time…
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…
We propose a micro-macro parallel-in-time Parareal method for scalar McKean-Vlasov stochastic differential equations (SDEs). In the algorithm, the fine Parareal propagator is a Monte Carlo simulation of an ensemble of particles, while an…
The high cost of sequential time integration is one major constraint that limits the speedup of a time-parallel algorithm like the Parareal algorithm due to the difficulty of coarsening time steps in a stiff numerical problem. To address…
Mathematical models for flow and reactive transport in porous media often involve non-linear, degenerate parabolic equations. Their solutions have low regularity, and therefore lower order schemes are used for the numerical approximation.…