Shared Memory Pipelined Parareal

Summary The computation of Gauss quadrature rules for arbitrary weight functions using the Stieltjes algorithm is a purely sequential process, and the computational cost significantly increases when high accuracy is required. ParaStieltjes is a new algorithm to compute the recurrence coefficients of the associated orthogonal polynomials in parallel, from which the nodes and weights of the quadrature rule can then be obtained. ParaStieltjes is based on the time‐parallel Parareal algorithm for solving time‐dependent problems, and thus enlarges the applicability of this time parallel technique to a further, new area of scientific computing. We study ParaStieltjes numerically for different weight functions, and show that substantial theoretical speedup can be obtained when high accuracy is needed. We also present an asymptotic approximation for the node and weight distribution of Gauss quadrature rules, which can be used effectively in ParaStieltjes.

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“…Furthermore, it was assumed that the computational cost of

𝒢

is negligible. A comparison between theoretical and effective speedup of Parareal can be found, for example, in References 25,26.…”

Section: Parallelization Of the Stieltjes Proceduresmentioning

confidence: 99%

ParaStieltjes: Parallel computation of Gauss quadrature rules using a Parareal‐like approach for the Stieltjes procedure

Gander

Lunet

2020

Numerical Linear Algebra App

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“…We first analyse the parallel speedup, defined as the ratio of the sequential to the parallel execution time for a given number of processes. As pointed out in [1,2,5,35], the Parareal algorithm is flexible enough to accommodate various implementations based on different programming paradigms. In the modeling, we consider a distributed memory implementation to handle the parallelization in time.…”

Section: Expected Parallel Performance Of Pararealmentioning

confidence: 99%

“…In the modeling, we consider a distributed memory implementation to handle the parallelization in time. We refer the reader to [35] for a discussion and analysis of other strategies. We consider a total of N proc processes for the space-time parallelism with N processes being devoted to the parallelization in time.…”

Section: Expected Parallel Performance Of Pararealmentioning

confidence: 99%

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Time-parallel simulation of the decay of homogeneous turbulence using Parareal with spatial coarsening

Lunet

Bodart

Gratton³

et al. 2018

Comput. Visual Sci.

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Direct Numerical Simulation of turbulent flows is a computationally demanding problem that requires efficient parallel algorithms. We investigate the applicability of the time-parallel Parareal algorithm to an instructional case study related to the simulation of the decay of homogeneous isotropic turbulence in three dimensions. We combine a Parareal variant based on explicit time integrators and spatial coarsening with the space-parallel Hybrid Navier-Stokes solver. We analyse the performance of this space-time parallel solver with respect to speedup and quality of the solution. The results are compared with reference data obtained with a classical explicit integration, using an error analysis which relies on the energetic content of the solution. We show that a single Parareal iteration is able to reproduce with high fidelity the main statistical quantities characterizing the turbulent flow field. Keywords Direct Numerical Simulation • Explicit time integrator • High-order method in space • Navier-Stokes equations • Parareal • Space-time parallelism This research is partly funded by "Région Occitanie/ Pyrénées-Méditerranée" as part of the "Développement de nouvelles stratégies pour le calcul massivement parallèleà l'échelle exa en mécanique des fluides numérique (DENSE)" project.

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“…This observation naturally encapsulates a family of powerful algorithms referred to as parallel in time or parareal methods, often invoked to simulate the system's dynamics on heterogeneous classical hardware 13,14 . The latter techniques effectively take advantage of the fact that a part of the evolution can be distributed and carried out in parallel.…”

mentioning

confidence: 99%

Parallel in time dynamics with quantum annealers

Jałowiecki

Więckowski

Gawron

et al. 2020

Sci Rep

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Recent years have witnessed an unprecedented increase in experiments and hybrid simulations involving quantum computers. in particular, quantum annealers. there exist a plethora of algorithms promising to outperform classical computers in the near-term future. Here, we propose a parallel in time approach to simulate dynamical systems designed to be executed already on present-day quantum annealers. in essence, purely classical methods for solving dynamics systems are serial. therefore, their parallelization is substantially limited. in the presented approach, however, the time evolution is rephrased as a ground-state search of a classical ising model. Such a problem is solved intrinsically in parallel by quantum computers. The main idea is exemplified by simulating the Rabi oscillations generated by a two-level quantum system (i.e. qubit) experimentally.

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Shared Memory Pipelined Parareal

Cited by 8 publications

References 30 publications

ParaStieltjes: Parallel computation of Gauss quadrature rules using a Parareal‐like approach for the Stieltjes procedure

ParaStieltjes: Parallel computation of Gauss quadrature rules using a Parareal‐like approach for the Stieltjes procedure

Time-parallel simulation of the decay of homogeneous turbulence using Parareal with spatial coarsening

Parallel in time dynamics with quantum annealers

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