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Convergent iterative schemes for time parallelization

MATHEMATICS OF COMPUTATION 2006年第255期75卷 1403-1428页

作者： Garrido, Izaskun Lee, Barry Fladmark, Gunnar E. Espedal, Magne S. Univ Bergen Dept Math N-5008 Bergen Norway Lawrence Livermore Natl Lab CASC Livermore CA 94551 USA

Parallel methods are usually not applied to the time domain because of the inherit sequentialness of time evolution. But for many evolutionary problems, computer simulation can benefit substantially from time parallelization methods. In this paper, we present several such algorithms that actually exploit the sequential nature of time evolution through a predictor-corrector procedure. This sequentialness ensures convergence of a parallel predictor-corrector scheme within a fixed number of iterations. The performance of these novel algorithms, which are derived from the classical alternating Schwarz method, are illustrated through several numerical examples using the reservoir simulator Athena.

关键词： alternating Schwarz time parallelization reservoir simulator multilevel full approximation storage

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A first approach toward a Proper Generalized Decomposition based time parallelization

A first approach toward a Proper Generalized Decomposition b...

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15th Conference of the European Scientific Association on Material Forming, (ESAFORM 2012)

作者： Poulhaon, Fabien Chinesta, Francisco Leygue, Adrien Ecole Cent Nantes Lab GeM UMR CNRS 6183 F-44321 Nantes 3 France

ISBN: (纸本)9783037853665

Many models encountered in computer science remain intractable because of their tremendous complexity. Among them, the numerical modeling of manufacturing processes involving several characteristic times is a challenging issue. Classical incremental methods often fail for solving efficiently such transient models. In that sense model reduction based simulation appears to be a very promising alternative. Multidimensional parametric models can be solved within the context of the Proper Generalized Decomposition (PGD). It opens new horizons regarding time parallelization. Indeed, by no more considering the initial condition of a transient problem as a static input data but as an extra- coordinate similarly to space and time, we demonstrate that it is possible to parallelize efficiently the computation and even reach real-time in some cases.

关键词： Model Reduction Parametric Models Proper Generalized Decomposition Separated Representations time parallelization

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EXPLORER: Supporting run-time parallelization of DO-ACROSS loops on general networks on workstations 4th

EXPLORER: Supporting run-time parallelization of DO-ACROSS l...

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Proceedings of the 1997 4th International Symposium on Solving Irregularly Structures Problems in Parallel, IRREGULAR

作者： Lius, Yung-Lin King, Chung-Ta Department of Computer Science National Tsing Hun University Hsinchu 30043 Taiwan

ISBN: (纸本)3540631380

Performing runtime parallelization on general networks of workstations (NOWs) without special hardware or system software supports is very difficult, especially for DOACROSS loops. With the high communication overhead on NOWs, there is hardly any performance gain for runtime parallelization, due to the latter's large amount of messages for dependence detection, data accesses, and computation scheduling. In this paper, we introduce the EXPLORER system for runtime parallelization of DOACROSS and DOALL loops on general NOWs. EXPLORER hides the communication overhead on NOWs through multithreading — a facility supported in almost all workstations. A preliminary version of EXPLORER was implemented on a NOW consisting of eight DEC Alpha workstations connected through an Ethernet. The Pthread package was used to support multithreading. Experiments on synthetic loops showed speedups of up to 6.5 in DOACROSS loops and 7 in DOALL Loops.

关键词： DOACROSS loops inspector/executor multithreading networks of workstations run time parallelization

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parallelization in time of numerical simulations of fully-developed plasma turbulence using the parareal algorithm

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JOURNAL OF COMPUTATIONAL PHYSICS 2010年第18期229卷 6558-6573页

作者： Samaddar, D. Newman, D. E. Sanchez, R. Univ Alaska Dept Phys Fairbanks AK 99775 USA Oak Ridge Natl Lab Div Fus Energy Oak Ridge TN 37831 USA

It is shown that numerical simulations of fully-developed plasma turbulence can be successfully parallelized in time using the parareal algorithm. The result is far from trivial, and even unexpected, since the exponential divergence of Lagrangian trajectories as well as the extreme sensitivity to initial conditions characteristic of turbulence set these type of simulations apart from the much simpler systems to which the parareal algorithm has been applied to this day. It is also shown that the parallel gain obtainable with this method is very promising (close to an order of magnitude for the cases and implementations described), even when it scales with the number of processors quite differently to what is typical for spatial parallelization. (C) 2010 Elsevier Inc. All rights reserved.

关键词： time parallelization Parareal algorithm Turbulent transport Plasma turbulence Magnetically confined plasmas

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Latency tolerance through parallelization of time in scientific applications

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PARALLEL COMPUTING 2005年第7期31卷 777-796页

作者： Srinivasan, A Chandra, N Florida State Univ Dept Comp Sci Tallahassee FL 32306 USA Florida State Univ Dept Mech Engn Tallahassee FL 32306 USA

Emerging computing environments, such as the Grid, promise enormous raw computational power. However, effective use of such platforms is often difficult, because conventional spatial decomposition leads to fine granularity, resulting in high communication overhead. We introduce the concept of guided simulations to parallelize along the time domain. Here, we use the fact that typically results of other simulations of closely related problems are available. In this approach, we automatically and dynamically determine a relationship between old simulations and the one being performed, and use this to parallelize along the time domain. We demonstrate the validity of this approach by applying the technique to an important application involving molecular dynamics simulation of nanomaterials. In this application, spatial decomposition is not effective due to the small size of the physical system. However, time parallelization is effective, since the granularity is much coarser. We also mention how this approach can be extended to make it inherently fault tolerant. (c) 2005 Elsevier B.V. All rights reserved.

关键词： parallel algorithm time parallelization molecular dynamics temporal decomposition

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Latency tolerance through parallelization of time in scientific applications

Latency tolerance through parallelization of time in scienti...

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3rd International Symposium on Parallel and Distributed Computing (ISPDC 2004)/3rd International Workshop on Algorithms, Models and Tools for Parallel Computing on Heterogeneous Networks (HeteroPar 04)

作者： Srinivasan, A Chandra, N Florida State Univ Dept Comp Sci Tallahassee FL 32306 USA Florida State Univ Dept Mech Engn Tallahassee FL 32306 USA

关键词： parallel algorithm time parallelization molecular dynamics temporal decomposition

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Temporal parallelization of edge plasma simulations using the parareal algorithm and the SOLPS code

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COMPUTER PHYSICS COMMUNICATIONS 2017年 221卷 19-27页

作者： Samaddar, D. Coster, D. P. Bonnin, X. Bergmeister, C. Havlickova, E. Berry, L. A. Elwasif, W. R. Batchelor, D. B. Culham Sci Ctr CCFE Abingdon OX14 3DB Oxon England Max Planck Inst Plasma Phys Garching Germany Univ Paris 13 Sorbonne Paris Cite CNRS LSPM Villetaneuse France ITER Org Route Vinon Sur Verdon F-13115 St Paul Les Durance France Oak Ridge Natl Lab Oak Ridge TN USA

It is shown that numerical modelling of edge plasma physics may be successfully parallelized in time. The parareal algorithm has been employed for this purpose and the SOLPS code package coupling the B2.5 finite-volume fluid plasma solver with the kinetic Monte-Carlo neutral code Eirene has been used as a test bed. The complex dynamics of the plasma and neutrals in the scrape-off layer (SOL) region makes this a unique application. It is demonstrated that a significant computational gain (more than an order of magnitude) may be obtained with this technique. The use of the IPS framework for event-based parareal implementation optimizes resource utilization and has been shown to significantly contribute to the computational gain. (C) 2017 EURATOM/CCFE Fusion Association. Published by Elsevier B.V. All rights reserved.

关键词： time parallelization Parareal algorithm Edge plasma Scrape off layer (SOL) SOLPS Eirene Magnetically confined plasmas

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Application of the parareal algorithm to simulations of ELMs in ITER plasma

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COMPUTER PHYSICS COMMUNICATIONS 2019年 235卷 246-257页

作者： Samaddar, D. Coster, D. P. Bonnin, X. Berry, L. A. Elwasif, W. R. Batchelor, D. B. Culham Sci Ctr CCFE Abingdon OX14 3DB Oxon England Max Planck Inst Plasma Phys D-85748 Garching Germany ITER Org Route Vinon Verdon F-13115 St Paul Les Durance France Oak Ridge Natl Lab Oak Ridge TN USA

This paper explores the application of the parareal algorithm to simulations of ELMs in ITER plasma. The primary focus of this research is identifying the parameters that lead to optimum performance. Since the plasma dynamics vary extremely fast during an ELM cycle, a straightforward application of the algorithm is not possible and a modification to the standard parareal correction is implemented. The size of the time chunks also have an impact on the performance and needs to be optimized. A computational gain of 7.8 is obtained with 48 processors to illustrate that the parareal algorithm can be successfully applied to ELM plasma. Crown Copyright (C) 2018 Published by Elsevier B.V. All rights reserved.

关键词： time parallelization Parareal algorithm Scrape off layer (SOL) SOLPS Magnetically confined plasmas Edge localized modes or ELMs ITER Tokamak

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Hybrid dynamic iterations for the solution of initial value problems

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JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING 2011年第11期71卷 1509-1517页

作者： Yu, Yanan Srinivasan, Ashok Florida State Univ Dept Comp Sci Tallahassee FL 32306 USA

Many scientific problems are posed as Ordinary Differential Equations (ODEs). A large subset of these are initial value problems, which are typically solved numerically. The solution starts by using a known state space of the ODE system to determine the state at a subsequent point in time. This process is repeated several times. When the computational demand is high due to large state space, parallel computers can be used efficiently to reduce the time to solution. Conventional parallelization strategies distribute the state space of the problem amongst cores and distribute the task of computing for a single time step amongst the cores. They are not effective when the computational problems have fine granularity, for example, when the state space is relatively small and the computational effort arises largely from the long time span of the initial value problem. We propose a hybrid dynamic iterations method(1) which combines conventional sequential ODE solvers with dynamic iterations to parallelize the time domain. Empirical results demonstrate a factor of two to four improvement in performance of the hybrid dynamic iterations method over a conventional ODE solver on an 8 core processor. Compared to Picard iterations (also parallelized in the time domain), the proposed method shows better convergence and speedup results when high accuracy is required. (C) 2011 Elsevier Inc. All rights reserved.

关键词： time parallelization Hybrid dynamic iterations ODE solver

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A second-order time parallel decoupled algorithm for the Stokes/Darcy model

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2024年 161卷 13-31页

作者： Xue, Dandan Hou, Yanren Li, Yi Chengdu Univ Technol Coll Math & Phys Chengdu 610059 Sichuan Peoples R China Xinjiang Univ Coll Math & Syst Sci Urumqi 830046 Peoples R China Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Shaanxi Peoples R China Northwest Univ Sch Math Xian 710127 Shaanxi Peoples R China

This paper focuses on investigating a second -order time parallel decoupled algorithm for the mixed Stokes/Darcy model. The main objective of this algorithm is to deal with the issue of low computational efficiency in solving the coupling problem directly. Our scheme not only reduces the computation scale through the decoupling method, but also realizes the parallelism in the time direction through parareal method. Furthermore, we implement a second -order spectral deferred correction method to improve accuracy. For some small time step size, we prove the stability and convergence results of the time parallel decoupled algorithm. Finally, we provide three numerical tests to demonstrate the reliability and computational efficiency of our algorithm.

关键词： time parallelization Decoupled method Parareal Spectral deferred correction Stokes-Darcy model

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