Parallel Solution of Ordinary Differential Equations

Franklin,

doi:10.1109/tc.1978.1675121

Cited by 86 publications

(20 citation statements)

References 14 publications

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“…These methods use different time stepping formulas to advance several time levels at once. For an early numerical comparison for parallel block methods and parallel predictor corrector methods, see Franklin [23]. These methods are ideally suited to be used on the few cores of a multicore processor, but they do not have the potential for large scale parallelism.…”

Section: Miranker and Liniger 1967mentioning

confidence: 99%

50 Years of Time Parallel Time Integration

Gander

2015

Contributions in Mathematical and Computational Sciences

281

226

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Time parallel time integration methods have received renewed interest over the last decade because of the advent of massively parallel computers, which is mainly due to the clock speed limit reached on today's processors. When solving time dependent partial differential equations, the time direction is usually not used for parallelization. But when parallelization in space saturates, the time direction offers itself as a further direction for parallelization. The time direction is however special, and for evolution problems there is a causality principle: the solution later in time is affected (it is even determined) by the solution earlier in time, but not the other way round. Algorithms trying to use the time direction for parallelization must therefore be special, and take this very different property of the time dimension into account. We show in this chapter how time domain decomposition methods were invented, and give an overview of the existing techniques. Time parallel methods can be classified into four different groups: methods based on multiple shooting, methods based on domain decomposition and waveform relaxation, space-time multigrid methods and direct time parallel methods. We show for each of these techniques the main inventions over time by choosing specific publications and explaining the core ideas of the authors. This chapter is for people who want to quickly gain an overview of the exciting and rapidly developing area of research of time parallel methods.

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Section: Miranker and Liniger 1967mentioning

confidence: 99%

50 Years of Time Parallel Time Integration

Gander

2015

Contributions in Mathematical and Computational Sciences

281

226

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“…This can be applied to some predictorcorrector methods [5,22,23], but leads only to a small degree of parallelization; (ii) the system of equations occurring in the generating method when applied to ODE-systems can be distributed among the processors. This form of parallelization is limited by the number of equations in the system.…”

Section: Parallel Implementation Of the Extrapolation Methodsmentioning

confidence: 99%

Load balancing schemes for extrapolation methods

Rauber

Rünger

1997

Concurrency: Pract. Exper.

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“…-Our method reduces runtime, yet preserves timestamp ordering and causal relationships of events. Ordinary differential equations [Franklin 1978] (2) Reservoir simulation [Rutledge et al 1991] (3)…”

Section: Parallel Simulation Problem Spacementioning

confidence: 99%

An analysis of queuing network simulation using GPU-based hardware acceleration

Park

Fishwick

2011

ACM Trans. Model. Comput. Simul.

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Queuing networks are used widely in computer simulation studies. Examples of queuing networks can be found in areas such as the supply chains, manufacturing work flow, and internet routing. If the networks are fairly small in size and complexity, it is possible to create discrete event simulations of the networks without incurring significant delays in analyzing the system. However, as the networks grow in size, such analysis can be time consuming, and thus require more expensive parallel processing computers or clusters. We have constructed a set of tools that allow the analyst to simulate queuing networks in parallel, using the fairly inexpensive and commonly available graphics processing units (GPUs) found in most recent computing platforms. We present an analysis of a GPU-based algorithm, describing benefits and issues with the GPU approach. The algorithm clusters events, achieving speedup at the expense of an approximation error which grows as the cluster size increases. We were able to achieve 10-x speedup using our approach with a small error in a specific implementation of a synthetic closed queuing network simulation. This error can be mitigated, based on error analysis trends, obtaining reasonably accurate output statistics. The experimental results of the mobile ad hoc network simulation show that errors occur only in the time-dependent output statistics.

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Parallel Solution of Ordinary Differential Equations

Cited by 86 publications

References 14 publications

50 Years of Time Parallel Time Integration

50 Years of Time Parallel Time Integration

Load balancing schemes for extrapolation methods

An analysis of queuing network simulation using GPU-based hardware acceleration

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