The Mathematical Institute, University of Oxford, Eprints Archive

A simple proposal for parallel computation over time of an evolutionary process with implicit time stepping

McDonald, E. G. and Wathen, A. J. (2014) A simple proposal for parallel computation over time of an evolutionary process with implicit time stepping. Technical Report. Not specified. (Submitted)

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Abstract

Evolutionary processes arise in many areas of applied mathematics, however since the solution at any time depends on the solution at previous time steps, these types of problems are inherently difficult to parallelize. Whilst an explicit time stepping scheme can be easily parallelized, stability considerations for such methods impose significant restriction on the size of the time step, particularly for parabolic problems. In this paper, we make a simple proposal of a parallel approach for the solution of evolutionary problems with implicit time step schemes. We derive and demonstrate our approach for the linear diffusion equation. Using an all-at-once approach, we solve for all time steps simultaneously using a preconditioned iterative method. The application of the preconditioner is parallelizable over time and significant speed up compared to standard sequential solving methods is achieved. In this short paper, we have not compared to any of the more sophisticated parallel in time methods, but rather simply describe our own elementary approach.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1860
Deposited By: Helen Taylor
Deposited On:04 Oct 2014 08:03
Last Modified:29 May 2015 19:33

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