Abstract
We consider the parallel solution of unsteady partial differential equations with the two-dimensional heat equation as a model problem. Conventional implicit integration methods for the solution of this type of equation proceed by solving a sequence of problems iteratively. It is shown that despite the sequential nature of this process, several processors may be employed to solve at several time-steps simultaneously. The accuracy of an integration method such as backward Euler may be enhanced by embedding it in an extrapolation method which itself contains algorithmic parallelism. A solution procedure based on the multigrid method is presented which utilizes both kinds of parallelism. The efficiencies obtained on a message-passing multiprocessor prove the suitability of the method for this type of problem.
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© 1992 Springer-Verlag Berlin Heidelberg
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Horton, G., Knirsch, R. (1992). Time-parallel multigrid in an extrapolation method for time-dependent partial differential equations. In: Zima, H.P. (eds) Parallel Computation. ACPC 1991. Lecture Notes in Computer Science, vol 591. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55437-8_96
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DOI: https://doi.org/10.1007/3-540-55437-8_96
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