Abstract
We started this book with the observation that time-marching methods for solving parabolic problems are inherently sequential. The computation proceeds from time-level to time-level, and the parallelism is limited to the parallelism inherent in the solvers applied in each time-step. It was further illustrated that standard solvers trade off numerical quality against parallel efficiency. Consequently, no time-stepping method proved to be really satisfactory for use on large-scale parallel processors.
Mathematics is full of unanswered questions, which far outnumber known theorems and results... It is its nature to pose more problems than it can solve.
—I. Peterson, “Searching for new mathematics” (SIAM Review, Vol. 33, No. 1,pp. 37–42, March 1991).
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© 1993 B. G. Teubner Stuttgart
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Vandewalle, S. (1993). Concluding Remarks and Suggestions for Future Research. In: Parallel Multigrid Waveform Relaxation for Parabolic Problems. Teubner Skripten zur Numerik. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-94761-1_9
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DOI: https://doi.org/10.1007/978-3-322-94761-1_9
Publisher Name: Vieweg+Teubner Verlag
Print ISBN: 978-3-519-02717-1
Online ISBN: 978-3-322-94761-1
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