Theoretically optimal inexact SDC methods

  • In several inital value problems with particularly expensive right hand side evaluation or implicit step computation, there is a trade-off between accuracy and computational effort. We consider inexact spectral deferred correction (SDC) methods for solving such initial value problems. SDC methods are interpreted as fixed point iterations and, due to their corrective iterative nature, allow to exploit the accuracy-work-tradeoff for a reduction of the total computational effort. On one hand we derive error models bounding the total error in terms of the evaluation errors. On the other hand, we define work models describing the computational effort in terms of the evaluation accuracy. Combining both, a theoretically optimal local tolerance selection is worked out by minimizing the total work subject to achieving the requested tolerance. The properties of optimal local tolerances and the predicted efficiency gain compared to simpler heuristics, and a reasonable practical performance, are illustrated on simple numerical examples.
Metadaten
Author:Martin Weiser, Sunayana Ghosh
Document Type:Article
Parent Title (English):Communications in Applied Mathematics and Computational Science
Issue:13-1
First Page:53
Last Page:86
Year of first publication:2018
Preprint:urn:nbn:de:0297-zib-53140
DOI:https://doi.org/10.2140/camcos.2018.13.53