TY - JOUR
A1 - Weiser, Martin
A1 - Ghosh, Sunayana
T1 - Theoretically optimal inexact SDC methods
T2 - Communications in Applied Mathematics and Computational Science
N2 - 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.
Y1 - 2018
UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/6195
IS - 13-1
SP - 53
EP - 86
ER -