A multirate time stepping strategy for parabolic PDE
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(2) Centrum voor Wiskunde en Informatica. MAS Modelling, Analysis and Simulation. Modelling, Analysis and Simulation A multirate time stepping strategy for parabolic PDE. V. Savcenco, W.H. Hundsdorfer, J.G. Verwer REPORT MAS-E0516 AUGUST 2005.
(3) CWI is the National Research Institute for Mathematics and Computer Science. It is sponsored by the Netherlands Organization for Scientific Research (NWO). CWI is a founding member of ERCIM, the European Research Consortium for Informatics and Mathematics. CWI's research has a theme-oriented structure and is grouped into four clusters. Listed below are the names of the clusters and in parentheses their acronyms. Probability, Networks and Algorithms (PNA) Software Engineering (SEN) Modelling, Analysis and Simulation (MAS) Information Systems (INS). Copyright © 2005, Stichting Centrum voor Wiskunde en Informatica P.O. Box 94079, 1090 GB Amsterdam (NL) Kruislaan 413, 1098 SJ Amsterdam (NL) Telephone +31 20 592 9333 Telefax +31 20 592 4199 ISSN 1386-3703.
(4) A multirate time stepping strategy for parabolic PDE ABSTRACT To solve PDE problems with different time scales that are localized in space, multirate time stepping is examined. We introduce a self-adjusting multirate time stepping strategy, in which the step size at a particular grid point is determined by the local temporal variation of the solution, instead of using a minimal single step size for the whole spatial domain. The approach is based on the `method of lines', where first a spatial discretization is performed, together with local error estimates for the resulting semi-discret system. We will primarily consider implicit time stepping methods, suitable for parabolic problems. Our multirate strategy is tested on several parabolic problems in one spatial dimension (1D). 2000 Mathematics Subject Classification: 65L06, 65L50, 65M06, 65M20 Keywords and Phrases: Multirate time stepping, local time stepping, partial differential equations Note: Acknowledgement: The work of V. Savcenco is supported by a Peterich Scholarship through the Netherlands Organisation for Scientific Research NWO..
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