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(1)A multirate time stepping strategy for parabolic PDE Citation for published version (APA): Savcenco, V., Hundsdorfer, W., & Verwer, J. G. (2005). A multirate time stepping strategy for parabolic PDE. (CWI report. MAS-E; Vol. 0516). Centrum voor Wiskunde en Informatica.. Document status and date: Published: 01/01/2005 Document Version: Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement: www.tue.nl/taverne. Take down policy If you believe that this document breaches copyright please contact us at: openaccess@tue.nl providing details and we will investigate your claim.. Download date: 17. Sep. 2021.

(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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