A New Stabilization of Adaptive Step Trapezoid Rule Based on Finite Difference Interrupts

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dc.citation.firstpageA725en_US
dc.citation.issueNumber2en_US
dc.citation.journalTitleSIAM Journal on Scientific Computingen_US
dc.citation.lastpageA746en_US
dc.citation.volumeNumber37en_US
dc.contributor.authorLee, J. Alexen_US
dc.contributor.authorNam, Jaewooken_US
dc.contributor.authorPasquali, Matteoen_US
dc.date.accessioned2015-07-09T15:30:03Zen_US
dc.date.available2015-07-09T15:30:03Zen_US
dc.date.issued2015en_US
dc.description.abstractThe adaptive step trapezoid rule (TR) is a generally effective numerical integrator, but it is prone to ringing instability and solution stall. We introduce a new stabilization algorithm based on finite difference interrupts (FDI) that reduces ringing and prevents stall. Unlike previously reported stabilization schemes, our algorithm achieves stability and second order accuracy without incurring significant computational cost or spurious diffusion. TR with FDI is at least as stable and accurate as existing methods when solving the prototypical scalar problem. We demonstrate that it has better stability, accuracy, and cost when solving the tightly coupled system describing free surface flows of viscoelastic liquids. Though we demonstrate TR with FDI in the context of a finite element method-of-lines, it is applicable to any TR-based algorithm.en_US
dc.identifier.citationLee, J. Alex, Nam, Jaewook and Pasquali, Matteo. "A New Stabilization of Adaptive Step Trapezoid Rule Based on Finite Difference Interrupts." <i>SIAM Journal on Scientific Computing,</i> 37, no. 2 (2015) Society for Industrial and Applied Mathematics: A725-A746. http://dx.doi.org/10.1137/140966915.en_US
dc.identifier.doihttp://dx.doi.org/10.1137/140966915en_US
dc.identifier.urihttps://hdl.handle.net/1911/80853en_US
dc.language.isoengen_US
dc.publisherSociety for Industrial and Applied Mathematicsen_US
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.en_US
dc.subject.keywordtrapezoid ruleen_US
dc.subject.keywordAdams -- Bashforth -- Moultonen_US
dc.subject.keywordmethod-of-linesen_US
dc.subject.keywordadaptive time stepen_US
dc.subject.keywordfluid mechanicsen_US
dc.subject.keywordfinite element methoden_US
dc.subject.keywordringing instabilityen_US
dc.subject.keywordstiff PDEen_US
dc.titleA New Stabilization of Adaptive Step Trapezoid Rule Based on Finite Difference Interruptsen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
dc.type.publicationpublisher versionen_US
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