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

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dc.citation.firstpageA725
dc.citation.issueNumber2
dc.citation.journalTitleSIAM Journal on Scientific Computing
dc.citation.lastpageA746
dc.citation.volumeNumber37
dc.contributor.authorLee, J. Alex
dc.contributor.authorNam, Jaewook
dc.contributor.authorPasquali, Matteo
dc.date.accessioned2015-07-09T15:30:03Z
dc.date.available2015-07-09T15:30:03Z
dc.date.issued2015
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.
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.
dc.identifier.doihttp://dx.doi.org/10.1137/140966915
dc.identifier.urihttps://hdl.handle.net/1911/80853
dc.language.isoeng
dc.publisherSociety for Industrial and Applied Mathematics
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.
dc.subject.keywordtrapezoid rule
dc.subject.keywordAdams -- Bashforth -- Moulton
dc.subject.keywordmethod-of-lines
dc.subject.keywordadaptive time step
dc.subject.keywordfluid mechanics
dc.subject.keywordfinite element method
dc.subject.keywordringing instability
dc.subject.keywordstiff PDE
dc.titleA New Stabilization of Adaptive Step Trapezoid Rule Based on Finite Difference Interrupts
dc.typeJournal article
dc.type.dcmiText
dc.type.publicationpublisher version
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