Multi-patch discontinuous Galerkin isogeometric analysis for wave propagation: Explicit time-stepping and efficient mass matrix inversion

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dc.citation.firstpage22
dc.citation.journalTitleComputer Methods in Applied Mechanics and Engineering
dc.citation.lastpage54
dc.citation.volumeNumber333
dc.contributor.authorChan, Jesse
dc.contributor.authorEvans, John A.
dc.date.accessioned2018-09-11T20:40:45Z
dc.date.available2018-09-11T20:40:45Z
dc.date.issued2018
dc.description.abstractWe present a class of spline finite element methods for time-domain wave propagation which are particularly amenable to explicit time-stepping. The proposed methods utilize a discontinuous Galerkin discretization to enforce continuity of the solution field across geometric patches in a multi-patch setting, which yields a mass matrix with convenient block diagonal structure. Over each patch, we show how to accurately and efficiently invert mass matrices in the presence of curved geometries by using a weight-adjusted approximation of the mass matrix inverse. This approximation restores a tensor product structure while retaining provable high order accuracy and semi-discrete energy stability. We also estimate the maximum stable timestep for spline-based finite elements and show that the use of spline spaces results in less stringent CFL restrictions than equivalentﾠC0ﾠor discontinuous finite element spaces. Finally, we explore the use of optimal knot vectors based onﾠL2n-widths. We show how the use of optimal knot vectors can improve both approximation properties and the maximum stable timestep, and present a simple heuristic method for approximating optimal knot positions. Numerical experiments confirm the accuracy and stability of the proposed methods.
dc.identifier.citationChan, Jesse and Evans, John A.. "Multi-patch discontinuous Galerkin isogeometric analysis for wave propagation: Explicit time-stepping and efficient mass matrix inversion." <i>Computer Methods in Applied Mechanics and Engineering,</i> 333, (2018) Elsevier: 22-54. https://doi.org/10.1016/j.cma.2018.01.022.
dc.identifier.doihttps://doi.org/10.1016/j.cma.2018.01.022
dc.identifier.urihttps://hdl.handle.net/1911/102498
dc.language.isoeng
dc.publisherElsevier
dc.rightsThis is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Elsevier.
dc.subject.keywordspline finite element method
dc.subject.keywordisogeometric analysis
dc.subject.keywordhigh order
dc.subject.keywordCFL
dc.subject.keywordexplicit timestepping
dc.subject.keywordwave propagation
dc.titleMulti-patch discontinuous Galerkin isogeometric analysis for wave propagation: Explicit time-stepping and efficient mass matrix inversion
dc.typeJournal article
dc.type.dcmiText
dc.type.publicationpost-print
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