Leapfrog Time-Stepping for Hermite Methods View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-03-18

AUTHORS

Arturo Vargas, Thomas Hagstrom, Jesse Chan, Tim Warburton

ABSTRACT

We introduce Hermite-leapfrog methods for first order linear wave systems. The new Hermite-leapfrog methods pair leapfrog time-stepping with the Hermite methods of Goodrich and co-authors et al. (Math Comput 75(254):595–630, 2006). The new schemes stagger field variables in both time and space and are high-order accurate for equations with smooth solutions and coefficients. We provide a detailed description of the method and demonstrate that the method conserves variable quantities. Higher dimensional versions of the method are constructed via tensor products. Numerical evidence and rigorous analysis in one space dimension establish stability and high-order convergence. Experiments demonstrating efficient implementations on a graphics processing unit are also presented. More... »

PAGES

1-26

References to SciGraph publications

  • 2018-07. Flux-Conservative Hermite Methods for Simulation of Nonlinear Conservation Laws in JOURNAL OF SCIENTIFIC COMPUTING
  • 2017. GPU Acceleration of Hermite Methods for the Simulation of Wave Propagation in SPECTRAL AND HIGH ORDER METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS ICOSAHOM 2016
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10915-019-00938-x

    DOI

    http://dx.doi.org/10.1007/s10915-019-00938-x

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1112853567


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