Uniformly best wavenumber approximations by spatial central difference operators

Viktor Linders, Jan Nordström

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)

Abstract

We construct accurate central difference stencils for problems involving high frequency waves or multi-frequency solutions over long time intervals with a relatively coarse spatial mesh, and with an easily obtained bound on the dispersion error. This is done by demonstrating that the problem of constructing central difference stencils that have minimal dispersion error in the infinity norm can be recast into a problem of approximating a continuous function from a finite dimensional subspace with a basis forming a Chebyshev set. In this new formulation, characterising and numerically obtaining optimised schemes can be done using established theory.

Original languageEnglish
Pages (from-to)695-709
Number of pages15
JournalJournal of Computational Physics
Volume300
DOIs
Publication statusPublished - 2015
Externally publishedYes

Keywords

  • Approximation theory
  • Dispersion relation
  • Finite differences
  • Wave propagation
  • Wavenumber approximation

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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