Strongly consistent marching schemes for the wave equation

Jing Rebecca Li, Leslie Greengard

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we consider a class of explicit marching schemes first proposed in [1] for solving the wave equation in complex geometry using an embedded Cartesian grid. These schemes rely on an integral evolution formula for which the numerical domain of dependence adjusts automatically to contain the true domain of dependence. Here, we refine and analyze a subclass of such schemes, which satisfy a condition we refer to as strong u-consistency. This requires that the evolution scheme be exact for a single-valued approximation to the solution at the previous time steps. We provide evidence that many of these strongly u-consistent schemes are stable and converge at very high order even in the presence of small cells in the grid, while taking time steps dictated by the uniform grid spacing.

Original languageEnglish (US)
Pages (from-to)194-208
Number of pages15
JournalJournal of Computational Physics
Volume188
Issue number1
DOIs
StatePublished - Jun 10 2003

Keywords

  • Small cell
  • Stability
  • Wave equation

ASJC Scopus subject areas

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

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