Strongly consistent marching schemes for the wave equation

Jing-Rebecca Li 1 Leslie Greengard
1 DeFI - Shape reconstruction and identification
Inria Saclay - Ile de France, CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
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.
Document type :
Journal articles
Complete list of metadatas

https://hal.inria.fr/hal-00781127
Contributor : Jing-Rebecca Li <>
Submitted on : Friday, January 25, 2013 - 2:01:08 PM
Last modification on : Wednesday, March 27, 2019 - 4:08:29 PM

Identifiers

  • HAL Id : hal-00781127, version 1

Collections

Citation

Jing-Rebecca Li, Leslie Greengard. Strongly consistent marching schemes for the wave equation. Journal of Computational Physics, Elsevier, 2003, 188 (1), pp.194--208. ⟨hal-00781127⟩

Share

Metrics

Record views

262