Structured computational grids are the basis for highly efficient numerical
approximations of wave propagation. When there are discontinuous material
coefficients the accuracy is typically reduced and there may also be
stability problems. In a sequence of recent papers Gustafsson et al. proved
stability of the Yee scheme and a higher order difference approximation
based on a similar staggered structure, for the wave equation with general
coefficients. In this paper, the Yee discretization is improved from first
to second order by modifying the material coefficients close to the material
interface. This is proven in the $L^2$ norm. The modified higher order
discretization yields a second order error component originating from the
discontinuities, and a fourth order error from the smooth regions. The
efficiency of each original method is retained since there is no special
structure in the difference stencil at the interface. The main focus of this
paper is on one spatial dimension, with the derivation of a second order
algorithm for a two dimensional example given in the last section.
Publié le : 2006-09-15
Classification:
Yee scheme,
discontinuous material coefficients,
regularization,
35L05,
35R05,
65M06,
65M12
@article{1200694904,
author = {Tornberg, Anna-Karin and Engquist, Bj\"orn},
title = {Regularization for Accurate Numerical Wave Propagation in Discontinuous Media},
journal = {Methods Appl. Anal.},
volume = {13},
number = {1},
year = {2006},
pages = { 247-274},
language = {en},
url = {http://dml.mathdoc.fr/item/1200694904}
}
Tornberg, Anna-Karin; Engquist, Björn. Regularization for Accurate Numerical Wave Propagation in Discontinuous Media. Methods Appl. Anal., Tome 13 (2006) no. 1, pp. 247-274. http://gdmltest.u-ga.fr/item/1200694904/