Time Compact Difference Methods for Wave Propagation in Discontinuous Media

Authors:
Bertil Gustafsson;Per Wahlund
Affiliations:
-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2005

Citing 0
Cited 7

Time Compact High Order Difference Methods for Wave Propagation, 2D

Journal of Scientific Computing
High-order difference methods for waves in discontinuous media

Journal of Computational and Applied Mathematics - Special issue on computational and mathematical methods in science and engineering (CMMSE-2004)
High order finite difference methods for wave propagation in discontinuous media

Journal of Computational Physics
Determining the locations and discontinuities in the derivatives of functions

Applied Numerical Mathematics
Stable and accurate wave-propagation in discontinuous media

Journal of Computational Physics
Error Estimate of Fourth-Order Compact Scheme for Linear Schrödinger Equations

SIAM Journal on Numerical Analysis
Summation by Parts Operators for Finite Difference Approximations of Second-Derivatives with Variable Coefficients

Journal of Scientific Computing

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Abstract

In [B. Gustafsson and E. Mossberg, SIAM J. Sci. Comput., 26 (2004), pp. 259--271], a fourth order one-step method was constructed for the solution of wave propagation problems. The method is based on the first order system form of the PDE and uses a staggered grid both in space and time. The method was also applied with good results to a problem with discontinuous coefficients without using any special procedure across the discontinuity. In this paper we will analyze a model problem from acoustics and demonstrate the theoretical foundation for this behavior. Furthermore, we shall present more detailed numerical experiments which confirm the theoretical results.