Construction and analysis of fourth-order finite difference schemes for the acoustic wave equation in nonhomogeneous media

Gary Cohen; Patrick Joly

doi:10.1137/S0036142993246445

Construction and analysis of fourth-order finite difference schemes for the acoustic wave equation in nonhomogeneous media

Gary Cohen
, Patrick Joly

INRIA Institut National de Recherche en Informatique et en Automatique

Research output: Contribution to journal › Article › peer-review

Abstract

In this article, we construct and analyse a family of finite difference schemes for the acoustic wave equation with variable coefficients. These schemes are fourth-order accurate in space and time in the case of smooth media and are designed to remain stable and "optimal" for reflection-transmission phenomena in the case of discontinuous coefficients. Together with a detailed mathematical study, various numerical results are presented.

Original language	English
Pages (from-to)	1266-1302
Number of pages	37
Journal	SIAM Journal on Numerical Analysis
Volume	33
Issue number	4
DOIs	https://doi.org/10.1137/S0036142993246445
Publication status	Published - 1 Jan 1996

Keywords

Finite differences
L-stability
Reflected and transmitted waves
Wave equation

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10.1137/S0036142993246445

Cite this

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title = "Construction and analysis of fourth-order finite difference schemes for the acoustic wave equation in nonhomogeneous media",

abstract = "In this article, we construct and analyse a family of finite difference schemes for the acoustic wave equation with variable coefficients. These schemes are fourth-order accurate in space and time in the case of smooth media and are designed to remain stable and {"}optimal{"} for reflection-transmission phenomena in the case of discontinuous coefficients. Together with a detailed mathematical study, various numerical results are presented.",

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AU - Cohen, Gary

AU - Joly, Patrick

PY - 1996/1/1

Y1 - 1996/1/1

N2 - In this article, we construct and analyse a family of finite difference schemes for the acoustic wave equation with variable coefficients. These schemes are fourth-order accurate in space and time in the case of smooth media and are designed to remain stable and "optimal" for reflection-transmission phenomena in the case of discontinuous coefficients. Together with a detailed mathematical study, various numerical results are presented.

AB - In this article, we construct and analyse a family of finite difference schemes for the acoustic wave equation with variable coefficients. These schemes are fourth-order accurate in space and time in the case of smooth media and are designed to remain stable and "optimal" for reflection-transmission phenomena in the case of discontinuous coefficients. Together with a detailed mathematical study, various numerical results are presented.

KW - Finite differences

KW - L-stability

KW - Reflected and transmitted waves

KW - Wave equation

UR - https://www.scopus.com/pages/publications/0000996995

U2 - 10.1137/S0036142993246445

DO - 10.1137/S0036142993246445

M3 - Article

AN - SCOPUS:0000996995

SN - 0036-1429

VL - 33

SP - 1266

EP - 1302

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 4

ER -

Construction and analysis of fourth-order finite difference schemes for the acoustic wave equation in nonhomogeneous media

Abstract

Keywords

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