NDLI: A Fourth Order Accurate Finite Difference Scheme for the Elastic Wave Equation in Second Order Formulation

Content Provider	Springer Nature Link
Author	Sjögreen, Björn Petersson, N. Anders
Copyright Year	2011
Abstract	We present a fourth order accurate finite difference method for the elastic wave equation in second order formulation, where the fourth order accuracy holds in both space and time. The key ingredient of the method is a boundary modified fourth order accurate discretization of the second derivative with variable coefficient, (μ(x)u $_{ x }$)$_{ x }$. This discretization satisfies a summation by parts identity that guarantees stability of the scheme. The boundary conditions are enforced through ghost points, thereby avoiding projections or penalty terms, which often are used with previous summation by parts operators. The temporal discretization is obtained by an explicit modified equation method. Numerical examples with free surface boundary conditions show that the scheme is stable for CFL-numbers up to 1.3, and demonstrate a significant improvement in efficiency over the second order accurate method. The new discretization of (μ(x)u $_{ x }$)$_{ x }$ has general applicability, and will enable stable fourth order accurate approximations of other partial differential equations as well as the elastic wave equation.
Starting Page	17
Ending Page	48
Page Count	32
File Format	PDF
ISSN	08857474
Journal	Journal of Scientific Computing
Volume Number	52
Issue Number	1
e-ISSN	15737691
Language	English
Publisher	Springer US
Publisher Date	2011-09-08
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Elastic wave equation Finite difference scheme Summation by parts Stability Energy estimate ApplicationMathematics/Computational Methods of Engineering Algorithms Theoretical, Mathematical and Computational Physics Computational Mathematics and Numerical Analysis
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Engineering Computational Theory and Mathematics Computational Mathematics Numerical Analysis Software

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