Summation by Parts Operators for Finite Difference Approximations of Second-Derivatives with Variable Coefficients

被引：53

作者：

Mattsson, Ken ^{[1
]}

机构：

[1] Uppsala Univ, Uppsala, Sweden

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2012年 / 51卷 / 03期

关键词：

High-order finite difference methods; Numerical stability; Second-derivatives; Variable coefficients; NAVIER-STOKES EQUATIONS; BOUNDARY-VALUE-PROBLEMS; ACOUSTIC-WAVE EQUATION; HETEROGENEOUS MEDIA; DISCONTINUOUS MEDIA; MAXWELLS EQUATIONS; ORDER; PROPAGATION; SCHEMES; DERIVATIVES;

D O I：

10.1007/s10915-011-9525-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Finite difference operators approximating second derivatives with variable coefficients and satisfying a summation-by-parts rule have been derived for the second-, fourth- and sixth-order case by using the symbolic mathematics software Maple. The operators are based on the same norms as the corresponding approximations of the first derivative, which makes the construction of stable approximations to general multi-dimensional hyperbolic-parabolic problems straightforward.

引用

页码：650 / 682

页数：33

共 31 条

[1]

[Anonymous], 1995, Time-Dependent Problems and Difference Methods

[2]

Appelö D, 2009, COMMUN COMPUT PHYS, V5, P84

[3] A domain decomposition method for the acoustic wave equation with discontinuous coefficients and grid change [J].