Finite difference schemes and digital waveguide networks for the wave equation: Stability, passivity, and numerical dispersion

被引：15
作者：
Bilbao, S [1 ]
Smith, JO
机构：
[1] Queens Univ Belfast, Son Arts Res Ctr, Belfast BT7 1NN, Antrim, North Ireland
[2] Queens Univ Belfast, Dept Mus, Belfast BT7 1NN, Antrim, North Ireland
[3] Stanford Univ, Ctr Comp Res Mus & Acoust, Dept Mus, Stanford, CA 94305 USA
来源：
IEEE TRANSACTIONS ON SPEECH AND AUDIO PROCESSING | 2003年 / 11卷 / 03期
关键词：
digital waveguide networks; finite difference schemes; Von Neumann analysis; waveguide meshes;
D O I：
10.1109/TSA.2003.811535
中图分类号：
O42 [声学];
学科分类号：
070206 ; 082403 ;
摘要：
In this paper, some simple families of explicit two-step finite difference methods for solving the wave equation in two and three spatial dimensions are examined. These schemes depend on several free parameters, and can be associated with so-called interpolated digital waveguide meshes. Special attention is paid to the stability properties of these schemes (in particular the bounds on the space-step/time-step ratio) and their relationship with the passivity condition on the related digital waveguide networks. Boundary conditions are also discussed. An analysis of the directional numerical dispersion properties of these schemes is provided, and minimally directionally-dispersive interpolated digital waveguide meshes are constructed.
引用
收藏
页码：255 / 266
页数：12
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