Steele C R, Taber L A
J Acoust Soc Am. 1979 Apr;65(4):1001-6. doi: 10.1121/1.382569.
There are many points of uncertainty in the subject of cochlear models. In this paper only the question of efficient computing methods is addressed. For the cochlear model with a one-dimensional approximation for the fluid motion, Zweig, Lipes, and Pierce [J. Acoust. Soc. Am. 59, 975-982 (1976)] have shown that the WKB method agrees well with a direct numerical integration. For the two-dimensional fluid model, Neely [E.D. thesis, California Institute of Technology, Pasadena, CA (1977)] has shown that a direct finite difference solution is an order of magnitude faster than the integral equation approach used by Allen [J. Acoust. Soc. Am 61, 110-119 (1977)]. In the present work, a formal WKB solution is derived following Whitham [Linear and Nonlinear Waves (Wiley, New York, 1974)]. The advantage of this formulation is simplicity, but the disadvantage is that no error estimate is available. We find that the numerical results from the WKB solution agree well with those of Neely (1977), while the computer time is reduced by another order of magnitude. Thus, the WKB method seems to offer the satisfactory accuracy, efficiency, and flexibility for treating the more realistic cochlear models.
在耳蜗模型这一领域存在许多不确定点。本文仅探讨有效计算方法的问题。对于流体运动采用一维近似的耳蜗模型，茨威格、利佩斯和皮尔斯[《美国声学学会杂志》59, 975 - 982 (1976)]已表明，WKB方法与直接数值积分结果吻合良好。对于二维流体模型，尼利[博士论文，加利福尼亚理工学院，帕萨迪纳，加利福尼亚州(1977)]已表明，直接有限差分法的求解速度比艾伦[《美国声学学会杂志》61, 110 - 119 (1977)]所使用的积分方程法快一个数量级。在当前工作中，按照惠特姆[《线性与非线性波》(威利出版社，纽约，1974)]的方法推导出了形式上的WKB解。这种公式化的优点是简单，但缺点是没有误差估计。我们发现，WKB解的数值结果与尼利(1977)的结果吻合良好，同时计算时间又减少了一个数量级。因此，WKB方法似乎为处理更实际的耳蜗模型提供了令人满意的精度、效率和灵活性。
