VLFEM Analysis of a Two-Dimensional Cochlear Model

A hybrid technique named here the Very Large Finite Element Method (VLFEM) is developed to analyze a two-dimensional model of the cochlea of the inner ear. In this method, the domain is divided into elements of constant material properties and the exact solution to the model equations obtained in each element. This involves two forms of eigenexpansion, allowing a one-dimensional instead of two-dimensional discretization. The discretization is related to the rate of change of the wavenumber of traveling waves on the elastic partition, producing an optimal mesh spacing. A full characterization of the multiple complex wavenumbers is obtained. The results of this analysis for partition (basilar membrane) amplitude and phase exactly correspond to those from previous finite difference and finite element analyses, but less computing effort is required for the same accuracy of results. Reflected waves, abrupt changes in material properties, and arbitrary boundary conditions pose no difficulties for VLFEM analysis, an advantage over the WKB (or LG) technique used previously on this problem.