A comparative analysis of numerical techniques applied to a model of the otolith membrane

AbstractThis paper describes three alternative finite difference methods applied to a model of the otolith membrane. The in-plane displacement of a thin elastic membrane is modeled by a second-order system of elliptic partial differential equations with a fixed boundary closely matching the shape of the otolith membrane. The first two finite difference methods impose a rectangular grid over the shape of the otolith membrane and use different boundary extrapolation schemes applied to boundary conditions. The third method uses an optimization technique to generate a non-uniform grid which conforms to the shape of the otolith membrane, and then generates a rectangular grid via general coordinate transformations. The coordinate transformations are applied to the partial differential equations and finite differences applied to the new rectangular grid with fixed boundary conditions. All three methods were used to simulate the membrane model on a digital computer. The numerical results are compared to evaluate the effectiveness of the coordinate transformation method