(A) stable treatment of time domain boundary condition in using the finite difference time domain method

Abstract

The finite difference time domain (FDTD) method is a potentially excellent numerical tool that employs finite difference scheme and leapfrog time-stepping to approximate the derivative operator of the wave equation. Solution of the initialboundary value problem is obtained explicitly by this algorithm. Time domain output from this method yields an easy analysis of the wave transient phenomena to enable sound visualization and auralization. One serious problem of this numerical method has is the method how to dealt with a frequency dependent boundary condition. In this study, a method to take account frequency dependent boundary condition by using surface impedance concept is proposed. To apply given surface impedance by direct convolution in time domain calculation will need a lot of storage for velocity history. In order to avoid that, recursive form of surface impedance should be used. To make this recursive surface impedance, measured surface impedance is fitted to an impedance model. The impedance model is summation of the second order rational polynomial function in frequency domain. This form is used instead of using high order rational polynomial function to ensure the stability of the function in time domain. In this study, Genetic algorithm is used to obtain the coefficients of the surface impedance model by minimizing the error between the measured impedance and the impedance model. After obtaining the coefficients, surface impedance model applied in FDTD calculation by using z-transformation technique. The summation form of the surface impedance is realized in the FDTD calculation by using direct form I parallel structures implementation for discrete time system. This realization introduce new variables as decomposition of pressure in the boundary, by this way recursive form of the surface impedance can be used to avoid the direct convolution with surface velocity. Finally, the tests are conducted in 1-dimensional, to implement porous material empiri...