计算小尺度封闭空间内低频声传递函数的自适应有限元方法研究

Research on Adaptive Finite Element for Calculating Sound Transfer Function in Small Enclosure

如何求解声传递函数成为实现小尺度封闭空间可听化的关键技术。基于Helmholtz方程的有限元法能真实反映出声场内的波动现象,成为求解该问题的有效方法。基于SPR法对求解声传递函数的有限元法进行误差估计;在此基础上结合Helmholtz方程求解的误差理论,提出了求解该问题的自适应有限元法,使用该方法能预测出在各求解频率段内有限元网格的划分情况,从而能满足预先给定的误差要求;使用该方法求解了一个矩形封闭空间内的声传递函数。结果表明提出的方法是有效可行的。

How to calculate sound transfer function （STF） is the key technology of auralization in small enclosure. Due to several reasons, evaluating the precision of finite element method （FEM） based on Helmholtz equation in calculating sound transfer function in small enclosure is impossible. We propose a new AFEM that appears to be quite promising for obtaining such evaluation. Our AFEM still, of cause, depends on basic error theory analysis of Helmholtz equation but it is also based on posterior error estimation, which is obtained with the help of superconvergent patch recovery （SPR） technique already existing in theory of elasticity. Our new AFEM appears to be promising for calculating STF with good precision in complex-shape enclosure.