摘　要：在使用有限元进行声场的数值模拟中，存在着两个主要误差，一个是数值方法中常规的插值误差，另外一个是计算声学中所特有的耗散误差(dispersion error)，后者则是影响声学模拟仿真置信度的最重要因素。产生耗散误差的本质原因是由于有限元的数值模型刚度“偏硬”造成的。为了控制耗散误差，最重要的是使数值模型更好的反映真实模型。本文采用了一种基于边光滑的有限元方法(ES-FEM)来对声场的时域和频域进行数值模拟研究。该方法只采用对复杂问题域适应性很强的三角形网格，通过引进基于边的广义梯度光滑技术，能够使得有限元系统得到适当的“软化”。关于时域和频域的算例表明了在使用同样网格的情况下，本方法在声学模拟中的精度都要比有限元模型的高。

Abstract：The standard finite element method (FEM) encounters two errors in the computational acoustic problems: the conventional interpolation error and the dispersion error which plays an important role in the computational acoustic. The dispersion error is rooted at the “overly-stiff” property of the FEM. In order to control the dispersion error, the most effective measure is to make the numerical model reflect the exact model. In this paper, an edge-based smoothed finite element method (ES-FEM) was adopted for acoustic problems both in the frequency domain and time domain. The present method using only triangular mesh which is very adaptive for any complicated domains and with gradient smoothing operation performed over each edge-based smoothing domain can reduce the stiffness and provide proper “softness” to the model. The results demonstrate that the ES-FEM can provide more accurate solution both in the time and frequency domain compared with the linear FEM using the same meshes.