中文摘要：

为了提高边界元法的计算精度和对具有复杂边界形状实际问题的应用能力,发展并应用非连续线性和二次边界单元进行数值计算.使用传统边界积分方程计算外声场,通过带有解析解数值算例,对比不同类型单元的计算精度,得到最有效的单元类型.然而使用传统边界积分法,在某些虚假特征频率处会产生解的非唯一性问题,Burton-Miller方法可以有效地克服这一问题.基于Burton-Miller法得到的非连续线性和二次单元的优化节点位置并不在勒让德多项式零点位置上,虽然表现得不像传统边界元法那样规律和统一,但是合适的经验值仍然被给出.

英文摘要：

To improve the computing accuracy and application ability for practical structures with complex bounda- ties, the discontinuous linear and quadratic boundary elements were discussed. The conventional boundary integral e- quation method （CBIE） was used for the numerical solution, the performance of different types of boundary elements were presented and compared, the effect of the nodal position at discontinuous elements on the computing accuracy was studied and the optional nodal position was obtained. But the CBIE may produce the non-uniqueness problems, Burton- Miller method （BM） could be used to overcome this problem. The performance of different types of boundary elements based on BM was presented and compared. The value of the optimal nodal position for discontinuous elements was very close to the zeroes of Legendre polynomial for CBIE. However, different performance was found when BM was used, and the empirical values for optimal nodal positions for BM were concluded.