水下声散射问题的奇异积分研究

Singular Research for Acoustic Scattering Problems

奇异积分和近奇异积分的数值计算是实施边界元法研究水下目标声散射特性的一个难点,全局法是一种可以将面积分转化为计算沿边界曲线的线积分,基于全局法的思想,推导得到了边界元法中奇异积分和近奇异积分的数值计算表达式.仿真结果表明通过奇异积分和近奇异积分的精确处理,提高了边界元法的数值计算精度;且由于得到的数值表达式是闭合的,提高了积分的计算速度;得到的数值表达式不仅可以用于水下声散射特性研究,在声辐射、电磁散射等研究中都可以得到满意的精度.

In order to compute acoustic scattering of objects by BEM, the numerical calculation of the singular integral and near-singular integral is a main difficulty, the global approach can transfer sur- face integral to line integral, then deduce numerical expression based on the global approach. Simula- tion results indicate by the high efficiency dealing with the singular integral and near-singular integral, the efficiency of BEM has been improved, and improve the calculation of the integral, the numerical expressions not only can be used in acoustic characteristic, but also can be used in acoustic radiation, electromagnetic and so on.