三维Helmholtz积分方程外问题几乎奇异积分的半解析算法

A semi-analytical algorithm for nearly singular integral of three dimensional exterior helmholtz integral equation problem

边界元法求解声场Helmholtz外问题时,由于简单闭合曲面外的无限域边界积分方程与原边值问题(外问题)不完全等价,从而会在某些激励波数(与相应内问题的特征波数重合)下不能获得唯一解。文章引入一种计算几乎奇异积分的半解析算法,结合CHIEF点法,在较宽的波数范围内计算了声场外问题近场和远场内的声压。计算结果表明,该算法不仅有效地克服了频域内解的非唯一问题,而且与单纯的CHIEF点法相比能够显著提高计算精度。

When boundary element method is used to solve Helmholtz problem, the solution of exterior problem is not unique under some wave number which corresponds with the interior problem eigenvalue wave number. It is because of the incomplete equivalence between the boundary integral equation of infinite domain out of simple closed surface and the original boundary problem (exterior problem). Combined with CHIEF points method, a semi-analytical algorithm for calculating the nearly singular integrals is employed in this paper. Both far field and near field inner points acoustic pressure are computed by using the new method in a wide wave number range. The numerical results show that the new method not only solves uniqueness of solution but also remarkably improves the result precision comparing with CHIEF points method.