耦合边界元法和等效源法的稳健CHIEF法

A robust CHIEF method for a coupling boundary element method and an equivalent source method

针对声学边界元法中解的非唯一性和奇异积分问题,基于组合亥姆霍兹积分方程公式(combined helmholtz integral equation formulation,CHIEF)法思想,将常规边界元方程和等效源方程进行联立,并利用两者方程系数矩阵间的耦合等价关系,间接替换计算常规边界元法中的奇异系数矩阵,进而提出一种具有全频域唯一解、高计算精度和高稳定性的耦合CHIEF法。该方法将等效源方程作为补充方程,不仅解决了传统CHIEF法内点补充方程失效的问题,而且矩阵的间接替换计算避免了直接计算奇异积分,显著提高了计算效率和精度。通过声辐射和声散射的典型算例对比了所提方法、常规边界元法、常规Burton-Miller法和等效源法的计算效果。结果表明,所提方法不仅在全波数域内均能获得唯一解,且其计算精度和效率均优于常规边界元法和常规Burton-Miller方法,其系数矩阵条件数远低于等效源法。

Aiming at the problem of non-uniqueness of solution and singular integral in acoustic boundary element methods,based on the idea of CHIEF methods,the conventional boundary element equation and the equivalent source equation werecombined,and the coupling equivalent relation between the coefficient matrix of the two equations was used to indirectly replace the singular coefficient matrix in the conventional boundary element method,and then a coupled CHIEF method with unique solution in full frequency domain,high computational accuracy and high stability wasproposed.In this method,the equivalent source equation wasused as the supplementary equation,which not only solves the failure of the interior point supplementary equation of the traditional CHIEF method,but also avoids direct calculation of singular integrals by the indirect substitution of matrix,which significantly improves computational efficiency and accuracy.Through typical examples of acoustic radiation and scattering,the proposed method,conventional boundary element method,conventional Burton-Miller method,and equivalent source method werecompared.Results show that not only the unique solution can be obtained in the full wavenumber domain,but also calculation accuracy and efficiency of the proposed method are better than those of the conventional boundary element method and the conventional Burton-Miller method,and the condition number of the coefficient matrix is much lower than that of the equivalent source method.