进一步改进边界元方法以克服振动声辐射计算中解的非唯一性

章利用基于三次B样条插值的边界元方法，对振动体外部声辐射问题进行了研究，对CHIEF法及其改进方法作了进一步的改进，提出在加权余量意义下，通过把内部Helmholtz积分方程与其对内点坐标取导后的方程式作线性叠加，在域外构作的一个小体积块上进行积分以形成补充方程，经与表面Helmholtz积分方程相结合，来求解任意频率下的声辐射问题，并以脉动球和摆动球作为算例，说明本提出的方法能够有效地克服在特殊频率处解的非唯一性问题。

Overcoming the non-uniqueness of solution in the calculation of acousticradiation by a vibrating body with a further improved boundaryelement method

A study is presented of the calculation of the acoustic radiation by the vi-brating body, based on the boundary element method using cubic B-spline interpolatingfunction. As a furthur improvement of the CHIEF method, we suggest in this paper tolinearly combine the interior Helmholtz integral equation with its derivatives with re-spect to the coordinates in a weighted residual sense over a small interior region to forman extra equation, in order to solve the acoustic radiation problems at any frequencywith the boundary Helmhotz integral equations. Taking pulsating sphere and oscillatingsphere as examples, it's verified that the method put forward in this paper can effectivelyovercome the non-uniqueness problem.