Chebyshev谱方法在声散射数值计算中的应用

基于声学边界元基本理论,并结合Chebyshev谱方法进行了声散射数值计算研究.采用2阶边界单元,谱点离散选用不包含边界的CG(Chebyshev-Gauss)配点法,克服了传统边界元在表面单元节点处出现的法向及法向导数不连续的现象;应用CHIEF(Combined Helmholtz Integral Equation Fomulation)方法进行了数值非唯一性处理,提高了计算的精度.与传统边界元方法进行了精度和效率的对比分析,证明该方法具有计算快速、精度高的特点.

Application of chebyshev spectral boundary element method to acoustic scattering computation

On the basis of boundary element theory, combined with Chebyshev spectral element method, acoustic scattering numerical computation was studied. The second order boundary element was used in the computation of acoustic scattering field.  Chebyshev-Gauss, a spectral collocation point method, was used to realize the whole process in which spectral point were dispersed. As a result, this method overcame some shortcomings of traditional ones such as the discontinuity of normal direction and normal derivative that appeared on the nodes of surface element. With the application of a combined Helmholtz integral equation formulation (CHIEF), numerical non-uniqueness was solved and the computational accuracy and efficiency would be improved. Therefore, the new method advantage such as fast computation and high accuracy are drawn through the comparison and analysis with the traditional method.