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 引用本文: 李珺璞, 陈文. 一种模拟大规模高频声场的双层奇异边界法[J]. 力学学报, 2018, 50(4): 961-969.
Li Junpu, Chen Wen. A DUAL-LEVEL SINGULAR BOUNDARY METHOD FOR LARGE-SCALE HIGH FREQUENCY SOUND FIELD ANALYSIS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(4): 961-969.
 Citation: Li Junpu, Chen Wen. A DUAL-LEVEL SINGULAR BOUNDARY METHOD FOR LARGE-SCALE HIGH FREQUENCY SOUND FIELD ANALYSIS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(4): 961-969.

## A DUAL-LEVEL SINGULAR BOUNDARY METHOD FOR LARGE-SCALE HIGH FREQUENCY SOUND FIELD ANALYSIS

• 摘要: 大规模高频声场的数值模拟是一项非常有计算挑战性的课题. 为了解决传统边界型离散方法由于全局支撑的满阵限制, 不易应用于大规模高频声场模拟的计算瓶颈, 本文提出了一种用于模拟大规模高频声场的双层奇异边界法. 在该方法中, 通过引入双层结构, 细网格上的全局支撑的满阵被转化为局部支撑的大规模稀疏矩阵, 传统奇异边界法模拟大规模问题时所面临的高计算量以及过度存储需求遂得以解决. 其次, 双层奇异边界法仅通过粗网格评估远场作用, 且独立于特定的插值核函数. 相较于快速多级方法, 该方法具有更强的适应性和灵活性, 且多层结构使该方法具有一定的预调节作用, 非常适合求解具有大规模、高秩、高条件数特点的高频波矩阵. 在其后的散射球模型算例中, 双层奇异边界法配置10万个节点, 成功模拟了无量纲波数高达160的声散射问题. 在对于人头模型的声散射特性分析中, 双层奇异边界法比COMSOL软件计算速度快了约78.13$\mathrm{%}$. 当配置8万个节点时, 双层奇异边界法成功模拟了频率高达25 kHz 的工况, 该频率已远远超出了人耳的听力极限.

Abstract: Numerical simulation of the large-scale high frequency sound field is a computational challenging task. To solve the difficulty that the traditional boundary collocation methods are not easy to be applied to large-scale problems thanks to the resulting large-scale fully-populated matrix, a dual-level singular boundary method is proposed in this study. By introducing a dual level structure, the fully-populated matrix is transformed to a large-scale locally supported sparse matrix on fine mesh. The bottleneck of excessive storage requirements and a large number of operations encountered by the traditional singular boundary method is hereby avoided. Secondly, the method uses only coarse mesh nodes to evaluate far-field contributions, and it is a kernel-independent algorithm. In comparison with the fast multipole method, the dual-level singular boundary method performs higher adaptability and flexibility. In addition, the dual level structure plays a role of preconditioner, which makes the method is very efficient for solving matrix with large scale, high rank and high condition number. In scattering sphere example, the dual-level singular boundary method simulates well the acoustic scattering problem with up to dimensionless wavenumber of 160 when the number of degrees of freedom is taken as 100 000. In the benchmark human head sound scattering, the dual-level singular boundary method using 80 000 degrees of freedom performs 78.13% faster than the COMSOL, and it is noted that the computational frequency is up to 25 kHz, which is far beyond the limit of hearing of human ear.

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