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Acoustic topology optimization of porous material distribution based on an adjoint variable FMBEM sensitivity analysis

机译：基于伴随变量FMBEM敏感性分析的多孔材料分布声学优化

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We develop an acoustic topology optimization approach in this work for the surface design of structures covered by porous materials. The fast multipole boundary element method (FMBEM) is employed for the sound scattering analysis. The acoustic absorption characteristics of porous materials are numerically modeled using the Delany-Bazley-Miki empirical model. Based on the solid isotropic material with penalization (SIMP) method, the optimization is performed by setting the artificial element densities of porous material as the design variables, minimizing the sound pressure or the dissipated sound power as the design objective. As a key treatment in this study, we develop a fast sensitivity analysis approach based on an adjoint variable method (AVM) and the fast multipole method (FMM) to calculate the sensitivities of the objective function with respect to a large number of design variables. The FMM is applied to accelerate the vector-matrix product required by the AVM. According to the gradient information, the method of moving asymptotes (MMA) is used for solving the optimization problem to find the optimal solution. We validate the proposed topology optimization approach through numerical examples of acoustic scattering over a single cylinder and multi cylinders, and demonstrate its ability to handle large-scale problems.
机译：我们在这项工作中开发了声学拓扑优化方法，用于多孔材料覆盖的结构表面设计。快速的多极边界元法（FMBEM）用于声音散射分析。多孔材料的声学吸收特性使用Delany-Bazley-Miki实证模型进行数值模拟。基于抗损失（SIMP）方法的固体各向同性材料，通过将多孔材料的人工元素密度设定为设计变量来进行优化，最小化声压或耗散的声音作为设计目标。作为本研究的关键待遇，我们基于伴随变量方法（AVM）和快速多极方法（FMM）来开发快速灵敏度分析方法，以计算关于大量设计变量的目标函数的灵敏度。 FMM应用于加速AVM所需的载体矩阵产品。根据梯度信息，移动渐近的方法（MMA）用于解决优化问题以找到最佳解决方案。我们通过单缸和多缸上的声学散射的数值示例验证所提出的拓扑优化方法，并展示其处理大规模问题的能力。

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