In this study, the Scaled Boundary Finite Element Method (SBFEM) was used to perform analyses and evaluate the objective function in shape optimization of devices relying on acoustic wave propagation. Similar to the Boundary Element Method (BEM), the SBFEM requires only the discretization of the boundary of the computational domain. However, unlike BEM, there is no need for a fundamental solution; thus, the SBFEM provides a flexibility similar to that of the Finite Element Method (FEM). The dimension reduction is achieved by representing the solution analytically inside the domain and numerically on the boundary. Consequently, the SBFEM provides a flexible platform for shape optimization and alleviates the re-meshing difficulties encountered in FEM. It was shown that domain boundaries can be optimized with a minimum number of design variables, while the existing accurate transparent boundary conditions effectively eliminate the artificial numerical reflections for a wide range of frequencies.

在这项研究中，使用比例边界有限元方法（SBFEM）进行分析和评估目标函数在依赖声波传播的设备形状优化中。与边界元素方法（BEM）相似，SBFEM仅要求计算域边界的离散化。但是，与BEM不同，不需要基本解决方案。因此，SBFEM提供了类似于有限元方法（FEM）的灵活性。通过在域内和边界上以解析方式表示解决方案，可以实现降维。因此，SBFEM为形状优化提供了灵活的平台，并减轻了FEM中遇到的重新啮合困难。结果表明，可以使用最少数量的设计变量来优化域边界，