高速時間領域境界要素法を用いた3次元非定常音響問題に関する形状最適化

抄録

We are developing a numerical method to solve shape optimization problems for the 3D wave equation with the help of the time-domain boundary element method (TDBEM) and the adjoint variable method (AVM). The TDBEM is useful to handle the underlying scattering problems in free space, but its computational cost can be huge. To overcome this issue, we exploit the fast TDBEM proposed by Takahashi (2014), which exploits the interpolation-based fast multipole method. Regarding the AVM, we basically follow the formulation by Bonnet (2002) , but we discretize the shape derivative through the control points that are introduced by approximating the surface of a scatterer with NURBS surfaces. Since the fast TDBEM uses the conventional mesh, we convert a NURBS surface to a mesh and vice versa. In this talk, we will verify our shape optimization system by comparing a reference solution in a certain problem. Then, we will demonstrate a shape optimization to focus a transient sound at a prescribed point.