Gradient-based shape optimizations for 3-D transient acoustics with using the fast boundary element method

While it will play a role as a cornerstone of next-generation AI-driven optimization, I believe that gradient-based shape optimization will still be useful in its own right. When considering its application to transient acoustic problems such as noise and impulsive sounds, I have been engaged in research into the sophistication, especially the acceleration, of the boundary element method (BEM), which can treat infinite domains as its basic analysis object. Based on the time-domain fast boundary element method that I developed, I have been researching robust shape optimization methods for transient acoustic scattering problems. I derived the gradient, or shape derivative, of the objective function that is the basis of the method, and numerically implemented shape optimization for scatterers represented by NURBS patches. Most recently, I developed a gradient-based shape optimization method for the wave equation with damping. In this talk, I will describe the methodology and numerical results that I have obtained so far.