3507 流れ場のトポロジー最適化においてニュートン法を用いることによる収束性の向上とグレースケール問題の回避(OS3-9 設計と最適化IX)

抄録

We propose a fluid topology optimization method using a Newton-gradient-hybrid scheme. The method converges in small computation time. In addition, the boundary between fluid and solid region is clearly distinguished. In the method, the domain is updated concurrently with solving a flow field. The flow field is solved by the lattice Boltzmann method (LBM). Due to the formulation of LBM and the optimization algorithm, the Hessian matrix is a diagonal matrix. The Hessian matrix is not generally positive semidefinite since the flow topology optimization problem is a nonconvex problem. Hence, we employ a Newton method for positive definite part of the Hessian marix, and employ a gradient method for negative semidefinite part.