Parallel domain decomposition based one-shot methods for shape optimization problems
Prof. Rongliang ChenShenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, China 上午 10:00–11:30 鴻經館 107 室Abstract:
In this talk , I will introduce a parallel domain decomposition method for general shape optimization problems constrained by the incompressible Navier–Stokes equations. The optimization problem is first discretized with a finite element method on an unstructured moving mesh that is implicitly defined without assuming that the computational domain is known and then solved by some one-shot Lagrange–Newton–Krylov–Schwarz algorithms. In this approach, the shape of the domain, its corresponding finite element mesh, the flow fields and their corresponding Lagrange multipliers are all obtained computationally in a single solve of a nonlinear system of equations.
Highly scalable parallel algorithms are absolutely necessary to solve such an expensive system. Aiming for machines with a large number of processors and robust nonlinear convergence, we introduce a two-level inexact Newton method with a hybrid two-level overlapping Schwarz preconditioner for shape optimization problems. As applications, we consider the shape optimization of a cannula problem and an artery bypass problem in 2D. Numerical experiments show that our algorithm performs well on a supercomputer with over 1000 processors for problems with millions of unknowns.