勷勤数学•专家报告

题      目：Topological optimization involving Stokes flows using Linear Algebra Tools

报  告  人：李治林 教授  (邀请人：彭小飞)

                                              North Carolina State University，USA

时      间：6月9日  10：30-11：30

地     点：数科院东楼401报告厅

报告人简介:

         李治林博士，北卡州立大学数学系教授。他在南京师范大学获得学士及硕士学位后进入美国华盛顿大学（西雅图）攻读博士学位，获得博士学位。他在加州大学洛杉矶分校曾任CAM/Hedrick教授，现为北卡州立大学教授。 李治林教授曾主持、参与多项研究项目。曾获得 Oak Ridge 联合大学杰青，波音讲座教授。法国马赛杰出访问教授。他先后发表高学术论文约200篇，培养20名博士研究生、多个硕士研究生和博士后。在著名出版社 SIAM, 剑桥发表三本专著和教课书，以及一系列专辑。

摘      要：

       A finite difference method based on the IIM-level set method for a topological optimization involving the Stokes flows is proposed. The method is fast because fast Poisson solvers for Stokes equations can be utilized with carefully chosen augmented variables and the GMRES iteration for the Schur complement of the augmented variables. 

The discretization of the PDE eventually becomes linear algebra problems. We discuss how to avoid forming large matrices and use only matrix-vector form to solve the Schur complement using the GMRES method. The method is validated through nontrivial solutions and benchmark examples in the literature. An exact solution of the topological  optimization is constructed, which is likely  to be the first of this type.

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