课程名称: Introduction to Shape and Topology Optimization
主讲人：Jan Sokolowski教授（洛林大学 & 波兰科学院）
时间：（1）4月16日 (周一), 4月18日(周三), 4月20日 (周五),4月23日（周一）
下午14:00—16:30
（2）4月24日（周二）上午9:00-11:30 地点：闵行数学楼402报告厅

摘要
The shape optimization problems for elliptic boundary value problems will be considered. There are two methods of shape sensitivity analysis: the velocity method described in the monograph [1] and the topological derivative method in [2].

We introduce both methods for elementary examples. The advanced applications of the first method are given in the monograph [3], where the compressible Navier-Stokes equations with nonhomogeneous boundary conditions are considered from the point of view of weak solutions. This will be a subject of a research seminar.

We will discuss in details the first and the second order shape derivatives of the shape functionals and the first order topological derivatives. The students should know the framework of weak solutions to elliptic boundary value problems in the Sobolev spaces as well as the calculus of variations in function spaces.

Reference Books：
[1] J. Sokolowski and J.-P. Zolesio, Introduction to shape optimization. Shape sensitivity analysis. Springer Series in Computational Mathematics, 16, Springer-Verlag, Berlin, 1992.
[2] A. Novotny and J. Sokolowski, Topological derivatives in shape optimization. Interaction of Mechanics and Mathematics. Springer, Heidelberg, 2013.
[3] P. Plotnikov and J. Sokolowski, Compressible Navier-Stokes equations. Theory and shape optimization. Mathematics Institute of the Polish Academy of Sciences. Birkhäuser/Springer Basel AG, Basel, 2012.

华东师范大学数学科学学院
上海市核心数学与实践重点实验室