题    目：Efficient and stable methods for computing partition problems

主讲人：王东 助理教授

单    位：香港中文大学（深圳）

时    间：2024年9月28日 16:00

地    点：数学与统计学院二楼会议室

摘    要：A Dirichlet k-partition of a domain is a collection of k pairwise disjoint open subsets such that the sum of their first Laplace--Dirichlet eigenvalues is minimal. In this talk, we propose a new relaxation of the problem by introducing auxiliary indicator functions of domains and develop a simple and efficient diffusion generated method to compute Dirichlet k-partitions for arbitrary domains. The method only alternates three steps: 1. convolution, 2. thresholding, and 3. projection. The method is simple, easy to implement, insensitive to initial guesses and can be effectively applied to arbitrary domains without any special discretization. At each iteration, the computational complexity is linear in the discretization of the computational domain. Moreover, we theoretically prove the energy decaying property of the method. Experiments are performed to show the accuracy of approximation, efficiency and unconditional stability of the algorithm. We will also extend the method for spectral classification problems and introduce deep learning based algorithms for these problems.

简    介：王东，国家优青和深圳市优青, 香港中文大学（深圳）助理教授，校长青年学者。于2013年在四川大学获得数学学士学位，于2017年在香港科技大学获得计算数学博士学位，2017-2020任犹他大学数学系助理教授讲师，主要从事材料、图像、拓扑优化等一系列实际应用问题的数学建模，高性能算法设计及相关理论等问题的研究。目前，已发表应用数学领域权威期刊(如Math Comp，SIAM系列，J. Comput. Phys.等)30余篇。曾入选中国工业与应用数学学会青年托举工程项目，获香港数学学会最佳博士论文奖、东亚工业与应用数学学会最佳论文等。（邀请人: 庞志峰）