报告题目：An Efficient Unconditionally Stable Method for Dirichlet Partitions in Arbitrary Domains

报告时间：2021-12-16  15:00-16:30

报告人：王东 助理教授 香港中文大学(深圳)

腾讯会议ID：345 773 4983 会议密码：174675

Abstract：ADirichletk-partition of a domain is a collection of k pairwise disjoint open subsets such that the sum of their first Laplace--Dirichleteigenvalues 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 Dirichletk-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 apply the proposed algorithms on both 2- and 3-dimensional flat tori, triangle, square, pentagon, hexagon, disk, three-fold star, five-fold star, cube, ball, and tetrahedron domains to compute Dirichletk-partitions for different k to show the effectiveness of the proposed method. Compared to previous work with reported computational time, the proposed method achieves hundreds of times acceleration.