学术报告

题      目： Pattern formation on evolving domains and on rough surfaces

报  告  人：李思卿   博士  (邀请人：叶颀 )

                                 太原理工大学

时      间：2022-08-16 10:30-12:00

腾 讯 会 议：504 302 808

报告人简介:

       李思卿博士，太原理工大学大数据学院讲师，从事基于径向基核函数的方法求解偏微分方程数值解的研究。太原理工大学本科及硕士，硕士导师为李明教授；香港浸会大学数学系博士，导师为径向基函数研究专家凌立云教授；南方科技大学杰曼诺夫数学中心博士后，合作导师为汤涛院士；2021年入职于太原理工大学大数据学院任讲师。目前在国际期刊上发表论文7篇，并先后主持博士后面上项目一项，山西省应用基础研究计划青年科技研究基金一项。

摘      要：

       Turing-type reaction-diffusion systems on evolving domains and on rough surfaces are considered in this talk. For RDS on the evolving domain, the kernel-based collocation method is applied after transforming the PDE into the reference domain. A global refinement strategy is proposed to reduce the computational cost. The convergence behavior of the proposed algorithm and the effectiveness of the refinement strategy are verified.  For RDS on the rough surfaces, we consider periodic rough surfaces with analytic parametric equations. The amplitude of such surfaces is an important variable in the provided eigenvalue analysis for the Laplace-Beltrami operator. Simulations show that the patterns become irregular as the amplitude and frequency of the rough surface increase. To further generalize to solve RDS on closed manifolds, we propose another construction method of rough surfaces by using random nodal values and discretized heat filters. Numerical evidence shows that both surface constructions yield comparable patterns to those found in real-life animals.