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数学学院、所2019年系列学术活动(第150场):赖明治教授 台湾交通大学

发表于: 2019-08-29 09:28  点击:

报告题目:An energy stable projection method for the inextensible interface problem with bending

报 告 人:赖明治教授 台湾交通大学

报告时间:93日上午10:00-1100

报告地点:数学楼一楼第二报告厅

报告摘要:

In this talk, we first introduce an unconditionally energy stable scheme to solve the inextensible interface problem with bending arising from vesicle dynamics in fluid flows.  The fundamental problem is formulated by the immersed boundary method where the non-stationary Stokes equations are considered, with the elastic tension and bending forces expressed in terms of Dirac delta function along the interface. The elastic tension is one of the solution variables and plays the role of Lagrange multiplier to enforce the inextensibility of the interface. The scheme uses a semi-implicit discretization for the non-stationary Stokes part and it is time-lagged for the interface position so that the whole scheme becomes linear.  Meanwhile, this time-lagging technique can be used to prove that the proposed immersed boundary scheme is unconditionally energy stable.  Furthermore, an efficient immersed boundary projection method based on the scheme is developed so that the whole numerical algorithm takes only a linearithmic complexity by using preconditioned GMRES and FFT-based solvers.

报告人简介:

赖明治,台湾交通大学讲座教授,台湾交通大学智能科学暨绿能学院合聘教授,台湾工业与应用数学会理事长,曾担任SIAM东亚分会(EASIAM)主席,香港浸会大学访问教授,日本京都大学数理解析所访问教授。赖教授于台湾中兴大学应用数学系获学士学位,台湾清华大学应用数学系获硕士学位,纽约大学库朗数学学院获博士学位。赖教授致力于偏微分方程的数值方法与计算流体力学等领域的研究,特别是内嵌边界/界面问题(immersed boundary/interface problem)数值方法的改善与Possion方程在非直角坐标系统的快速算法及研究,已在 SIAM Journal on Numerical Analysis, SIAM Journal on Scientific Computing, Journal of Computational Physics等国际著名杂志发表论文60余篇。