Ping Lin, Professor, University of Dundee

于海军 研究员

Phase-field models, energy stable schemes and error analysis for a tumour-nutrient interaction of tumour growth and for a transmembrane transport of species and reaction at the interface

6月5日（周五）10:30-11:30， 南楼202

We will first introduce our method to develop thermodynamically consistent phase-field models and then extend it to build a phase-field model for tumour growth that takes into account nutrient consumption and chemotaxis. For this tumour growth model described by a nonlinear system consisting of a Cahn--Hilliard-type equation coupled with a reaction-diffusion equation, we constructed an efficient scheme based on the idea of the scalar auxiliary variable (SAV), which we show are not only decoupled, but also having the properties of mass conservation and unconditional energy stability. We will also mention rigorous error estimates for the fully discrete finite element scheme. Several numerical examples are presented to validate the accuracy, mass conservation and energy dissipation of the proposed scheme, and to illustrate complex biological phenomena, including the aggregation of multiple tumours of varying shapes and chemotaxis-driven growth patterns. Furthermore, we extend the modelling idea to a much more difficult problem - transmembrane transport of species and reaction at the interface. A real application of this is the formation of retina microaneurysms. We will show how to derive the thermodynamically consistent phase-field model, to design a simple first order energy stable scheme and to rigorously analyse its error for a simplified illustrative case. Several numerical examples are presented to validate the accuracy, mass conservation and energy dissipation of the designed scheme, and to illustrate the model properties and formation of microaneurysms. The talk is based on a few joint papers with Z Wang and J Yang, with A Soenjaya and T Tran, and with Z Wang, H Huang and S Xu.

报告人简介：林平，本科、硕士均毕业于南京大学数学系。1995年获加拿大不列颠哥伦比亚大学应用数学博士学位。1996年在美国斯坦福大学应用力学与计算机系做博士后研究，1998年秋在伦斯勒理工大学短期访问后开始担任新加坡国立大学数学系助理教授，后升为副教授、教授，2007年开始担任英国邓迪大学数值分析和计算数学教授（chair of numerical analysis）。主要从事偏微分方程建模、数值方法设计与分析，以及应用数学和科学工程计算等交叉学科研究 。目前的应用研究主要集中在多相流、非牛顿流体、多尺度问题、流体管壁作用、图像处理、和一些生物、医疗中的建模计算问题。