弗吉尼亚理工大学林涛教授将于6月12日-13日来我中心作学术报告。
报告题目：Application of Immersed Finite Elements to Interface Inverse Problems
报告时间：2019年6月13日，星期四，下午2:30—4:00
报告地点：数学楼112
报告摘要:
This talk is about shape optimization algorithms based on immersed finite elements for solving some interface inverse problems with fixed meshes. We consider an interface forward problem modeling a certain physics in a domain formed with different materials; hence, the coefficients in the partial differential equation of this forward problem are usually discontinuous across the interface separating the materials. An interface inverse problem associated with this forward problem is to use some measurements about the solution of the underlying forward problem, either on the boundary and/or in the interior of the domain, to determine the material interface. We formulate the interface inverse problem as a shape optimization problem whose objective functional depends on the interface. Both the governing partial differential equation and objective functional are discretized accurately by an immersed finite element (IFE) method on a fixed mesh independent of the interface varying in the shape optimization. Formulas for the shape sensitivities of the discretized objective function are derived within the IFE framework that can be computed accurately and efficiently through the discretized adjoint method. We demonstrate features of the IFE-based shape optimization algorithms by a group of representative interface inverse/design problems.
报告人简介：
林涛教授1990年在怀俄明大学取得博士学位，1989年至今在弗吉尼亚理工大学工作，2001年起担任数学系教授。他的研究兴趣涉及偏微分方程和积分微分方程的数值求解方法，尤其是在界面问题的浸入式有限元方法及其应用方面取得了开创性的研究成果。林涛教授是计算数学和数值科学方面的专家，在计算数学一流期刊上有超过80篇文章发表，他引超过1200次。
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