Title: Immersed Finite Element Methods and The Applications in Interface Inverse Problems
Speaker: Ruchi Guo (Ohio State University)
Abstract: Interface problems and the related inverse problems widely appear in many engineering applications. These problems in general involve multiple materials coupled through interfaces which cause challenges to numerical methods. The basic idea of immersed finite element (IFE) methods is to solve interface problems on unfitted meshes which circumvents the burden of mesh regeneration. In this talk, I will firstly review our recent works on developing and analyzing IFE methods to solve various interface problems on unfitted meshes. Then I will describe a parameterized shape optimization algorithm based on IFE methods to solve a group of interface inverse problems including electrical impedance tomography (EIT) and elastography. A set of numerical experiments are shown to demonstrate the strength and versatility of the proposed method.
Seminar URL: https://people.math.osu.edu/xing.205/seminar.html
