Math Modeling Seminar: Regularization of the Factorization Method with Applications

Math Modeling Seminar
Regularization of the Factorization Method with Applications

Dr. Isaac Harris
Assistant Professor
Department of Mathematics
Purdue University

You may attend this lecture in person at 2300 Gosnell Hall or virtually via Zoom.
If you’d like to attend virtually, you may register here for Zoom link.

Abstract:
In this talk, we discuss a new regularized version of the Factorization Method. The Factorization Method uses Picard’s Criteria to define an indicator function to image an unknown region. In most applications, the data operator is compact which gives that the singular values can tend to zero rapidly which can cause numerical instabilities. The regularization of the Factorization Method presented here seeks to avoid the numerical instabilities in applying Picard’s Criteria. This method allows one to image the interior structure of an object with little a priori information in a computationally simple and analytically rigorous way. Here we will focus on an application of this method to diffuse optical tomography which will prove that this method can be used to recover an unknown subregion from the Dirichlet-to-Neumann mapping.

Speaker Bio:
As an undergraduate, my favorite class was Differential Equations. One of the things that fascinated me about the class was how different areas of mathematics came together to solve interesting problems. Ideas from Calculus and Linear Algebra were no longer separate entities but part of something bigger. Being able to study different applications of mathematics as a McNair Scholar help me cultivate my interest in mathematics. After graduating from the University of Delaware I was a postdoc at Texas A&M university then I joined Purdue’s Mathematics Department in Fall 2018 as an Assistant Professor. This was an exciting prospect where I could join a department with extremely talented mathematicians from many different fields.

Intended Audience:
Undergraduates, graduates, and experts. Those with interest in the topic.

The Math Modeling Seminar will recur each week throughout the semester on the same day and time. Find out more about upcoming speakers on the Mathematical Modeling Seminar Series webpage.
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