Yuan Liu


1.  What interested you in the doctoral program in Applied and Computational Mathematics and Statistics at Notre Dame?

I was a master's student in numerical analysis and scientific computing before I came to the University of Notre Dame. I knew I wanted to continue my studies in this area, as well as some application with it. The ACMS PhD program is such a program, providing me with an excellent opportunity. One of my advisors, Professor Yongtao Zhang, is an expert in designing high order numerical methods for partial differential equations. My other advisor, Professor Mark Alber, is an expert in computational biology, with many collaborators at various medical schools.

2.  Tell us about your doctoral thesis.

There were two topics in my thesis work. One was about high order finite volume WENO schemes on unstructured mesh. We designed an algorithm for solving hyperbolic conservation law on the irregular domains which may not be partitioned by 'good' meshes. The other topic was about computational biology, including three projects, zebrafish dorsal-ventral patterning, tumor growth problem and blood vessel formation.