Zhiliang Xu

Applied and Computational Mathematics and Statistics Department
170 Hurley Hall
Notre Dame, IN 46556 
Phone: (574)631-3423
E-mail: zxu2@nd.edu

Course Materials
Fall 2016
Past Courses (All courses are moved to Sakai)
Spring 2016
Fall 2015
Spring 2015
Blood clot project
Research Codes for Download

Research Interests

I am broadly interested in computational and applied mathematics. My recent research interests include:
  • developing high-order accurate numerical schemes for solving partial differential equations;
  • scientific computing;
  • mathematical modeling;
  • and machine learning.

I am currently working on:
  • developing discontinuous Galerkin finite element methods, finite volume methods and finite element methods for solving PDEs (e.g., Euler equations, Navier-Stokes equations, MHD equations and Cahn-Hilliard equation), and PDEs on manifold;
  • developing numerical methods for solving fluid-structure interaction problems;
  • developing discrete and continuous models and multiscale models for problems arising from physics and biology, e.g., blood thrombus (clot) formation, blood cell dynamics, bio-gel, and bacterial swarming;
  • developing thermodynamically consistent phase-field models for multiphase fluid flow;
  • and developing neural-network-based methods for solving PDEs.
  • Clot (geomview files)

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Zhiliang Xu ( zxu2@nd.edu )