You've reached the website of James Lai. I am currently a fourth year Ph.D. candidate in computer science at the University of Illinois at Urbana-Champaign. I am part of the scientific computing group and I work with Professor Luke Olson. This past summer I interned at Sandia National Labs where I worked with Dr. Pavel Bochev on discontinuous least squares finite elements.

My research is concerned with the numerical solution of partial differential equations. In particular, I work on least squares finite element methods. I also work on efficient iterative methods for solving linear systems.

Academic info

I spent my undergraduate years at Columbia University where I studied computer science. I graduated in 2007. Since then I've been studying for my Ph.D. in Illinois. [CV]

Publications

• J. Lai and L. Olson. Multigrid for high-order interpolatory H(curl) conforming finite elements. Numerical Linear Algebra with Applications, 2011. Submitted.
• P. Bochev, J. Lai and L. Olson. A locally conservative, discontinuous least-squares finite element method for the Stokes equations. International Journal for Numerical Methods in Fluids, 2010. [preprint]
• J. Lai, P. Bochev, L. Olson, K. Peterson, D. Ridzal and C. Siefert. A discontinuous velocity least squares finite element method for the Stokes equations with improved mass conservation. In CSRI Summer Proceedings 2010, Sandia National Laboratories, 2010.
  
• J. Lai and L. Olson. Algebraic multigrid for high-order hierarchical H(curl) finite elements. SIAM Journal on Scientific Computing, 2010. To appear.
  

Conference presentations

• High-order interpolatory bases for compatible finite elements and efficient solvers. 15th Copper Mountain Conference on Multigrid Methods. March 2011. Copper Mountain, CO.
  
• Smoothers for high order H(curl) bases. SIAM Conference on Computational Science and Engineering. March 2011. Reno, NV.
  
• A locally conservative, discontinuous least-squares finite element method for the Stokes equations. SIAM Conference on Computational Science and Engineering. March 2011. Reno, NV.
  
• Algebraic multigrid for high order hierarchical H(curl) finite elements. 11th Copper Mountain Conference on Iterative Methods. April 2010. Copper Mountain, CO.
  

Teaching

Illinois

• CS 257: Numerical methods 1
  
• CS 273: Theory of computation
  
• CS 450: Introduction to numerical analysis
  
• CS 556: Iterative and multigrid methods (guest lecturer)
  

• CS 3137: Data structures and algorithms
  
• CS 3251: Computational linear algebra
  
• CS 4241: Numerical algorithms and complexity
  
• CS 4281: Introduction to quantum computing