Computing Skills

• Operating Systems:  UNIX/Linux, Windows.
• Programming Languages:  Fortran77/90, C/C++, Java, Matlab.
• Parallel Environments:  MPI, PVM, OpenMP.

Grant Support

• Department of Energy, DE-FG02-07ER64431, PI, 2007/7-2011/7.
• National Science Foundation, DMS-0609575, PI, 2006/8-2009/7.
• USC Research Foundation, RPS-13060-06-12306, PI, 2006/4-2007/6.

Publications

• ``Parallel implementation of a pressure-correction projection method for the unsteady incompressible Navier-Stokes equations'', Mathematica Numerica Sinica, Vol. 20, pp. 325-336, 1998; with L.B. Zhang.
• ``Probabilistic methods for centroidal Voronoi tessellations and their parallel implementations'', Parallel Computing, Vol. 28, pp. 1477-1500, 2002; with Q. Du and M. Gunzburger.
• ``Meshfree, probabilistic determination of point sets and support regions for meshless computing'', Computer Methods in Applied Mechanics and Engineering, Vol. 191, pp. 1349-1366, 2002; with Q. Du and M. Gunzburger.
• ``A numerical method for controllability problems for the wave equation'', Hyperbolic Problems: Theory, Numerics, Applications, Pasadena, March, pp. 557-568, 2002; with M. Gunzburger and L.S. Hou.
• ``Comparing the performance of MPICH with Cray's MPI and with SGI's MPI'', Concurrency and Computation: Practice and Experience, Vol. 15, pp. 779-802, 2003; with G. Luecke and M. Kraeva.
• ``Constrained centroidal Voronoi tessellations for surfaces'', SIAM Journal on Scientific Computing, Vol. 24, pp. 1488-1506, 2003; with Q. Du and M. Gunzburger.
• ``Approximation of exact boundary controllability problems for the 1-D wave equation by optimization based methods'', Contemporary Mathematics, Vol. 330, pp. 133-153, 2003; with M. Gunzburger and L.S. Hou.
• ``Voronoi-based finite volume methods, optimal Voronoi meshes, and PDEs on the sphere'', Computer Methods in Applied Mechanics and Engineering, Vol. 192, pp. 3933-3957, 2003; with Q. Du and M. Gunzburger.
• ``Cortical surface flattening using least square conformal mapping with minimal metric distortion'', Proceedings of International Symposium on Biomedical Imaging 2004, pp. 77-80, Arlington, April, 2004; with D. Rottenberg and et al..
• ``Numerical simulations of the quantized vortices in a thin superconducting hollow sphere'', Journal of Computational Physics, Vol. 201, pp. 511-530, 2004; with Q. Du.
• ``Approximations of a Ginzburg-Landau model for superconducting hollow spheres based on spherical centroidal Voronoi tessellations'', Mathematics of Computation, Vol. 74, pp. 1257-1280, 2005; with Q. Du.
• ``Finite volume methods on spheres and spherical centroidal Voronoi meshes'', SIAM Journal on Numerical Analysis, Vol. 43, pp. 1673-1692, 2005; with Q. Du.
• ``Quantitative evaluation of three cortical surface flattening methods'', Neuroimage, Vol. 28, pp. 869-880, 2005; with D. Rottenberg and et al..
• ``Convergence of the Lloyd algorithm for computing centroidal Voronoi tessellations'', SIAM Journal on Numerical Analysis, Vol. 44, pp. 102-119, 2006; with Q. Du and M. Emelianenko.
• ``Centroidal Voronoi tessellation algorithms for image compression, segmentation, and multichannel restoration'', Journal of Mathematical Imaging and Vision, Vol. 24, pp. 177-194, 2006; with Q. Du, M. Gunzburger and X. Wang.
• ``A numerical method for exact boundary controllability problems for the 2-D wave equation'', Computer & Mathematics with Applications, Vol. 51, pp. 721-750, 2006; with M. Gunzburger and L.S. Hou.
• ``Adaptive finite element methods for elliptic PDEs based on conforming centroidal Voronoi Delaunay triangulations'', SIAM Journal on Scientific Computing, Vol. 28, pp. 2023-2053, 2006; with M. Gunzburger and W.-D. Zhao.
• ``Conforming centroidal Voronoi Delaunay triangulation for quality mesh generation'', International Journal of Numerical Analysis and Modeling, Vol. 4, pp. 531-547, 2007.
• ``Numerical simulations of the steady Navier-Stokes equations using adaptive meshing schemes'', International Journal for Numerical Methods in Fluids, Vol. 56, pp. 703-721, 2008; with H.-C. Lee and L. Tian.
• ``Nondegeneracy and weak global convergence of the Lloyd algorithm in R^d'', SIAM Journal on Numerical Analysis, Vol. 46, pp. 1423-1441, 2008; with M. Emelianenko and A. Rand.
• ``Convergence analysis of a splitting method for stochastic differential equations'', International Journal of Numerical Analysis and Modeling, Vol. 5, pp. 673-692, 2008; with W.D. Zhao and L. Tian.
• ``Effects of director angle anchoring conditions on the dynamic moduli of heterogeneous nematic polymers", Proceedings of the XVth International Congress on Rheology, pp. 481-483, 2008; with E. Choate, M. Gorrest and Z. Cui.
• ``Analysis of a mixed finite-volume discretization for fourth-order equations on general surfaces'', IMA Journal of Numerical Analysis, doi: 10.1093/imanum/drn021, 2008; with Q. Du and L. Tian.
• ``Constrained CVT meshes and a comparison of triangular mesh generators'', Computational Geometry: Theory and Applications, to appear; with H. Nguyen, J. Burkardt, M. Gunzburger and Yuki Saka.
• ``Adaptive finite volume vethods for steady convection-diffusion equations with mesh optimization'', Discrete and Continuous Dynamical Systems B, to appear; with W. Wu and W.-D. Zhao.
• ``A finite volume method on general surfaces and its error estimates'', submitted; with Qiang Du. [pdf]
• ``Open-surface shape correspondenceby identifying topologically consistent landmarks'', submitted; with S. Wang and et. al..
• ``A posteriori error estimates for finite volume approximation of elliptic equations on general surfaces'', submiited; with L. Tian and D. Wang. [pdf]
• ``A multi-resolution method for climate system modeling'', submitted; with T. Ringler and M. Gunzburger. [pdf]
• ``Adaptive anisotropic meshing for steady convection-dominated problems'', submitted; with H. Nguyen, J. Burkardt and M. Gunzburger. [pdf]
• ``Finite element approximation of a continuum model of phase transition on surfaces", preprint; with Q. Du and L. Tian.