Publications

1. ``Voronoi diagrams and their application to climate and global modeling'', Lecture Notes in Computational Science and Engineering, Vol. 80, Numerical Techniques for Global Atmospheric Models, pp. 313-342, Springer, 2011; with T. Ringler and M. Gunzburger.

1. ``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.
2. ``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.
3. ``A numerical method for controllability problems for the wave equation'', Proceedings of the Ninth International Conference on Hyperbolic Problems, Pasadena, March, pp. 557-568, 2002; with M. Gunzburger and L.S. Hou.
4. ``Probabilistic methods for centroidal Voronoi tessellations and their parallel implementations'', Parallel Computing, Vol. 28, pp. 1477-1500, 2002; with Q. Du and M. Gunzburger.
5. ``Constrained centroidal Voronoi tessellations for surfaces'', SIAM Journal on Scientific Computing, Vol. 24, pp. 1488-1506, 2003; with Q. Du and M. Gunzburger.
6. ``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.
7. ``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.
8. ``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.
9. ``Cortical surface flattening using least square conformal mapping with minimal metric distortion'', Proceedings of the Second IEEE International Symposium on Biomedical Imaging (ISBI'2004), pp. 77-80, Arlington, VA, April, 2004; with D. Rottenberg and et al..
10. ``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.
11. ``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.
12. ``Finite volume methods on spheres and spherical centroidal Voronoi meshes'', SIAM Journal on Numerical Analysis, Vol. 43, pp. 1673-1692, 2005; with Q. Du.
13. ``Quantitative evaluation of three cortical surface flattening methods'', Neuroimage, Vol. 28, pp. 869-880, 2005; with D. Rottenberg and et al..
14. ``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.
15. ``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.
16. ``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.
17. ``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.
18. ``Conforming centroidal Voronoi Delaunay triangulation for quality mesh generation'', International Journal of Numerical Analysis and Modeling, Vol. 4, pp. 531-547, 2007.
19. ``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.
20. ``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.
21. ``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, Monterey, CA, August, 2008; with E. Choate, M. Gorrest and Z. Cui.
22. ``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.
23. ``A multi-resolution method for climate system modeling'', Ocean Dynamics, Vol. 58, pp. 475-498, 2008; with T. Ringler and M. Gunzburger.
24. ``Constrained CVT meshes and a comparison of triangular mesh generators'', Computational Geometry: Theory and Applications, Vol. 42, pp. 1-19, 2009; with H. Nguyen, J. Burkardt, M. Gunzburger and Yuki Saka.
25. ``A finite volume method on general surfaces and its error estimates'', Journal of Mathematical Analysis and Applications, Vol. 352, pp. 645-668, 2009; with Qiang Du.
26. ``Analysis of a mixed finite-volume discretization for fourth-order equations on general surfaces'', IMA Journal of Numerical Analysis, Vol. 29, pp. 376-403, 2009; with Q. Du and L. Tian.
27. ``Adaptive finite volume methods for steady convection-diffusion equations with mesh optimization'', Discrete and Continuous Dynamical Systems B, Vol. 11, pp. 669-690, 2009; with W. Wu and W.-D. Zhao.
28. ``Adaptive anisotropic meshing for steady convection-dominated problems'', Computer Methods in Applied Mechanics and Engineering, Vol. 198, pp. 2964-2981, 2009; with H. Nguyen, J. Burkardt and M. Gunzburger.
29. ``An edge-weighted centroidal Voronoi tessellation model for image segmentation'', IEEE Transactions on Image Processing, Vol. 18, pp. 1844-1858, 2009; with J. Wang and X. Wang.
30. ``3D open-surface shape correspondence for statistical shape modeling: Identifying topologically consistent landmarks'', Proceedings of the Twelfth IEEE International Conference on Computer Vision (ICCV'2009), pp. 1857-1864, Kyoto, Japan, September-October, 2009; with P. Dahal, S. Wang and et al..
31. ``A posteriori error estimates for finite volume approximations of elliptic equations on general surfaces'', Computer Methods in Applied Mechanics and Engineering, Vol. 198, pp. 716-726, 2009; with L. Tian and D. Wang.
32. ``A variational phase field method for curve smoothing'', Journal of Computational Physics, Vol. 229, pp. 2390-2400, 2010; with L. Zhu, Y. Wang and D. Wang.
33. ``Advances in studies and applications of centroidal Voronoi tessellations'', Numerical Mathematics: Theory, Methods and Applications, Vol. 3, pp. 119-142, 2010; with Q. Du and M. Gunzburger.
34. ``Effects of strong anchoring on the dynamic moduli of heterogeneous nematic polymers II: Oblique anchoring angles'', Rheologica Acta, Vol. 49, pp. 335-347, 2010; with E. Choate and M. Forest.
35. ``A stable multi-step scheme for solving backward stochastic differential equations'', SIAM Journal on Numerical Analysis, Vol. 48, pp. 1369-1394, 2010; with W.-D. Zhao and G. Zhang.
36. ``A multichannel edge-weighted centroidal Voronoi tessellation algorithm for 3D super-alloy image segmentation'', Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR'2011), pp. 17-24, 2011; with Y. Cao and et al.. (Corresponging author)
37. ``Coupled models and parallel simulations for three dimensional full-Stokes ice sheet modeling'', Numerical Mathematics: Theory, Methods and Applications, Vol. 4, pp. 359-381, 2011; with H. Zhang and et al..
38. ``Finite element approximation of the Cahn-Hilliard equations on surfaces", Computer Methods in Applied Mechanics and Engineering, Vol. 200, pp. 2458-2470, 2011; with Q. Du and L. Tian.
39. ``Image segmentation using local variation and edge-weighted centroidal Voronoi tessellations'', IEEE Transactions on Image Processing, Vol. 20, pp. 3242-3256, 2011; with J. Wang and X. Wang.
40. ``Exploring a multi-resolution modeling approach within the shallow-water equations'', Monthly Weather Review, Vol. 139, pp. 3348-3368, 2011; with T. Ringler and et al..
41. ``A parallel high-order accurate finite element nonlinear Stokes ice sheet model and benchmark experiments'', Journal of Geophysical Research, Vol. 117, F01001 (24 pages), 2012; with W. Leng and et al.
42. ``A posteriori error analysis of finite element method for linear nonlocal diffusion and peridynamic models'', Mathematics of Computation, to appear; with Q. Du, L. Tian and K. Zhou.
43. ``Covolume-upwind finite volume approximations for linear elliptic partial differential equations'', Journal of Computational Physics, to appear; with X. Xiao, L. Tian, and W.-D. Zhao.
44. ``Grain segmentation in 3D superalloy images using multichannel EWCVT with human annotation constraints'', ECCV'2012, to appear; with Y. Cao and S. Wang.
45. ``Generalized edge-weighted centroidal Voronoi tessellations for geometry smoothing'', under revision; with Y. Wang, D. Wang and X. Wang.
46. ``Error estimates of the Crank-Nicolson scheme for solving backward stochastic differential equations'', submitted; with W.-D. Zhao and Y. Li.
47. ``Manufactured solutions for numerical verifications of isothermal, nonlinear, three-dimensional Stokes ice sheet models'', preprint; with W. Leng, M. Gunzburger and S. Price.
48. ``A numerical method and its error estimates for the decoupled forward-backward stochastic differential equations'', preprint; with W-D. Zhao and W. Zhang.

1. ``Probabilistic algorithms for determining non-uniformly distributed point sets and support'', Proceedings of the Sixth US National Congress on Computational Mechanics, pp. 21, Dearborn, MI, August 2001; with Q. Du and M. Gunzburger.
2. ``Cortical surface flattening using discrete conformal mapping with minimal metric distortion'', NeuroImage, Vol. 19, Supplement 1, Abstract 865, 2003; with D. Rottenberg and et al.
3. ``Evaluation of three cortical surface flattening methods'', NeuroImage, Vol. 22, Supplement 1, Abstract WE-207, 2004; with D. Rottenberg and et al.
4. ``ParcelMan and Pigment: interactive tools for parcellation of cortical grey matter'', NeuroImage, Vol. 22, Supplement 1, Abstract WE-287, 2004; with K. Rehm, D. Rottenberg and et al.
5. ``The dependence of the dynamic moduli on the director angle anchoring condition for heterogeneous nematic polymers'', Proceedings of the Ninth International Conference on Mathematical and Numerical Aspects of Waves Propagation, Pau, France, June 2009; with E. Choate and M. Forrest.