Selected Publications:
- Houde Han and Xiaonan Wu,
Approximation of infinite boundary conditions and its application
to finite element methods,
J. Comp. Math., 3 (1985), 179-192.
- Houde Han and Xiaonan Wu,
The approximation of the exact boundary conditions at an artificial
boundary for linear elastic equations and its application,
Math. Comput., 59 (1992), 21-37.
- Xiaonan Wu and Youlan Zhu,
A highly accurate numerical method for two and three dimensional
shock reflection problems,
Comput. Fluids, 25 (1996), 295-317.
- R.A. Nicolaides and Xiaonan Wu,
Analysis and Convergence of the MAC Scheme 2. Navier-Stokes
equations,
Math. Comput., 65 (1996), 29-44.
- Xiaonan Wu, E.M. Cliff and M.D. Gunzburger,
An optimal design problem for a two dimensional flow in a duct,
Optim. Contr. Appl. Meth., 17 (1996), 329-339.
- Xiaonan Wu and Houde Han,
A finite element method for Laplace and Helmholtz type boundary
value problems with singularities,
SIAM J. Numer. Anal., 34 (1997), 1037-1050.
- R.A. Nicolaides and Xiaonan Wu,
Covolume Solution of Three Dimensional Div-Curl Equations,
SIAM J. Numer. Anal., 34 (1997), 2195-2203.
- Houde Han and Xiaonan Wu,
A new mixed finite element formulation and the MAC method for
the Stokes equations,
SIAM J. Numer. Anal., 35 (1998), 560-571.
- Q. Du, R.A. Nicolaides and Xiaonan Wu,
Analysis and convergence of a covolume approximation of the
Ginzburg-Landau model of superconductivity,
SIAM J. Numer. Anal., 35 (1998), 1049-1072.
- Q. Du and X. Wu,
Numerical Solution of the Three-Dimensional Ginzburg-Landau Model
Using Artificial Boundary,
SIAM J. Numer. Anal., 36 (1999), 1482-1506.
- X. Wu and C.Y. Cheung,
An Iteration Method Using Artificial Boundary for Some Elliptic
Boundary Value Problems with Singularities,
Int. J. Numer. Meth. Engng., 46 (1999), 1917-1931.
- H. Han, C. He and X. Wu,
Analysis of artificial boundary conditions for exterior boundary
value problems in three dimensions,
Numer. Math., 85 (2000), 367-386.
- Xiaonan Wu and Houde Han,
Discrete boundary conditions for problems with interface,
Comp. Meth. Appl. Mech. Eng., 190 (2001), 4987-4998.
- G.H. Golub, X. Wu and J.Y. Yuan,
SOR-like methods for augmented systems.
BIT, 41 (2001), 71-85.
- Xiaonan Wu and Youlan Zhu,
A highly accurate numerical method for flow problems with
interactions of discontinuities,
J. Comp. Math., 20 (2002), 1-14.
- Xiaonan Wu and Weimin Xue,
Discrete boundary conditions for elasticity problems with
singularities,
Comp. Meth. Appl. Mech. Eng., 192 (2003), 3777-3795.
- Houde Han and Xiaonan Wu,
A fast numerical method for Black-Scholes equations of American
options,
SIAM J. Numer. Anal., 41 (2003), 2081-2095.
- Xiaonan Wu and Zhi-zhong Sun,
Convergence of difference scheme for heat equation in
unbounded domains using artificial boundary conditions,
Appl. Numer. Math., 50 (2004), 261-277.
- Jicheng Jin and Xiaonan Wu,
The singular finite element method for some elliptic boundary
value problems with interface,
J. Comp. Appl. Math., 170 (2004), 197-216.
- You-lan Zhu, Xiaonan Wu and I-Liang Chern,
Derivative Securities and Finite Difference Methods, (Book),
Springer-Verlag New York, 2004.
- Xiaonan Wu and Jicheng Jin,
A finite element method for Stokes equations using discrete
singularity expansion,
Comp. Meth. Appl. Mech. Eng., 194 (2005), 83-101.
- Zhi-zhong Sun and Xiaonan Wu,
The stability and convergence of a difference scheme for the
Schrodinger equation on an infinite domain by using artifial
boundary conditions,
J. Comp. Phy., 214 (2006), 209-223.
- Zhenli Xu, Houde Han and Xiaonan Wu,
Adaptive absorbing boundary conditions for Schrodinger-type
equations: application to nonlinear and multi-dimensional problems,
J. Comp. Phy., 225 (2007), 1577-1589.
- Houde Han, Zhi-zhong Sun and Xiaonan Wu,
Convergence of a difference scheme for the heat equation in
a long strip,
Numer. Meth. PDE., 24 (2008), 272-295.
- Xiaonan Wu and Jiwei Zhang,
Artificial boundary method for two-dimensional Burgers' equation,
Comp. Math. Appl., 56 (2008), 242-256.
- Jiwei Zhang, Zhenli Xu, and Xiaonan Wu,
Unified approach to spit absorbing boundary conditions for
nonlinear Schrodinger equations,
Phys. Rev. E, 78 (2008), 026709.
- Zhi-zhong Sun and Xiaonan Wu,
A difference scheme for Burgers' equation in an unbounded
domain,
Appl. Math. Comp., 209 (2009), 285-304.
- Jiwei Zhang, Zhenli Xu, and Xiaonan Wu,
Unified approach to split absorbing boundary conditions for
nonlinear Schrodinger equations: Two-dimensional case,
Phys. Rev. E, 79 (2009), 046711.
- Houde Han and Xiaonan Wu,
Artificial Boundary Method, (Book, in Chinese)
Tsinghua University Press, Beijing, 2009.
- Hermann Brunner, Xiaonan Wu and Jiwei Zhang,
Computational solution of blow-up problems for semilinear
parabolic PDEs on unbounded domains,
SIAM J. Sci. Comp., 31 (2010), 4478-4496.
- Jicheng Jin and Xiaonan Wu,
Convergence of a finite element scheme for the two-dimensional
time-dependent Schrodinger equation in a long strip,
J. Comp. Appl. Math., 234 (2010), 777-793.
- Xiaonan Wu and Jiwei Zhang,
High order local absorbing boundary conditions for heat equations
in unbounded domains,
J. Comp. Math., 29 (2011), 74-90.