**List
of Publications**

**In Refereed Journals:**

2017

44. *The direct method of lines
for elliptic problems in star-shaped domains*, (with Zhizhang Wu, Wei-Cheng
Wang, Yi Yang), J. Comput. Appl. Math, 327: 350-361, 2017. (DOI: **10.1016/j.cam.2017.06.028**)

2016

43. *Tailored finite point
method for parabolic problems, *(with Yi Yang), *Comput. Meth. Appl. Math. 16 (4):543-562, 2016. *(DOI: **10.1515/cmam-2016-0017
**)

42. *Monotone finite point
method for non-equilibrium radiation diffusion equations*, (with Y. Li), BIT
Numer. Math. 56 (2016): 659–679 (DOI: **10.1007/s10543-015-0573-x
**)

41. *A Bloch
decomposition-based stochastic Galerkin method for quantum dynamics with a
random external potential,* (with Zhizhang Wu), J. Comput. Phys. 317 (2016):
257–275 (DOI: **10.1016/j.jcp.2016.04.051)**

2015

40. *An equation decomposition
based tailored finite point method for linearized incompressible flow in two
dimensional space*, (with Y. Li, H. Han), *Comput.
Meth. Appl. Math. *15 (1): 39–58, 2015. *(*DOI: **10.1515/cmam-2014-0028**)

2014

39. *Numerical simulations of X-rays Free Electron Lasers
(XFEL)*, (with P. Antonelli, A. Athanassoulis, P. Markowich), Multiscale Model. Simul. 12 (4): 1607-1621, 2014.

38. *The Tailored finite point method, **(with H. Han), Comput. Meth. Appl. Math., 14 (3):
321-345, 2014. (*DOI: **10.1515/cmam-2014-0012**)

2013

37. *A
Semi-discrete tailored finite point method for a class of anisotropic diffusion
problems*, *(with H. Han and W.
Ying), *Comput. Math. Appl*. *65 (11): 1760–1774,
2013.

36. *An
Iterative Method based on equation decomposition for the fourth-order singular
perturbation problem*, (with H. Han and S. Zhang),* Numer. Meth. Part. D. E. *29 (3):
961-978, 2013.

35. *A
class of nonconforming quadrilateral finite elements for incompressible flow*,
(with Y. Li), Sci. China Math. 56 (2): 379-393, 2013.

34. *Tailored
finite point method based on exponential bases for
convection-diffusion-reaction equation, **(with H. Han), Math.
Comput., 82 (281): 213-226, *2013*.*

*2012*

33. *Gaussian
Beam Methods for the Dirac Equation in the Semi-classical Regime,* (with
H. Wu, S. Jin and D. Yin), Commun. Math. Sci. 10 (4): 1301–1315, 2012.

32. *Tailored
finite cell method for solving Helmholtz equation in layered heterogeneous
medium, *(with X. Yang), J Comput. Math. 30 (4): 381–391, 2012.

31. *An equation decomposition method
for the numerical solution of a fourth-order elliptic singular perturbation
problem*, *(with H. Han), Numer. Meth.
Part. D. E., 28 (3): 942-953, 2012.*

*2011*

30. *Tailored
finite point methods for first order wave equation*, (with X. Yang), *J Sci. Comput., *49 (3): 351-366, 2011.

2010

29.* Tailored finite point method for
steady-state reaction-diffusion equation*, *(with H. Han), Commun. Math. Sci., 8 (4): 887-899, 2010.*

28. *Bloch Decomposition Based Gaussian Beam Method
for the Schrödinger equation with Periodic Potentials,* (with S. Jin, H.
Wu and X. Yang), J. Comput. Phys., 229 (13): 4869-4883, 2010.

27.* Numerical simulation of trapped dipolar quantum
gases: Collapse studies and vortex dynamics*, *(with P. Markowich, and C. Sparber), Kinet. Relat.
Models, 3 (1):181-194, 2010.*

*2009*

26.* Tailored finite point method for a singular
perturbation problem with variable coefficients in two dimensions,** (with H. Han), J Sci. Comput., 41 (2): 200-220,
2009.*

*25. Tailored
finite point method for the interface problem, *Netw. Heterog. Media,

*24. On the
Bloch decomposition based spectral method for wave propagation in periodic
media, (with S. Jin, P. Markowich, and C. Sparber), Wave Motion, 46
(1): 15-28, 2009.*

*2008*

*23. A Hybrid
Phase-Flow Method for Hamiltonian Systems with Discontinuous Hamiltonians,
(with S. Jin, H. Wu), *31(2):1303-1321, 2008.

*22. A Tailored
finite point method for the Helmholtz equation with high wave numbers in
heterogeneous medium*

*21. A Tailored
finite point method for a singular perturbation problem on an unbounded domain*

*20.** Numerical
simulation of the nonlinear Schrödinger equation with multi-dimensional
periodic potentials,** (with S. Jin, P. Markowich, and C.
Sparber), *Multiscale Model. Sim.*, 7 (2): *539-564, 2008.

*19. Exact
artificial boundary conditions for quasilinear elliptic equation in unbounded
domains, (with H. Han and D. Yin), Commun. Math. Sci., 6 (1): 71-82,
2008.*

*2007*

*18. **Numerical
solutions of Schrödinger equations in R*^{3}*,** **(with H.
Han and D. Yin), Numer. Meth. Part. D. E., *23 (3):
511-533, 2007.

*17. A Bloch
decomposition based split-step pseudo spectral method for quantum dynamics with
periodic potentials, (with S. Jin, P. Markowich, and C. Sparber), SIAM
J Sci. Comput., 29 (2): 515-538, 2007.*

*2006*

*16.** Numerical Simulation for Crack
Propagation in Two-Dimensional**, (in Chinese) (with Q. Liu), J. Tsinghua University,
46 (9): 1604-1607, 2006.*

*15.** Wavelet-Galerkin method for
reaction-diffusion equation**, (in Chinese) (with X. Yang and L. Zhu), J. Tsinghua University, 46
(3): 392-395, 2006.*

*14. Numerical
Study of a Domain Decomposition Method for a Two-Scale Linear Transport
Equation, (with X. Yang, F. Golse, S. Jin), *Netw. Heterog. Media, 1(1):143-166, 2006

*2005*

*13. A
time-splitting spectral method for Maxwell-Dirac system, (with S. Jin,
P. Markowich, C. Sparber, C. Zheng), J. Comput. Phys, 208 (2): 761-789, 2005.*

*2004*

*12. Exact
artificial boundary conditions for Schrödinger equation in R** ^{2}*, (with H. Han) Commun. Math Sci., 2 (1): 79-94, 2004.

2003

*11. Heterogeneous
multiscale method: A general methodology for multiscale modeling*, (with W. E and B. Engquist) Phys. Rev. B, 67 (9): Art. No. 092101,
2003

*10. High accuracy
numerical method of thin-film problems in micromagnetics*, J. Comput. Math. 21 (1): 33-40, 2003.

2002

*9. A dynamic
atomistic-continuum method for the simulation of crystalline materials*, (with W. E), J Comput. Phys. 182 (1): 234-261, 2002.

*8. Exact and Approximating
Boundary Conditions for the Parabolic Problems on Unbounded Domains*, (with H. Han), Comput. Math. Appl., 44 (5-6): 655-666, 2002.

*7. A Class of Artificial
Boundary Conditions for Heat Equation in Unbounded Domains*, (with H. Han), Comput. Math. Appl., 43 (6-7): 889-900, 2002.

2001

*6. The discrete
method of separation of variables for composite material problems*, (with H. Han), Int. J Fracture, 112 (4): 379-402, 2001.

*5. Matching
conditions in atomistic-continuum modeling of materials*, (with W. E), Phys. Rev. Lett., 87 (13): 5501-5504, 2001.

*4. Numerical
simulations of fracture problems by coupling the FEM and the direct method of
lines*, (with W.Z. Bao and H. Han), Comput.
Method Appl. Mech. Eng., 190 (37-38): 4831-4846, 2001.

2000

*3. Wavelet-Galerkin
method for the singular perturbation problem with boundary layers*, Tsinghua Science & Technology, 5(4): 365-369, 2000.

*2. The discrete
method of separation of variables for computation of stress intensity factors*, (with H. Han and W.Z. Bao), Chinese J Comput. Phys., 17(5):
483-496, 2000.

1999

*1. The direct
method of lines for the numerical solutions of interface problem* , (with H. Han), Comput. Method Appl. Mech. Eng., 171(1): 61-75,
1999.

**In Refereed Conference Proceedings:**

4. *Tailored finite
point method for numerical simulation of partial differential equations,*
AMS/IP Studies in Advanced Mathematics, Vol 51, 593-608, 2012.

3.* Bloch Decomposition method for waves in periodic
media*, *(with S. Jin, P. Markowich,
and C. Sparber), *in: Series in Contemporary Applied Mathematics,
CAM 15, Some Problems on Nonlinear Hyperbolic Equations and Applications,
Higher Education Press, Beijing, 2010: pp. 161-188.

*2. **A semi-discrete numerical procedure for
composite material problems, **(with H. Han), Mathematical Sciences and Applications Vol. 12(1999),
Advances in numerical mathematics, pp. 35-44.*

*1.** A semi-discrete method for the solution of
elliptic equation with singularities, **(with H. Han), CSIAM’98 VI: 17 (1998), pp.541-545.*

**Preprints:**

5. *Asymptotic analysis and
numerical method for singularly perturbed eigenvalue problems*, (with Wang
Kong)

4. *An Efficient Tailored
Finite Point Method for Rician Denoising and Deblurring*, (with Wenli Yang,
Wei Zhu)

3. *Convergence Analysis on
Stochastic Collocation Methods for Schrodinger Equation with Random
Perturbations,* (with Zhizhang Wu)

2. *Mixed finite element formulation for fourth-order elliptic
problem based on equation decomposition*, *(with
H. Han).*

*1. The tailored finite point method and a
problem of P. Hemker*