List of Publications
In Refereed Journals:
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)
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)
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)
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)
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.
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.
30. Tailored finite point methods for first order wave equation, (with X. Yang), J Sci. Comput., 49 (3): 351-366, 2011.
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.
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, 4 (1): 91-106, 2009.
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.
23. A Hybrid
Phase-Flow Method for Hamiltonian Systems with Discontinuous Hamiltonians,
(with S. Jin, H. Wu),
22. A Tailored finite point method for the Helmholtz equation with high wave numbers in heterogeneous medium, (with H. Han), J. Comput. Math., 26 (5):728-739, 2008.
21. A Tailored finite point method for a singular perturbation problem on an unbounded domain, (with H. Han and B. Kellogg), J Sci. Comput., 36 (2): 243-261, 2008.
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.
18. Numerical solutions of Schrödinger equations in R3, (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.
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.
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.
12. Exact artificial boundary conditions for Schrödinger equation in R2, (with H. Han) Commun. Math Sci., 2 (1): 79-94, 2004.
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.
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.
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.
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.
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.
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, (with H.
Han and B. Kellogg), International
Conference BAIL 2008, Boundary and Interior Layers - Computational
& Asymptotic Methods, the University of Limerick, Ireland, July 28-