Layton,
A., Stockie, J., Li, Z. L., and Huang, H. X. (2012). Special
issue on fluid motion driven by immersed structures preface.
Communications in Computational Physics, 12(2), I-III.
T. Witelski, D. Ambrose, A. Bertozzi, A. Layton, Z. Li, M.
Minion, Special Issue of
Discrete and continuous dynamical systems. Series B, 2012;
17(4).
Fluid dynamics, Analysis, and Numerics (FAN), A conference
in honor of J. Thomas Beale,
Immersed Interface/Boundary Method, K. Ito and Z. Li, in
Encyclopedia of Applied and Computational Mathematics, editor,
Springer-Verlag Berlin Heidelberg 2015 Björn Engquist,
10.1007/978-3-540-70529-1_387
SIAM Book Review:
Introduction to Scientific Computing and Data Analysis (Mark
H. Holmes), SIAM Review, Vol. 59, No.3, 689-690, 2017.
Generalized Difference Methods for Differential Equations.
By R. Li, Z. Chen, and W. Wu. Marcel Dekker, N, SIAM
Review, Vol. 43, No.1, 203-205, 2001.
Selected Publications:
1.S.
Deng, Z. Li, K. Pan (2021), An ADI-Yee's scheme for Maxwell's
equations with discontinuous coefficients, Journal of
Computational Physics, https://doi.org/10.1016/j.jcp.2021.110356
2.B.
Dong, X. Feng, & Z. Li* (2020), An FE-FD Method for
Anisotropic Elliptic Interface Problems, SIAM SISC,
42(4), B1041–B1066.
3.Tong,
F.,
Wang, W., Feng, X., Zhao, J., & Li, Z*. (2020). How to
obtain an accurate gradient for interface problems? Journal of
Computational Physics, 405, 109070. https://doi.org/10.1016/j.jcp.2019.109070
4.H.
Jiang, Z. Yang & Z. Li, Non-parallel hyperplanes ordinal
regression machine KNOWLEDGE-BASED SYSTEMS, 216, 106593, 2021.
5.P.
Huang & Z. Li, Partially penalized IFE methods and
convergence analysis for elasticity interface problems, JOURNAL
OF COMPUTATIONAL AND APPLIED MATHEMATICS, 382.
10.1016/j.cam.2020.113059,2021
6.J.
Ye, Z. Yang & Z. Li,Quadratic
hyper-surface
kernel-free least squares support vector regression,INTELLIGENT
DATA ANALYSIS, 25(2), 265–281, 2021
7.C.
Zhang, Z. Li, X. Yue, An Acceleration Technique for the
Augmented IIM for 3D Elliptic Interface Problems, Numer. Math.
Theor. Meth. Appl. doi: 10.4208/nmtma.
8.X.
Xiao, X. Feng & Z. Li, A gradient recovery-based adaptive
finite element method for convection-diffusion-reaction
equations on surfaces,INTERNATIONAL JOURNAL FOR NUMERICAL
METHODS IN ENGINEERING, DOI: 10.1002/nme.6163
9.Z.
Li, M. Lai, X. Peng & Z. Zhang, A least squares augmented
immersed interface method for solving Navier–Stokes and Darcy
coupling equations, Computers & Fluids, 167, 384–399, 2018.
10.Z.
Li, B. Dong, F. Tong & W. Wang, An Augmented IB Method &
Analysis for Elliptic BVP on Irregular Domains. CMES-COMPUTER
MODELING IN ENGINEERING & SCIENCES, 119(1), 63–72.
11.R.
Hu & Z. Li, Error analysis of the immersed interface method
for Stokes equations with an interface, Applied Mathematics
Letters, 83, 207–211, 2018.
12.Z.
Li, X. Chen & Z. Zhang, ON MULTISCALE ADI METHODS FOR
PARABOLIC PDEs WITH A DISCONTINUOUS COEFFICIENT, MULTISCALE
MODELING & SIMULATION, 16(4), 1623–1647, 2018.
13.Y.
Yao, Y. Zhang, L. Tian, N. Zhou, Z. Li & M. Wang, Analysis
of Network Structure of Urban Bike-Sharing System: A Case Study
Based on Real-Time Data of a Public Bicycle System
SUSTAINABILITY, 11(19).
14.T.
Zhao, J. Zhang, Z. Li & Z. Zhang, Numerical Validations of
the Tangent Linear Model for the Lorenz Equations CMES-COMPUTER
MODELING IN ENGINEERING & SCIENCES, 120(1), 83–104.
15.Y.
Yao, X. Jiang & Z. Li, Spatiotemporal characteristics of
green travel: A classification study on a public bicycle system
JOURNAL OF CLEANER PRODUCTION, 238
16.Li, Z. L., Ji, H.
F., & Chen, X. H. (2017). Accurate
solution
and gradient computation for elliptic interface problems with
variable coefficients. SIAM Journal on Numerical Analysis,
55(2), 570-597.
17.Huang, P. Q.,
& Li, Z. L. (2017). A
uniformly stable nonconforming FEM based on weighted interior
penalties for Darcy-Stokes-Brinkman equations. Numerical
Mathematics: Theory, Methods and Applications, 10(1), 22-43.
18.Yan, J. L., Lai,
M. C., Li, Z. L., & Zhang, Z. Y. (2017). New
conservative finite volume element schemes for the modified
regularized long wave equation. Advances in Applied Mathematics
& Mechanics, 9(2), 250-271.
19.Qin, F. F., Chen,
J. R., Li, Z. L., & Cai, M. C. (2017). A
Cartesian grid nonconforming immersed finite element method for
planar elasticity interface problems. Computers &
Mathematics with Applications, 73(3), 404-418.
20.Li, Z. L., & Mikayelyan, H. (2016). Fine
numerical analysis of the crack-tip position for a Mumford-Shah
minimizer. Interfaces and Free Boundaries,18(1),
75-90.
21.Ji, H. F., Chen, J. R., & Li, Z. L. (2016). Augmented immersed
finite element methods for some elliptic partial differential
equations. International
Journal of Computer Mathematics, 93(3), 540-558.
22.Zhang, S. D. M., &
Li, Z. L. (2016). An augmented IIM for Helmholtz/Poisson
equations on irregular domains in complex space. International
Journal of Numerical Analysis and Modeling, 13(1), 166-178.
23.Melnyk, L. J.,
Wang, Z. H., Li, Z. L., & Xue, J. P. (2016). Prioritization
of
pesticides based on daily dietary exposure potential as
determined from the SHEDS model. Food and Chemical Toxicology,
96, 167-173.
24.Zhang, Q., Li, Z. L.,
& Zhang, Z. Y. (2016). A sparse grid stochastic
collocation method for elliptic interface problems with random
input. Journal of Scientific Computing, 67(1), 262-280.
25.Zhu, L., Zhang, Z. Y.,
& Li, Z. L. (2016). The immersed finite volume
element method for some interface problems with nonhomogeneous
jump conditions. International Journal of Numerical Analysis and
Modeling, 13(3), 368-382.
26.Li,
Z.
L. (2016). An augmented Cartesian grid method for Stokes-Darcy
fluid-structure interactions. International Journal for Numerical
Methods in Engineering, 106(7), 556-575.
27.Su, X. L., Feng,
X. F., & Li, Z. L. (2016). Fourth-order
compact
schemes for Helmholtz equations with piecewise wave numbers in
the polar coordinates. Journal of Computational Mathematics,
34(5), 499-510.
28.Ji, H. F., Chen, J.
R., & Li, Z. L. (2016). A new augmented immersed
finite element method without using SVD interpolations. Numerical
Algorithms, 71(2), 395-416.
29.Zhang, Q., Ito, K.,
Li, Z. L., & Zhang, Z. Y. (2015). Immersed finite
elements for optimal control problems of elliptic PDEs with
interfaces. Journal of Computational Physics, 298, 305-319.
30.Li,
Z.
L., Xiao, L., Cai, Q., Zhao, H. K., & Luo, R. (2015). A
semi-implicit augmented IIM for Navier-Stokes equations with open,
traction, or free boundary conditions. Journal of Computational
Physics, 297, 182-193.
31.Zhu, L., Zhang, Z. Y.,
& Li, Z. L. (2015). An immersed finite volume
element method for 2D PDEs with discontinuous coefficients and
non-homogeneous jump conditions. Computers & Mathematics with
Applications, 70(2), 89-103.
32.Alvarez, J. R., &
Li, Z. L. (2015). The immersed interface method for
axis-symmetric problems and application to the Hele-Shaw flow.
Applied Mathematics and Computation, 264, 179-197.
34.Xia, J. L., Li, Z. L.,
& Ye, X. (2015). Effective matrix-free
preconditioning for the augmented immersed interface method.
Journal of Computational Physics, 303, 295-312.
35.Zeng,
Y.
P., Chen, J. R., & Li, Z. L. (2015). A parallel Robin-Robin
domain decomposition method for H(div)-elliptic problems.
International Journal of Computer Mathematics, 92(2), 394-410.
36.H.
Ji,
J. Chen, Z. Li, A symmetric and consistent immersed finite element
method for interface problems, Journal of Scientific Computing,
Volume 61, Number 3, December 2014, pp.533-557.
37.Xu,
J.
J., Huang, Y. Q., Lai, M. C., and Li, Z. L. (2014). A coupled
immersed interface and level set method for three-dimensional
interfacial flows with insoluble surfactant. Communications in
Computational Physics, 15(2), 451-469.
38.Li,
Z.
L., Wang, L., Aspinwall, E., Cooper, R., Kuberry, P., Sanders, A.,
& Zeng, K. (2015). Some new analysis results for a class of
interface problems. Mathematical Methods in the Applied Sciences,
38(18), 4530-4539.
39.Liu, X. P., Wang, C.
H., Wang, J., Li, Z. L., Zhao, H. K., and Luo, R. (2013). Exploring
a charge-central strategy in the solution of Poisson's equation
for biomolecular applications. Physical Chemistry Chemical
Physics, 15(1), 129-141.
40.Botello-Smith,
W.
M., Liu, X. P., Cai, Q., Li, Z. L., Zhao, H. K., and Luo, R.
(2013). Numerical Poisson-Boltzmann model for continuum membrane
systems. Chemical Physics Letters, 555, 274-281.
41.Z.
Wang, Z. Li, S. Lubkin, A Robin-Robin Domain Decomposition
Method for a Stokes-Darcy Structure Interaction with a Locally
Modified Mesh, Numer. Math. Theor. Meth. Appl., 7 (2014),
pp. 435-446.
42.Song,
P.,
Xue, J. P., and Li, Z. L. (2013). Simulation of longitudinal
exposure data with variance-covariance structures based on mixed
models. Risk Analysis, 33(3), 469-479.
43.Wang, Q. X., Zhang, Z.
Y., and Li, Z. L. (2013). A Fourier finite volume
element method for solving two-dimensional quasi-geostrophic
equations on a sphere. Applied Numerical Mathematics, 71, 1-13.
44.Li,
Z.
L., and Song, P. (2013). Adaptive mesh refinement techniques for
the immersed interface method applied to flow problems. Computers
and Structures, 122, 249-258.
45.Wang,
C.
H., Wang, J., Cai, Q., Li, Z. L., Zhao, H. K., and Luo, R. (2013).
Exploring accurate Poisson-Boltzmann methods for biomolecular
simulations. Computational and theoretical chemistry, 1024, 34-44.
46.Li,
Z.
L., and Song, P. (2012). An adaptive mesh refinement strategy for
immersed boundary/interface methods. Communications in
Computational Physics, 12(2), 515-527.
47.Hou,
S.
M., Li, Z. L., Wang, L. Q., and Wang, W. (2012). A numerical
method for solving elasticity equations with interfaces.
Communications in Computational Physics, 12(2), 595-612.
48.Ito, K., Li, Z. L.,
and Qiao, Z. H. (2012). The sensitivity analysis for the
flow past obstacles problem with respect to the Reynolds number.
Advances in Applied Mathematics and Mechanics, 4(1), 21-35.
49.Wan,
X.
H., and Li, Z. L. (2012). Some new finite difference methods for
Helmholtz equations on irregular domains or with interfaces.
Discrete and Continuous Dynamical Systems-Series B, 17(4),
1155-1174.
50.Caraus,
I.,
and Li, Z. L. (2012). Numerical solutions of the system of
singular integro-differential equations in classical holder
spaces. Advances in Applied Mathematics and Mechanics, 4(6),
737-750.
51.Ho, J., Li, Z. L., and
Lubkin, S. R. (2012). An augmented immersed interface
method for moving structures with mass. Discrete and Continuous
Dynamical Systems-Series B, 17(4), 1175-1184.
52.Alvarez,
J.
A., Chen, J. R., and Li, Z. L. (2011). The IIM in polar
coordinates and its application to electro capacitance tomography
problems. Numerical Algorithms, 57(3), 405-423.
53.Xie, H., Li, Z. L.,
and Qiao, Z. H. (2011). A finite element method for
elasticity interface problems with locally modified
triangulations. International Journal of Numerical Analysis and
Modeling, 8(2), 189-200.
54.Wu,
C.
T., Li, Z. L., and Lai, M. C. (2011). Adaptive mesh refinement for
elliptic interface problems using the non-conforming immersed
finite element method. International Journal of Numerical Analysis
and Modeling, 8(3), 466-483.
55.Xu,
J.
J., Li, Z. L., Lowengrub, J., and Zhao, H. K. (2011). Numerical
study of surfactant-laden drop-drop interactions. Communications
in Computational Physics, 10(2), 453-473.
56.Feng,
X.
F., Li, Z. L., and Qiao, Z. H. (2011). High order compact finite
difference schemes for the helmholtz equation with discontinuous
coefficients. Journal of Computational Mathematics, 29(3),
324-340.
57.Li,
Z.
L., Lai, M. C., He, G. W., and Zhao, H. K. (2010). An augmented
method for free boundary problems with moving contact lines.
Computers and Fluids, 39(6), 1033-1040.
58.Gong,
Y.,
and Li, Z. L. (2010). Immersed Interface Finite Element Methods
for Elasticity Interface Problems with Non-Homogeneous Jump
Conditions. Numerical Mathematics: Theory, Methods and
Applications, 3(1), 23-39.
59.The
sensitivity
analysis for the flow past obstacles problem with respect to the
Reynolds number, K. Ito, Z. Li, and Z. Qiao, Advances in Applied Mathematics and Mechanics, in press,
2011.
60.Analysis
and
numerical methods for some crack problems, International Journal of
Numerical Analysis & Modeling, Series B, Vol.
2, 155-166,2011,
X.Feng, Z. Li, and
L. Wang.
61.New
Finite
Difference Methods Based on IIM for Inextensible Interfaces in
Incompressible Flows, East Asian Journal of Applied Mathematics
Vol. 1, No. 2, pp. 155-171, Zhilin Li and Ming-Chih Lai
62.A
well-conditioned augmented system for solving Navier-Stokes
equations in irregular domains, J. Comput. Phys. 228, (2009), 2616-2628,
doi:10.1016/j.jcp.2008.12.028, K. Ito, M. Lai, and Zhilin Li .
63.Numerical
Study
of Surfactant-Laden Drop-Drop Interactions, CiCP, Vol. 10, 2011, No. 2, pp.
453-473, doi: 10.4208/cicp.090310.020610a, J. Xu,
Z. Li, J. Lowengrub, and H. Zhao.
64.A
finite element method for elasticity interface problems with
locally modified triangulations,International
Journal of Numerical Analysis & Modeling,Volume 8,
Number 2, Pages 189–200, 2010, H. Xie, Z. Li,and Z. Qiao
65.An
additive
Schwartz preconditioner for the mortar-type rotated Q1 FEM for
elliptic problems with discontinuous coefficients, Applied
Numerical Mathematics, Vol
59, Issue 7, 2009, Pages 1657-1667, F. Wang, J. Chen, W. Xu,
Z. Li.
66.Achieving
energy
conservation in Poisson Boltzmann molecular dynamics: Accuracy and
precision with finite-difference algorithms, Chemical Physics
Letters, Volume 468, Issues 4-6, 22 January 2009, Pages 112-118,
Jun Wang, Qin Cai, Zhilin Li, Hong-Kai Zhao, and Ray Luo.
67.Correction
to:
"A comparison of the extended finite element method with the
immersed interface method ..."[CAMCoS 1 (2006), 207--228], T.
Beale, D. Chopp, R. LeVeque, and Z. Li, Comm. App. Math. Comp.
Sci., Vol. 3, 95-100, 2008.
68.Immersed-Interface
Finite-Element
Methods for Elliptic Interface Problems with Non-homogeneous Jump
Conditions, SIAM J.
Numer. Anal., Vol. 46, 472-495, 2008, Y. Gong, B. Li, and
Z. Li
69.Introduction
to
Immersed Boundary/Interface Method, Robert Dillion and
Zhilin Li, Lecture
Notes Series, Vol. 17, 2009, World Scientific Publisher,
ISBN-13-981-283-784-1.
70.Interface
Problems
and Methods in Biological Flows, B-C. Khoo, Z. Li, and P. Lin, IMS
Lecture Notes Series, Vol. 17, 2009, World Scientific Publisher
71.A
smoothing technique for discrete delta functions with application
to immersed boundary method in moving boundary simulations, J.
Comput. Phys. Vol.
228, 2009, Pages 7821-7836, X. Yang, X. Zhang, Z. Li, and G. He
72.An
Implicit-forcing
Immersed Interface Method for the Incompressible Navier-Stokes
Equations, AMS
Contemporary Mathematics, Vol. 466, 2008, 73-94, D-V.
Le, B-C. Khoo, Z. Li
73.An
Immersed
Interface Method for Solving Incompressible Viscous Flows with
Piecewise Constant Viscosity Across a Moving Elastic Membrane, J. of Comput. Physics, Vol.
227 Issue 23, p9955-9983, 2008, Z. Tan, D. V. Le, Z. Li,
K. M. Lim, and B. C. Khoo
74.Mechanics
of
mesenchymal contribution to clefting force in branching
morphogenesis, Biomechanics and Modeling in Mechanobiology,
Vol. 7, 417-426, 2008, X. Wan, Z. Li, and S. Lubkin.
75.An
augmented
approach for Stokes equations with a discontinuous viscosity and
singular forces, Computers and Fluids, Vol. 36, 622-635, 2007, K.
Ito, M-C. Lai, and Z. Li
76.Pressure
Jump
Conditions for Stokes Equations with Discontinuous Viscosity in 2D
and 3D, Methods and Applications of Analysis, Vol. 13,
199-214, 2006, K. Ito, Z. Li, and X. Wan.
77.A
fast finite difference method for biharmonic equations on
irregular domains, Advances in Comput. Math., on-line, DOI
10.1007/s10444-007-9043-6, Vol. 29, 113-133, 2008, G. Chen, Z. Li,
and P. Lin.
78.Theoretical
&
numerical analysis for a fluid mixure model of tissue
deformation, Q. Jiang, Z. Li, and S. Lubkin., Comm. in Comput. Phy.
Vol. 3, 620-634, 2009.
79.A
finite element method for interface problems with locally modified
triangulations, AMS
Contemporary Mathematics, Vol. 466, 2008, 179-190, H.
Xie, K. Ito, Z. Li, J. Toivanen
80.A
study of numerical methods for the level set approach, Appl.
Numer. Math., 837-846, 2006, P. Gremaud, C. Kuster, and Z. Li
81.An
Explicit
Jump Immersed Interface Method for Two-Phase Navier Stokes
Equations with Interfaces, Computer Methods in Applied
Mechanics and Engineering, Vol. 197, 2317-2328, 2008, with V.
Rutka.
82.An
augmented
IIM-level set method for Stokes equations with discontinuous
viscosity, Electron. J. Diff. Eqns., 193-210,2007
83.A
level-set method for interfacial flows with surfactant, J.
of Comput. Physics, Vol.
212,
590-616, 2006, with Jian-Jun Xu, John Lowengrub, and Hongkai
Zhao.
84.Fast
solvers for 3D Poisson equations involving interfaces in a finite
or the infinite domain, Journal of Computational and Applied
Mathematics, Volume 191, Issue 1, 15 June 2006, Pages 106–125,
Ming-Chih Lai, Zhilin Li, Xiaobiao Lin.
85.A
FINITE DIFFERENCE SCHEME FOR SOLVING THE NONLINEAR
POISSON-BOLTZMANN EQUATION MODELING CHARGED SPHERES, Journal of
Computational Mathematics, Vol.24, No.3, 2006, 252–264. Z. Qiao,
Z. Li, T. Tang
86.An
augmented
approach for the pressure boundary condition in a Stokes
flow, Comm. in Comp. Physics, Vol. 1, (2006), pp.
874-885., Z. Li, X. Wan, K. Ito and S. R. Lubkin
87.A
Finite Difference Method and Analysis for 2D Nonlinear
Poisson–Boltzmann Equations, Journal of Scientific
Computing, 1573-7691 (Online) DOI: 10.1007/s10915-005-9019-y, With
C.V. Pao and Z. Qiao.
88.Immersed
finite
element for elasticity system with discontinuities,
AMS Contemporary Mathematics, Vol. 383, pp285-298,
2005, Z. Li and X.Yang.
89.Augmented
Strategies
for Interface and Irregular Domain Problems, in Lecture
Notes in Mathematics and Computer Sciences, Springer-Verlag, pp.
66-79, 2005.
90.The
numerical
solution of singular integro-differential equations by reduction
method using the Faber-Laurent polynomials, Iurie Caraus,
Zhilin Li, and V. A. Zolotarevskii, Differential Equations, Vol.
40, No. 12, 2004, pp. 1764-1769.
91.Interface
conditions
for stokes equations with discontinuous viscosity and surface
sources, Applied Mathematics Letters , Vol. 19, Issue
3, March 2006, Pages 229-234.
92.Numerical
Analysis
and Its Applications, Edited by Zhilin Li, Lubin
Vulkov, and Jerzy Was'niewski, Lecture Notes in Computer
Science, Springer-Verlag, GmbH, Volume 3401 / 2005,
ISBN 3-540-24937-0.
93.An
immersed
finite element space and its approximation capability, Numerical
Methods of PDEs, Vol. 20, pp. 338-367, 2004, DOI
10.1002/num.10092, Z. Li. T. Lin, Y. Lin and R. C. Rogers.
94.Error
estimates
of an immersed finite element method for interface problems, NCSU
CRSC Technical report, CRSC-TR00-07.
95.Generalized
Snell's
law for weighted minimal surface, Methods and Applications of
Analysis Vol. 10,
pp. 199-214, 2003, Z. Li , X. Lin, M. Torres, and H.
Zhao.
96.Three
dimensional
elliptic solvers for interface problems and applications, J. of
Comput. Physics, Vol. 184,
pp.
215-243, 2003, with S. Deng and K. Ito, 2003.
97.The
Immersed
Interface Method for Elasticity Problems with Interface, Dynamics
of Continuous, Discrete and Impulsive Systems, Part A, Vol.10, No.5, 783-808 ,
2003, with X. Yang and B. Li.
98.Solving
a
Nonlinear Interface Problems in Magneto-Rheological Fluids using
the Immersed Interface Method. Journal of Scientific
Computing, Vol. 19, pp. 253-266, 2003, with K. Ito.
99.An
overview
of the immersed interface method and its applications, Taiwanese
J. Mathematics, Vol.
7, No. 1, pp. 1-49, 2003.
100. AN L ∞
SECOND ORDER CARTESIAN METHOD FOR 3D ANISOTROPIC
INTERFACE PROBLEMS, B. Dong, X. Feng, & Z. Li*
(2020), J. Comput. Math., 2021
101. Introduction to Partial
Differential Equations, Z. Li & L. Norris, World
Scientific, https://dx.doi.org/10.1142/12052, 2021
102.Force and
Deformation on Branching Rudiments: Cleaving Between
Hypotheses, Biomechanics and Modeling in mechanobiology, Vol. 1, pp. 5-16, 2002, with Sharon Lubkin.
103.A fast finite
difference method for solving Navier-Stokes
Equations on irregular domains, J. of Commu.
in Math. Sci., Vol.
1, pp. 180-196, 2003. with C.
Wang.
104.The Level-Set
Function Approach to an Inverse Interface Problem, Inverse Problems, Vol. 17,
No. 5, October, 2001, pp. 1225-1242, with K. Ito and K. Kunish.
105.Maximum Principle
Preserving Schemes for Interface Problems with Discontinuous
Coefficients, SIAM J. Sci. Comput.
23, No.1, pp.
339-361, 2001, with K. Ito
106.Immersed Interface
Method for the Navier-Stokes
Equations with Singular Forces, J.
of Comput. Physics,
171,
822-842 (2001), with M. Lai.
107.Numerical Analysis
of Interfacial 2D Stokes Flow with Discontinuous Viscosity and
Variable Surface Tension, Numerical
Methods in Fluids, 37,
525-540, 2001, with S. Lubkin.
108.A remark on jump
conditions for the three-dimensional Navier-Stokes
equations involving an immersed moving membrane, Applied Math.
Letters, 14,
pp. 149-154, 2001 with M. Lai.
109.A Level Set-Boundary
Element Method for Simulation of Dynamic Powder Consolidation
of Metals, in Numerical Analysis and Its Application, edited
by L. Vulkov, J. Wasniewski, and P. Yalamov, Springer-Verlag, pp. 527-534,
2001, with W. Cai
110.Numerical method for
simulation of bubbles flowing through another fluid, in
Advances in Scientific Computing, edited by Z-C Shi et. el.,
Science Press, pp. 86-94, 2001, with Y. Shen.
111.A Numerical Study of
Electro-migration Voiding by Evolving Level Set Functions on a
Fixed Cartesian Grid, J. of
Comput. Physics,
152:281-304,
1999, with H. Zhao and H Gao.
112.New Cartesian grid
methods for interface problems using the finite element
formulation, NumerischeMathematik, 96:61-98,
2003, also, NCSU CRSC-TR99-5, 1999, with T. Lin,
and X. Wu.
113.A numerical method
for solving heat equations involving interfaces, Electron. J.
Diff. Eqns., Conf. 03, 1999, pp. 100-108, with Y. Shen.
114.The immersed finite
volume element methods for the elliptic interface problems,
Mathematics and Computers In
Simulation, (50)1-4
(1999) pp. 43-61, with R. E. Ewing, T. Lin, and Y. Lin
115.A fast iterative algorithm for elliptic
interface problems. SIAM J. Numer.
Anal. 35:230--254,
1998.
116.The immersed
interface method using a finite element formulation. Applied Numer. Math. 27:253--267, 1998.
117.Convergence analysis of the immersed interface
method. IMA J. Numer. Anal.,
19:583-608, 1999,
with H. Hunag.
118.Fast and Accurate Numerical Approaches for
Stefan Problems and Crystal Growth. Numerical Heat Transfer, Part B: Fundamentals,35: 461-484, 1999,
with B. Soni
119.Theoretical and numerical analysis on a
thermo-elastic system with discontinuities. J. of Comput. Appl. Math. 91:1--22, 1998, with
J. Zou.
120.An Inverse Problem in a Parabolic Equation,
Electronic Journal of Differential Equations, Conference 01,
1997, pp. 193--199, Published November 12, 1998, with K. Zheng.
121.Crack jump conditions for elliptic problems,
Applied Math. Letters,12(6):81--88, 1999, with A. Wiegmann and R. LeVeque
122.A hybrid method for moving interface problems
with application to the Hele-shaw
flow, J. Comput. Phys.
134:236--252, 1997, with T. Hou, S. Osher,
and H.
123.A numerical method for diffusive transport with
moving boundaries and discontinuous material properties.
International J. Numer. & Anal.
Method in Geomechanics, 21:653--662,
1997, with D. McTigue, and J. Heine.
124.Convergence analysis of the immersed interface
method. IMA J. Numer. Anal.,
19:583-608, 1999, with H. Hunag.
125.Fast and Accurate Numerical Approaches for
Stefan Problems and Crystal Growth. Numerical Heat Transfer, Part B: Fundamentals,35:
461-484, 1999, with B. Soni
126.Theoretical and numerical analysis on a
thermo-elastic system with discontinuities. J. of Comput. Appl. Math. 91:1--22, 1998, with
J. Zou.
127.An Inverse Problem in a Parabolic Equation,
Electronic Journal of Differential Equations, Conference 01,
1997, pp. 193--199, Published November 12, 1998, with K. Zheng.
128.Crack jump conditions for elliptic problems,
Applied Math. Letters,12(6):81--88, 1999, with A. Wiegmann and R. LeVeque
129.A hybrid method for moving interface problems
with application to the Hele-shaw
flow, J. Comput. Phys.
134:236--252, 1997, with T. Hou, S. Osher,
and H.
130.Immersed interface
method for Stokes flow with elastic boundaries or surface
tension. SIAM J. Sci. Comput. 18:709--735, 1997,
with R. J. LeVeque.
132.A note on immersed
interface methods for three-dimensional elliptic equations.
Computers Math. Appl. 31:9--17, 1996.
133.Simulation of
bubbles in creeping flow using the immersed interface method,
in Proc. Sixth International Symposium on Computational Fluid, pp 688-693, 1995,
with R. J. LeVeque
134.The Immersed
Interface Method --- A Numerical Approach for Partial
Differential Equations with Interfaces, PhD thesis, University
of Washington, 1994.
135.The immersed
interface method for elliptic equations
with discontinuous coefficients and singular sources, SIAM J. Numer. Anal. 31:1019--1044,
1994, with R. J. LeVeque
136.Erratum: "The
immersed interface method for elliptic equations with
discontinuous coefficients and singular sources", SIAM J. Numer.
Anal. 32:1704,
1995, with
137.ADI methods for heat
equations with discontinuities along an arbitrary interface.
Proc. Symp. Appl. Math. W. Gautschi, editor,
48, 311--315. AMS, 1993, with A. Mayo
138.Perturbation
theorems of eigenvectors. Numer.
Math., a Journal of Chinese Universities, 12(1990), No.3, pp.
284--289, with K. Huang.
139.Uniform treatment of
linear systems -- algorithm and numerical stability. Numer. Comput.
Appl. 2: 71-86, 1989.
140.A generalized
conjugate gradient method for solving real skew-symmetric
systems. J. on Numer. Methods
& Comput. Appl., 8(1987),
No.4, pp. 31--37.
141.An equivalent
theorem on the numerical stability for an algorithm, Numer. Math., a Journal of Chinese
Universities, 9(1987), No. 1, pp.
59--65, with K. Huang
142.Round off error
analysis for polynomial interpolation. Research and
Review in Mathematics, 1989, No. 2, with K. Huang.
143.On the relation
between the behavior and the distribution of the zeros of a
polynomial. J. of Nanjing University, Mathematics.
Biquarterly, 2(1985), No. 1, pp. 53--59, with K. Huang.
144.Optimal conjugate
gradient method for solving arbitrary linear equations. J. of
Nanjing Normal University. 1988, No. 3, pp. 28--34.
145.Round-off error
analysis for a class of conjugate gradient methods with
restarting. J. of Nanjing Normal University. 1986, No.
1, pp. 26--34.
146.The effect of
deflation on the condition number of zeros of polynomials. J.
of Nanjing Normal University. 1986, No. 2, pp. 31--37.
147.Autophobic
Spreading
of Drops, J. of Comput. Physics, Vol. 183, No. 2,
pp. 335-366, 2002, with J. K. Hunter, and H. Zhao
148.New
Formulations
for Interface Problems in Polar coordinates, SIAM J.
Sci. Comput., 25,
No 1, 224-245, (2003) , with W. Wang, I Chern, and M. Lai
149.The
immersed
interface/multigrid methods for interface problems, SIAM J.
Sci. Comput., Vol.
24, No.2, pp. 463 - 479, 2002, with L. Adams.