1.
An
augmented method for free boundary problems with moving contact lines,
Computers & Fluids, 39 (2010) 1033–1040, Zhilin
Li, Ming-Chih Lai, Guowei
He, and Hongkai Zhao.
2.
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.
3.
The
IIM in Polar Coordinates and its Application to Electro Capacitance Tomography
Problems, Numerical Algorithms, (2011) 57:405–423, DOI 10.1007/s11075-010-9436-3, J. Ruiz Alvarez, J. Chen, Z. Li.
4. An
augmented immersed interface method for moving structures with mass, Discrete and Continuous Dynamical Systems -
Series B (DCDS-B), 2011, in
press, J. Hao, Z. Li, and S. R. Lubkin
5. A
numerical method for solving elasticity equations with sharp-edged interfaces, Commun. Comput. Phys., 2011, in press, S. Hou,
Z. Li, L. Wang, and W. Wang
6. An
Adaptive Mesh Refinement Strategy for Immersed Boundary/Interface Methods, Commun. Comput. Phys.,
in press, 2011, Z. Li and P. Song
7. Some
new finite difference methods for Helmholtz equations on irregular domains or
with interfaces, Discrete and
Continuous Dynamical Systems - Series B (DCDS-B), in press, 2011, Z. Li, and X. Wan
8. Analysis
and numerical methods for some crack problems, International Journal of
Numerical Analysis & Modeling, Series B, in press, 2011, X. Feng, Z. Li, and L.
Wang.
9. Adaptive mesh refinement for elliptic
interface problems using the non-conforming immersed finite element method,
International journal of Numerical Analysis and Modeling, Volume 1, Number 1,
Pages -18, 2010, C-T. Wu, Z. Li, and M-C. Lai
10. High order compact finite difference
schemes for the Helmholtz equation with discontinuous coefficients, Journal of
Computational Mathematics Vol.29, No.3, 2011, 324-340, X. Feng,
Z. Li, Z. Qiao.
11.
New
Finite Difference Methods Based on IIM for Inextensible Interfaces in
Incompressible FlowsEast Asian Journal of Applied
Mathematics Vol. 1, No. 2, pp. 155-171, Zhilin Li and
Ming-Chih Lai
12.
Immersed
Interface Finite Element Methods for Elasticity Interface Problems with
Non-homogeneous Jump Conditions, Numer. Math. Theo.
Meth. Appl., Vol. 3, 2010, pp. 23-39, Y. Gong and Z. Li.
13.
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 .
14.
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.
15.
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
16.
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.
17.
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.
18.
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.
19.
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
20.
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.
21.
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
22.
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
23.
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
24.
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
25.
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.
26.
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
27.
Pressure
Jump Conditions for Stokes Equations with Discontinuous Viscosity in 2D and
3D, Methods and Applications of Analysis,
28.
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.
29.
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.
30.
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
31.
A
study of numerical methods for the level set approach, Appl. Numer. Math., 837-846, 2006, P. Gremaud,
C. Kuster, and Z. Li
32.
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.
33.
An
augmented IIM-level set method for Stokes equations with discontinuous
viscosity, Electron. J. Diff. Eqns.,
193-210,2007
34.
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.
35.
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
36.
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.
37.
Immersed
finite element for elasticity system with discontinuities,
AMS Contemporary Mathematics, Vol. 383, pp285-298, 2005, Z.
Li and X.Yang.
38.
Augmented
Strategies for Interface and Irregular Domain Problems,
in Lecture Notes in Mathematics and Computer Sciences, Springer-Verlag, pp. 66-79, 2005.
39.
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.
40.
Interface
conditions for stokes equations with discontinuous viscosity and surface
sources, Applied Mathematics Letters , Vol. 19, Issue 3,
March 2006, Pages 229-234.
41.
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.
42.
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.
44.
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.
45.
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.
46.
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.
47.
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.
48.
An
overview of the immersed interface method and its applications, Taiwanese J.
Mathematics, Vol. 7, No. 1, pp. 1-49, 2003.
49.
Autophobic Spreading of Drops, J. of Comput.
Physics, Vol. 183, No. 2, pp. 335-366, 2002, with J. K. Hunter,
and H. Zhao
50.
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
51.
The
immersed interface/multigrid methods for interface
problems, SIAM J. Sci. Comput., Vol.
24, No.2, pp. 463 - 479, 2002, with L. Adams.
52.
Force
and Deformation on Branching Rudiments: Cleaving Between Hypotheses,
Biomechanics and Modeling in mechanobiology, Vol.
1, pp. 5-16, 2002, with Sharon Lubkin.
53.
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.
54.
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.
55.
Maximum
Principle Preserving Schemes for Interface Problems with Discontinuous
Coefficients, SIAM J. Sci. Comput. 23, No.1,
pp. 339-361, 2001, with K. Ito
56.
Immersed
Interface Method for the Navier-Stokes Equations with
Singular Forces, J. of Comput.
Physics, 171, 822-842 (2001), with M.
Lai.
57.
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.
58.
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.
59.
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
60.
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.
61.
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.
62.
New
Cartesian grid methods for interface problems using the finite element
formulation, Numerische Mathematik,
96:61-98, 2003, also, NCSU CRSC-TR99-5, 1999, with T. Lin,
and X. Wu.
63.
A
numerical method for solving heat equations involving interfaces, Electron. J.
Diff. Eqns., Conf. 03, 1999, pp. 100-108, with Y. Shen.
64.
The
immersed finite volume element methods for the elliptic interface problems, Mathematicsand Computers In
Simulation, (50)1-4 (1999) pp. 43-61, with R. E. Ewing, T.
Lin, and Y. Lin
65.
A
fast iterative algorithm for elliptic interface problems. SIAM J. Numer. Anal. 35:230--254, 1998.
66.
The
immersed interface method using a finite element formulation. Applied Numer. Math. 27:253--267, 1998.
67.
Convergence
analysis of the immersed interface method. IMA J. Numer.
Anal., 19:583-608, 1999, with H. Hunag.
68.
Fast
and Accurate Numerical Approaches for Stefan Problems and Crystal Growth.
Numerical Heat Transfer, Part B: Fundamentals,35: 461-484, 1999,
with B. Soni
69.
Theoretical
and numerical analysis on a thermo-elastic system with discontinuities. J. of Comput. Appl. Math. 91:1--22, 1998, with J. Zou.
70.
Crack
jump conditions for elliptic problems, Applied Math. Letters,12(6):81--88,
1999, with A. Wiegmann and R. LeVeque.
71.
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
72.
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. Zhao.
73.
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.
74.
Immersed
interface method for {S}tokes flow with elastic
boundaries or surface tension. SIAM J. Sci. Comput. 18:709--735,
1997, with R. J. LeVeque.
75.
Immersed
interface method for moving interface problems. Numerical Algorithms,
14:269-293, 1997
76.
A
note on immersed interface methods for three dimensional elliptic equations.
Computers Math. Appl. 31:9--17, 1996.
77.
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
78.
The
Immersed Interface Method --- A Numerical Approach for Partial Differential
Equations with Interfaces, PhD thesis, University of Washington, 1994.
79.
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
80.
Erratum:
"The immersed interface method for elliptic equations with discontinuous
coefficients and singular sources", SIAM J.
Numer. Anal. 32:1704, 1995, with
81.
ADI
methods for heat equations with discontinuties along
an arbitrary interface. Proc. Symp. Appl. Math. W. Gautschi, editor, 48,
311--315. AMS, 1993, with A. Mayo
82.
Perturbation
theorems of eigenvectors. Numer. Math., a
Journal of Chinese Universities, 12(1990), No.3, pp. 284--289, with K.
Huang.
83.
Uniform
treatment of linear systems -- algorithm and numerical stability. Numer. Comput. Appl. 2: 71-86,
1989.
84.
A
generalized conjugate gradient method for solving real
skew-symmetric systems. J. on Numer. Methods
& Comput. Appl., 8(1987), No.4, pp. 31--37.
85.
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
86.
Roundoff error analysis for polynomial
interpolation. Research and Review in Mathematics, 1989, No. 2, with K.
Huang.
87.
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.
88.
Optimal
conjugate gradient method for solving arbitrary linear equations. J. of Nanjing
Normal University. 1988, No. 3, pp. 28--34.
89.
Round-off
error analysis for a class of congugate gradient
methods with restarting. J. of Nanjing Normal University. 1986, No. 1,
pp. 26--34.
90.
The
effect of deflation on the condition number of zeros of polynomials. J. of
Nanjing Normal University. 1986, No. 2, pp. 31--37.