Zhilin Li

A new FV scheme and fast cell-centered multigrid solver for 3D anisotropic diffusion equations with discontinuous coefficients

JOURNAL OF COMPUTATIONAL PHYSICS, 449, 110794.

A High Order Compact FD Framework for Elliptic BVPs Involving Singular Sources, Interfaces, and Irregular Domains

JOURNAL OF SCIENTIFIC COMPUTING, 88(3).

A generalized modulus-based Newton method for solving a class of non-linear complementarity problems with P-matrices

Li, R., Li, Z.-L., & Yin, J.-F. (2021, June 3). NUMERICAL ALGORITHMS, Vol. 6.

Acceleration Technique for the Augmented IIM for 3D Elliptic Interface Problems

NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 8.

An ADI-Yee's scheme for Maxwell's equations with discontinuous coefficients

JOURNAL OF COMPUTATIONAL PHYSICS, 438, 110356.

Fourth order compact FD methods for convection diffusion equations with variable coefficients

APPLIED MATHEMATICS LETTERS, 121, 107413.

Non-parallel hyperplanes ordinal regression machine

KNOWLEDGE-BASED SYSTEMS, 216, 106593.

Optimal convergence of three iterative methods based on nonconforming finite element discretization for 2D/3D MHD equations

Xu, J., Su, H., & Li, Z. (2021, November 13). NUMERICAL ALGORITHMS, Vol. 11.

Partially penalized IFE methods and convergence analysis for elasticity interface problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 382.

Partially penalized IFE methods and convergence analysis for elasticity interface problems

Journal of Computational and Applied Mathematics.

Quadratic hyper-surface kernel-free least squares support vector regression

INTELLIGENT DATA ANALYSIS, 25(2), 265–281.

The local tangential lifting method for moving interface problems on surfaces with applications

JOURNAL OF COMPUTATIONAL PHYSICS, 431, 110146.

AN FE-FD METHOD FOR ANISOTROPIC ELLIPTIC INTERFACE PROBLEMS

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 42(4), B1041–B1066.

How to obtain an accurate gradient for interface problems?

Journal of Computational Physics, 405, 109070.

A direct method for accurate solution and gradient computations for elliptic interface problems

NUMERICAL ALGORITHMS, 80(3), 709–740.

A gradient recovery-based adaptive finite element method for convection-diffusion-reaction equations on surfaces

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING.

An Augmented IB Method & Analysis for Elliptic BVP on Irregular Domains

An Augmented IB Method & Analysis for Elliptic BVP on Irregular Domains. CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 119(1), 63–72.

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).

Introduction to Partial Differential Equations

Numerical Validations of the Tangent Linear Model for the Lorenz Equations

CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 120(1), 83–104.

Spatiotemporal characteristics of green travel: A classification study on a public bicycle system

JOURNAL OF CLEANER PRODUCTION, 238.

A direct IIM approach for two-phase Stokes equations with discontinuous viscosity on staggered grids

Computers & Fluids, 172, 549–563.

A high-order source removal finite element method for a class of elliptic interface problems

Applied Numerical Mathematics, 130, 112–130.

A least squares augmented immersed interface method for solving Navier–Stokes and Darcy coupling equations

Computers & Fluids, 167, 384–399.

Error analysis of the immersed interface method for Stokes equations with an interface

Applied Mathematics Letters, 83, 207–211.

Numerical solution of differential equations: Introduction to finite difference and finite element methods

New York: Cambridge University Press.

ON MULTISCALE ADI METHODS FOR PARABOLIC PDEs WITH A DISCONTINUOUS COEFFICIENT

MULTISCALE MODELING & SIMULATION, 16(4), 1623–1647.

A Cartesian grid nonconforming immersed finite element method for planar elasticity interface problems

Computers & Mathematics With Applications, 73(3), 404–418.

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.

Accurate gradient computations at interfaces using finite element methods

International Journal of Applied Mathematics and Computer Science, 27(3), 527–537.

Accurate solution and gradient computation for elliptic interface problems with variable coefficients

SIAM Journal on Numerical Analysis, 55(2), 570–597.

An augmented IIM & preconditioning technique for jump embedded boundary conditions

An augmented IIM & preconditioning technique for jump embedded boundary conditions. International Journal of Numerical Analysis and Modeling, 14(4-5), 712–729.

An augmented method for 4th order PDEs with discontinuous coefficients

Journal of Scientific Computing, 73(2-3), 968–979.

New conservative finite volume element schemes for the modified regularized long wave equation

Advances in Applied Mathematics & Mechanics, 9(2), 250–271.

Numerical Solution of Differential Equations

In Cambridge University Press.

On an New Algorithm for Function Approximation with Full Accuracy in the Presence of Discontinuities Based on the Immersed Interface Method

Journal of Scientific Computing, 75(3), 1500–1534.

A new augmented immersed finite element method without using SVD interpolations

Numerical Algorithms, 71(2), 395–416.

A sparse grid stochastic collocation method for elliptic interface problems with random input

Journal of Scientific Computing, 67(1), 262–280.

An augmented Cartesian grid method for Stokes-Darcy fluid-structure interactions

International Journal for Numerical Methods in Engineering, 106(7), 556–575.

An augmented iim for helmholtz/poisson equations on irregular domains in complex space

International Journal of Numerical Analysis and Modeling, 13(1), 166–178.

Augmented immersed finite element methods for some elliptic partial differential equations

International Journal of Computer Mathematics, 93(3), 540–558.

Fine numerical analysis of the crack-tip position for a Mumford-Shah minimizer

Interfaces and Free Boundaries, 18(1), 75–90.

Fourth-order compact schemes for Helmholtz equations with piecewise wave numbers in the polar coordinates

Journal of Computational Mathematics, 34(5), 499–510.

Prioritization of pesticides based on daily dietary exposure potential as determined from the SHEDS model

Food and Chemical Toxicology, 96, 167–173.

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.

A parallel Robin-Robin domain decomposition method for H(div)-elliptic problems

International Journal of Computer Mathematics, 92(2), 394–410.

A semi-implicit augmented IIM for Navier-Stokes equations with open, traction, or free boundary conditions

Journal of Computational Physics, 297, 182–193.

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.

Effective matrix-free preconditioning for the augmented immersed interface method

Journal of Computational Physics, 303, 295–312.

Immersed finite elements for optimal control problems of elliptic PDEs with interfaces

Journal of Computational Physics, 298, 305–319.

Some new analysis results for a class of interface problems

Mathematical Methods in the Applied Sciences, 38(18), 4530–4539.

The immersed interface method for axis-symmetric problems and application to the Hele-Shaw flow

Applied Mathematics and Computation, 264, 179–197.

A coupled immersed interface and level set method for three-dimensional interfacial flows with insoluble surfactant

Communications in Computational Physics, 15(2), 451–469.

A multi-scale method for dynamics simulation in continuum solvent models. I: Finite-difference algorithm for Navier–Stokes equation

Chemical Physics Letters, 616-617, 67–74.

A symmetric and consistent immersed finite element method for interface problems

Journal of Scientific Computing, 61(3), 533–557.

On convergence of the immersed boundary method for elliptic interface problems

Mathematics of Computation, 84(293), 1169–1188.

Special issue on fluid structure interactions preface

Numerical Mathematics: Theory, Methods and Applications, 7(4), I-.

A Fourier finite volume element method for solving two-dimensional quasi-geostrophic equations on a sphere

Applied Numerical Mathematics, 71, 1–13.

Adaptive mesh refinement techniques for the immersed interface method applied to flow problems

Computers and Structures, 122, 249–258.

Exploring a charge-central strategy in the solution of Poisson's equation for biomolecular applications

Physical Chemistry Chemical Physics, 15(1), 129–141.

Exploring accurate Poisson-Boltzmann methods for biomolecular simulations

Computational and Theoretical Chemistry, 1024, 34–44.

Numerical Poisson-Boltzmann model for continuum membrane systems

Chemical Physics Letters, 555, 274–281.

Simulation of longitudinal exposure data with variance-covariance structures based on mixed models

Risk Analysis, 33(3), 469–479.

A numerical method for solving elasticity equations with interfaces

Communications in Computational Physics, 12(2), 595–612.

An adaptive mesh refinement strategy for immersed boundary/interface methods

Communications in Computational Physics, 12(2), 515–527.

An augmented immersed interface method for moving structures with mass

Discrete and Continuous Dynamical Systems-Series B, 17(4), 1175–1184.

Discrete and Continuous Dynamical Systems, Series B: Mathematical Modeling, Analysis and Computations

(Vol. 17) [Special Issue dedicated to Thomas Beale and the FAN conference].

Numerical solutions of the system of singular integro-differential equations in classical holder spaces

Advances in Applied Mathematics & Mechanics, 4(6), 737–750.

SPECIAL ISSUE ON FLUID DYNAMICS, ANALYSIS AND NUMERICS

Simplified immersed interface methods for elliptic interface problems with straight interfaces

Numerical Methods for Partial Differential Equations, 28(1), 188–203.

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.

Special Issue on Fluid Motion Driven by Immersed Structures

In Global Sciences.

Special issue on fluid motion driven by immersed structures preface

Communications in Computational Physics, 12(2), I-.

The sensitivity analysis for the flow past obstacles problem with respect to the reynolds number

Advances in Applied Mathematics & Mechanics, 4(1), 21–35.

A finite element method for elasticity interface problems with locally modified triangulations

International Journal of Numerical Analysis and Modeling, 8(2), 189–200.

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.

High order compact finite difference schemes for the helmholtz equation with discontinuous coefficients

Journal of Computational Mathematics, 29(3), 324–340.

Numerical study of surfactant-laden drop-drop interactions

Communications in Computational Physics, 10(2), 453–473.

The IIM in polar coordinates and its application to electro capacitance tomography problems

Numerical Algorithms, 57(3), 405–423.

An augmented method for free boundary problems with moving contact lines

Computers & Fluids, 39(6), 1033–1040.

Immersed Interface Finite Element Methods for Elasticity Interface Problems with Non-Homogeneous Jump Conditions

Numerical Mathematics: Theory, Methods and Applications, 3(1), 23–39.

A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations

Journal of Computational Physics, 228(20), 7821–7836.

A well-conditioned augmented system for solving Navier-Stokes equations in irregular domains

Journal of Computational Physics, 228(7), 2616–2628.

Achieving energy conservation in Poisson-Boltzmann molecular dynamics: Accuracy and precision with finite-difference algorithms

Chemical Physics Letters, 468(4-6), 112–118.

An additive Schwarz preconditioner for the mortar-type rotated Q(1) FEM for elliptic problems with discontinuous coefficients

Applied Numerical Mathematics, 59(7), 1657–1667.

Analysis and computation for a fluid mixture model

Communications in Computational Physics, 5(2-4), 620–634.

Interface Problems and Methods in Biological and Physical Flows

In B. C. Khoo, Z. Li, & P. Lin (Eds.), WORLD SCIENTIFIC.

Interface problems and methods in biological and physical flows

New Jersey: World Scientific.

A fast finite difference method for biharmonic equations on irregular domains and its application to an incompressible Stokes flow

Advances in Computational Mathematics, 29(2), 113–133.

A finite element method for interface problems with locally modified triangulations

Moving interface problems and applications in fluid dynamics, 466, 179–190.

An explicit jump immersed interface method for two-phase Navier-Stokes equations with interfaces

Computer Methods in Applied Mechanics and Engineering, 197(25-28), 2317–2328.

An immersed interface method for solving incompressible viscous flows with piecewise constant viscosity across a moving elastic membrane

Journal of Computational Physics, 227(23), 9955–9983.

Mechanics of mesenchymal contribution to clefting force in branching morphogenesis

Biomechanics and Modeling in Mechanobiology, 7(5), 417–426.

A Finite Difference Method and Analysis for 2D Nonlinear Poisson–Boltzmann Equations

Journal of Scientific Computing, 30(1), 61–81.

A study of numerical methods for the level set approach

Applied Numerical Mathematics, 57(5-7), 837–846.

An augmented approach for Stokes equations with a discontinuous viscosity and singular forces

Computers & Fluids, 36(3), 622–635.

An augmented immersed interface-level set method for Stokes equations with discontinuous viscosity

Electronic Journal of Differential Equations, Conference, 15, 193–210.

An immersed interface method for the Navier-Stokes equations on irregular domains

PAMM, 7(1), 1025401–1025402.

Applied Numerical Mathematics for the International Conference on Scientific Computing

In Contemporary Mathematics (Vol. 57) [Special Issues]. American Mathematical Society.

Immersed-interface finite-element methods for elliptic interface problems with nonhomogeneous jump conditions

SIAM Journal on Numerical Analysis, 46(1), 472–495.

Moving Interface Problems and Applications in Fluid Dynamics

In AMS Contemporary mathematics 466.

Preface of the special issue of APNUM - International Conference on Scientific Computing in Nanjing, China

Applied Numerical Mathematics, 57(5-7), 473–474.

Special Issue for the International Conference on Scientific Computing

An augmented approach for the pressure boundary condition in a Stokes flow

Communications in Computational Physics, 1(5), 874–885.

Efficient numerical methods for the 2D nonlinear Poisson–Boltzmann equation modeling charged spheres

Journal of Computational Mathematics, 24(3), 252–264.

Fast solvers for 3D Poisson equations involving interfaces in a finite or the infinite domain

Journal of Computational and Applied Mathematics, 191(1), 106–125.

Interface conditions for Stokes equations with a discontinuous viscosity and surface sources

Applied Mathematics Letters, 19(3), 229–234.

The immersed interface method: Numerical solutions of PDEs involving interfaces and irregular domains

A level-set method for interfacial flows with surfactant

Journal of Computational Physics, 212(2), 590–616.

Augmented Strategies for Interface and Irregular Domain Problems

In Z. Li, L. Vulkov, & J. Wasniewski (Eds.), Numerical Analysis and Its Applications (pp. 66–79).

Higher-order, Cartesian grid based finite difference schemes for elliptic equations on irregular domains

SIAM Journal on Scientific Computing, 27(1), 346–367.

Immersed finite element for elasticity system with discontinuities

AMS Contemporary Mathematics, 383, 285–298.

Numerical Analysis and Its Applications

An immersed finite element space and its approximation capability

Numerical Methods for Partial Differential Equations, 20(3), 338–367.

Approximate solution of singular integro-differential equations by reduction over Faber-Laurent polynomials

Differential Equations, 40(12), 1764–1769.

A Fast Finite Differenc Method For Solving Navier-Stokes Equations on Irregular Domains

Communications in Mathematical Sciences, 1(1), 180–196.

An overview of the immersed interface method and its applications

Taiwanese Journal of Mathematics, 7(1), 1–49.

Generalized Snell's Law for Weighted Minimal Surface in Heterogeneous Media

Methods and Applications of Analysis, 10(2), 199–214.

New Cartesian grid methods for interface problems using the finite element formulation

Numerische Mathematik, 96(1), 61–98.

New formulations for interface problems in polar coordinates

SIAM Journal on Scientific Computing, 25(1), 224–245.

Solving a nonlinear problem in magneto-rheological fluids using the immersed interface method

Journal of Scientific Computing, 19(03-Jan), 253–266.

The immersed interface method for elasticity problems with interfaces

Dynamics of Continuous, Discrete & Impulsive Systems. Series A, Mathematical Analysis, 10(5), 783–808.

Three-dimensional elliptic solvers for interface problems and applications

Journal of Computational Physics, 184(1), 215–243.

Force and deformation on branching rudiments: Cleaving between hypotheses

Biomechanics and Modeling in Mechanobiology, 1(1), 5–16.

Industrial Mathematics Modeling Workshop for Graduate Students Series

[CRSC Technical Reports].

Reactive autophobic spreading of drops

Journal of Computational Physics, 183(2), 335–366.

The immersed interface/multigrid methods for interface problems

SIAM Journal on Scientific Computing, 24(2), 463–479.

A Level Set-Boundary Element Method for Simulation of Dynamic Powder Consolidation of Metals

In J. W. L. Vulkov & P. Yalamov (Eds.), Lecture Notes in Computer Science (Vol. 1988, pp. 527–534).

A remark on jump conditions for the three-dimensional Navier-Stokes equations involving an immersed moving membrane

Applied Mathematics Letters, 14(2), 149–154.

Book Review: Generalized Difference Methods for Differential Equations

[Review of Generalized Difference Methods for Differential Equations, by Z. Chen, R. Li, & W. Wu]. SIAM Review, 43(1), 203–205,

Industrial Mathematics Modeling Workshop for Graduate Students Series

[CRSC Technical Reports].

Level-set function approach to an inverse interface problem

Inverse Problems, 17(5), 1225–1242.

Maximum principle preserving schemes for interface problems with discontinuous coefficients

SIAM Journal on Scientific Computing, 23(1), 339–361.

Numerical Method for Simulation of Bubbles Flowing Through Another Fluid

In M. Mu, Z. Shi, W. Xue, & J. Zou (Eds.), Advances in Scientific Computing (pp. 74–81). Beijing: Science Pr.

Numerical analysis of interfacial two-dimensional Stokes flow with discontinuous viscosity and variable surface tension

International Journal for Numerical Methods in Fluids, 37(5), 525–540.

The immersed interface method for the Navier-Stokes equations with singular forces

Journal of Computational Physics, 171(2), 822–842.

Industrial Mathematics

Philadelphia: SIAM.

Industrial Mathematics Modeling Workshop for Graduate Students Series

[CRSC Technical Reports].

A numerical method for solving heat equations involving interfaces

Electronic Journal of Differential Equations, 3, 100–108.

A numerical study of electro-migration voiding by evolving level set functions on a fixed cartesian grid

Journal of Computational Physics, 152(1), 281–304.

Convergence analysis of the immersed interface method

IMA Journal of Numerical Analysis, 19(4), 583–608.

Crack jump conditions for elliptic problems

Applied Mathematics Letters, 12(6), 81–88.

Fast and accurate numerical approaches for Stefan problems and crystal growth

Numerical Heat Transfer. Part B, Fundamentals, 35(4), 461–484.

Industrial Mathematics Modeling Workshop for Graduate Students series

[CRSC Technical Reports].

Numerical Study of Two Dimensional Electro-migration

Journal of Computational Physics, 152, 281–304.

The immersed finite volume element methods for the elliptic interface problems

Mathematics and Computers in Simulation, 50(1-4), 63–76.

Types of reductive monoids

Journal of Algebra, 221(1), 102–116.

A fast iterative algorithm for elliptic interface problems

SIAM Journal on Numerical Analysis, 35(1), 230–254.

The immersed interface method using a finite element formulation

Applied Numerical Mathematics, 27(3), 253–267.

Theoretical and numerical analysis on a thermo-elastic system with discontinuities

Journal of Computational and Applied Mathematics, 92(1), 37–58.

A Hybrid Method for Moving Interface Problems with Application to the Hele–Shaw Flow

Journal of Computational Physics, 134(2), 236–252.

An Inverse Problem in a Parabolic Equation

Electronic Journal of Differential Equations, 1, 193–199.

Front fixing vs. front tracking for diffusive transport with moving boundaries

International Journal for Numerical & Analytical Methods in Geomechanics, 21, 653–662.

Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension

SIAM Journal on Scientific Computing, 18(3), 709–735.

Immersed interface methods for moving interface problems

Numerical Algorithms, 14, 269–293.

A note on immersed interface method for three-dimensional elliptic equations

Computers & Mathematics with Applications, 31(3), 9–17.

Simulation of bubbles in creeping flow using the immersed interface method

Proceedings of the sixth international symposium on computational fluid dynamics, 688–693.

The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources

SIAM Journal on Numerical Analysis, 31(4), 1019–1044.

The Immersed Interface Method — A Numerical Approach for Partial Differential Equations with Interfaces

(PhD thesis). University of Washington.

ADI methods for heat equations with discontinuities along an arbitrary interface

In W. Gautschi (Ed.), Proceedings of Symposia in Applied Mathematics (Vol. 48, pp. 311–315). Providence, Rhode Island: AMS.

Perturbation theorems of eigenvectors

Numerical Mathematics, a Journal of Chinese Universities, 12(3), 284–289.

Roundoff error analysis for polynomial interpolation

Research and Review in Mathematics, (2).

The uniform treatment for linear system — Algorithm and numerical stability

Journal on Numerical Methods & Computer Applications, 10(2).

Optimal conjugate gradient method for solving arbitrary linear equations

Journal of Nanjing Normal University (Natural Science Edition), (3), 28–34.

A generalized conjugate gradient method for solving real skew-symmetric systems

Journal on Numerical Methods & Computer Applications, 8(4), 31–37.

An equivalent theorem on the numerical stability for an algorithm

Numerical Mathematics, a Journal of Chinese Universities, 9(1), 59–65.

On the relation between the behavior and the distribution of the zeros of a polynomial

Journal of Nanjing University, Mathematics Biquarterly, 2(1), 53–59.

Industrial Mathematics

In SIAM, USA.

Numerical Analysis and Its Applications