2021 journal article
Non-parallel hyperplanes ordinal regression machine
Knowledge-Based Systems, 11, 106593.
2021 journal article
Partially penalized IFE methods and convergence analysis for elasticity interface problems
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 382.
2021 journal article
Partially penalized IFE methods and convergence analysis for elasticity interface problems
Journal of Computational and Applied Mathematics.
2021 journal article
The local tangential lifting method for moving interface problems on surfaces with applications
Journal of Computational Physics, 431, 110146.
2020 journal article
AN FE-FD METHOD FOR ANISOTROPIC ELLIPTIC INTERFACE PROBLEMS
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 42(4), B1041–B1066.
2020 journal article
How to obtain an accurate gradient for interface problems?
Journal of Computational Physics, 405, 109070.
2019 journal article
A direct method for accurate solution and gradient computations for elliptic interface problems
NUMERICAL ALGORITHMS, 80(3), 709–740.
2019 article
A gradient recovery-based adaptive finite element method for convection-diffusion-reaction equations on surfaces
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING.
2019 journal article
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.
2019 journal article
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).
2019 book
Introduction to Partial Differential Equations
2019 journal article
Numerical Validations of the Tangent Linear Model for the Lorenz Equations
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 120(1), 83–104.
2019 journal article
Spatiotemporal characteristics of green travel: A classification study on a public bicycle system
JOURNAL OF CLEANER PRODUCTION, 238.
2018 journal article
A direct IIM approach for two-phase Stokes equations with discontinuous viscosity on staggered grids
Computers & Fluids, 172, 549–563.
2018 journal article
A high-order source removal finite element method for a class of elliptic interface problems
Applied Numerical Mathematics, 130, 112–130.
2018 journal article
A least squares augmented immersed interface method for solving Navier–Stokes and Darcy coupling equations
Computers & Fluids, 167, 384–399.
2018 journal article
Error analysis of the immersed interface method for Stokes equations with an interface
Applied Mathematics Letters, 83, 207–211.
2018 book
Numerical solution of differential equations: Introduction to finite difference and finite element methods
New York: Cambridge University Press.
2018 journal article
ON MULTISCALE ADI METHODS FOR PARABOLIC PDEs WITH A DISCONTINUOUS COEFFICIENT
MULTISCALE MODELING & SIMULATION, 16(4), 1623–1647.
2017 journal article
A Cartesian grid nonconforming immersed finite element method for planar elasticity interface problems
Computers & Mathematics With Applications, 73(3), 404–418.
2017 journal article
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.
2017 journal article
Accurate gradient computations at interfaces using finite element methods
International Journal of Applied Mathematics and Computer Science, 27(3), 527–537.
2017 journal article
Accurate solution and gradient computation for elliptic interface problems with variable coefficients
SIAM Journal on Numerical Analysis, 55(2), 570–597.
2017 journal article
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.
2017 journal article
An augmented method for 4th order PDEs with discontinuous coefficients
Journal of Scientific Computing, 73(2-3), 968–979.
2017 journal article
New conservative finite volume element schemes for the modified regularized long wave equation
Advances in Applied Mathematics & Mechanics, 9(2), 250–271.
2017 book
Numerical Solution of Differential Equations
In Cambridge University Press.
2017 journal article
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.
2016 journal article
A new augmented immersed finite element method without using SVD interpolations
Numerical Algorithms, 71(2), 395–416.
2016 journal article
A sparse grid stochastic collocation method for elliptic interface problems with random input
Journal of Scientific Computing, 67(1), 262–280.
2016 journal article
An augmented Cartesian grid method for Stokes-Darcy fluid-structure interactions
International Journal for Numerical Methods in Engineering, 106(7), 556–575.
2016 journal article
An augmented iim for helmholtz/poisson equations on irregular domains in complex space
International Journal of Numerical Analysis and Modeling, 13(1), 166–178.
2016 journal article
Augmented immersed finite element methods for some elliptic partial differential equations
International Journal of Computer Mathematics, 93(3), 540–558.
2016 journal article
Fine numerical analysis of the crack-tip position for a Mumford-Shah minimizer
Interfaces and Free Boundaries, 18(1), 75–90.
2016 journal article
Fourth-order compact schemes for Helmholtz equations with piecewise wave numbers in the polar coordinates
Journal of Computational Mathematics, 34(5), 499–510.
2016 journal article
Prioritization of pesticides based on daily dietary exposure potential as determined from the SHEDS model
Food and Chemical Toxicology, 96, 167–173.
2016 journal article
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.
2015 journal article
A parallel Robin-Robin domain decomposition method for H(div)-elliptic problems
International Journal of Computer Mathematics, 92(2), 394–410.
2015 journal article
A semi-implicit augmented IIM for Navier-Stokes equations with open, traction, or free boundary conditions
Journal of Computational Physics, 297, 182–193.
2015 journal article
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.
2015 journal article
Effective matrix-free preconditioning for the augmented immersed interface method
Journal of Computational Physics, 303, 295–312.
2015 journal article
Immersed finite elements for optimal control problems of elliptic PDEs with interfaces
Journal of Computational Physics, 298, 305–319.
2015 journal article
Some new analysis results for a class of interface problems
Mathematical Methods in the Applied Sciences, 38(18), 4530–4539.
2015 journal article
The immersed interface method for axis-symmetric problems and application to the Hele-Shaw flow
Applied Mathematics and Computation, 264, 179–197.
2014 journal article
A coupled immersed interface and level set method for three-dimensional interfacial flows with insoluble surfactant
Communications in Computational Physics, 15(2), 451–469.
2014 journal article
A symmetric and consistent immersed finite element method for interface problems
Journal of Scientific Computing, 61(3), 533–557.
2014 journal article
On convergence of the immersed boundary method for elliptic interface problems
Mathematics of Computation, 84(293), 1169–1188.
2014 journal article
Special issue on fluid structure interactions preface
Numerical Mathematics: Theory, Methods and Applications, 7(4), I-.
2013 journal article
A Fourier finite volume element method for solving two-dimensional quasi-geostrophic equations on a sphere
Applied Numerical Mathematics, 71, 1–13.
2013 journal article
Adaptive mesh refinement techniques for the immersed interface method applied to flow problems
Computers and Structures, 122, 249–258.
2013 journal article
Exploring a charge-central strategy in the solution of Poisson's equation for biomolecular applications
Physical Chemistry Chemical Physics, 15(1), 129–141.
2013 journal article
Exploring accurate Poisson-Boltzmann methods for biomolecular simulations
Computational and Theoretical Chemistry, 1024, 34–44.
2013 journal article
Numerical Poisson-Boltzmann model for continuum membrane systems
Chemical Physics Letters, 555, 274–281.
2013 journal article
Simulation of longitudinal exposure data with variance-covariance structures based on mixed models
Risk Analysis, 33(3), 469–479.
2012 journal article
A numerical method for solving elasticity equations with interfaces
Communications in Computational Physics, 12(2), 595–612.
2012 journal article
An adaptive mesh refinement strategy for immersed boundary/interface methods
Communications in Computational Physics, 12(2), 515–527.
2012 journal article
An augmented immersed interface method for moving structures with mass
Discrete and Continuous Dynamical Systems-Series B, 17(4), 1175–1184.
2012 journal article
Numerical solutions of the system of singular integro-differential equations in classical holder spaces
Advances in Applied Mathematics & Mechanics, 4(6), 737–750.
2012 book
SPECIAL ISSUE ON FLUID DYNAMICS, ANALYSIS AND NUMERICS
2012 journal article
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.
2012 book
Special Issue on Fluid Motion Driven by Immersed Structures
In Global Sciences.
2012 journal article
Special issue on fluid motion driven by immersed structures preface
Communications in Computational Physics, 12(2), I-.
2012 journal article
The sensitivity analysis for the flow past obstacles problem with respect to the reynolds number
Advances in Applied Mathematics & Mechanics, 4(1), 21–35.
2011 journal article
A finite element method for elasticity interface problems with locally modified triangulations
International Journal of Numerical Analysis and Modeling, 8(2), 189–200.
2011 journal article
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.
2011 journal article
High order compact finite difference schemes for the helmholtz equation with discontinuous coefficients
Journal of Computational Mathematics, 29(3), 324–340.
2011 journal article
Numerical study of surfactant-laden drop-drop interactions
Communications in Computational Physics, 10(2), 453–473.
2011 journal article
The IIM in polar coordinates and its application to electro capacitance tomography problems
Numerical Algorithms, 57(3), 405–423.
2010 journal article
An augmented method for free boundary problems with moving contact lines
Computers & Fluids, 39(6), 1033–1040.
2010 journal article
Immersed Interface Finite Element Methods for Elasticity Interface Problems with Non-Homogeneous Jump Conditions
Numerical Mathematics: Theory, Methods and Applications, 3(1), 23–39.
2009 journal article
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.
2009 journal article
A well-conditioned augmented system for solving Navier-Stokes equations in irregular domains
Journal of Computational Physics, 228(7), 2616–2628.
2009 journal article
Achieving energy conservation in Poisson-Boltzmann molecular dynamics: Accuracy and precision with finite-difference algorithms
Chemical Physics Letters, 468(4-6), 112–118.
2009 journal article
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.
2009 conference paper
Analysis and computation for a fluid mixture model
Communications in Computational Physics, 5(2-4), 620–634.
2009 book
Interface Problems and Methods in Biological and Physical Flows
In WORLD SCIENTIFIC.
2009 book
Interface problems and methods in biological and physical flows
New Jersey: World Scientific.
2008 journal article
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.
2008 conference paper
A finite element method for interface problems with locally modified triangulations
Moving interface problems and applications in fluid dynamics, 466, 179–190.
2008 journal article
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.
2008 journal article
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.
2008 journal article
Mechanics of mesenchymal contribution to clefting force in branching morphogenesis
Biomechanics and Modeling in Mechanobiology, 7(5), 417–426.
2007 journal article
A finite difference method and analysis for 2D nonlinear Poisson-Boltzmann equations
Journal of Scientific Computing, 30(1), 61–81.
2007 journal article
A study of numerical methods for the level set approach
Applied Numerical Mathematics, 57(5-7), 837–846.
2007 journal article
An augmented approach for Stokes equations with a discontinuous viscosity and singular forces
Computers & Fluids, 36(3), 622–635.
2007 journal article
Immersed-interface finite-element methods for elliptic interface problems with nonhomogeneous jump conditions
SIAM Journal on Numerical Analysis, 46(1), 472–495.
2007 book
Moving Interface Problems and Applications in Fluid Dynamics
In AMS Contemporary mathematics 466.
2007 journal article
Preface of the special issue of APNUM - International Conference on Scientific Computing in Nanjing, China
Applied Numerical Mathematics, 57(5-7), 473–474.
2007 book
Special Issue for the International Conference on Scientific Computing
2006 journal article
An augmented approach for the pressure boundary condition in a Stokes flow
Communications in Computational Physics, 1(5), 874–885.
2006 journal article
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.
2006 journal article
Interface conditions for Stokes equations with a discontinuous viscosity and surface sources
Applied Mathematics Letters, 19(3), 229–234.
2006 book
The immersed interface method: Numerical solutions of PDEs involving interfaces and irregular domains
2005 journal article
A level-set method for interfacial flows with surfactant
Journal of Computational Physics, 212(2), 590–616.
2005 chapter
Augmented strategies for interface and irregular domain problems
In Numerical analysis and its applications: Third international conference, NAA 2004, Rousse, Bulgaria, June 29-July 3, 2004: Revised selected papers (Lecture notes in computer science ; 3401) (Vol. 3401, pp. 66–79). Berlin; New York: Springer.
2005 journal article
Higher-order, Cartesian grid based finite difference schemes for elliptic equations on irregular domains
SIAM Journal on Scientific Computing, 27(1), 346–367.
2004 journal article
An immersed finite element space and its approximation capability
Numerical Methods for Partial Differential Equations, 20(3), 338–367.
2004 journal article
Approximate solution of singular integro-differential equations by reduction over Faber-Laurent polynomials
Differential Equations, 40(12), 1764–1769.
2003 journal article
An overview of the immersed interface method and its applications
Taiwanese Journal of Mathematics, 7(1), 1–49.
2003 journal article
New Cartesian grid methods for interface problems using the finite element formulation
Numerische Mathematik, 96(1), 61–98.
2003 journal article
New formulations for interface problems in polar coordinates
SIAM Journal on Scientific Computing, 25(1), 224–245.
2003 journal article
Solving a nonlinear problem in magneto-rheological fluids using the immersed interface method
Journal of Scientific Computing, 19(03-Jan), 253–266.
2003 journal article
The immersed interface method for elasticity problems with interfaces
Dynamics of Continuous, Discrete & Impulsive Systems. Series A, Mathematical Analysis, 10(5), 783–808.
2003 journal article
Three-dimensional elliptic solvers for interface problems and applications
Journal of Computational Physics, 184(1), 215–243.
2002 journal article
Force and deformation on branching rudiments: Cleaving between hypotheses
Biomechanics and Modeling in Mechanobiology, 1(1), 5–16.
2002 journal article
Reactive autophobic spreading of drops
Journal of Computational Physics, 183(2), 335–366.
2002 journal article
The immersed interface/multigrid methods for interface problems
SIAM Journal on Scientific Computing, 24(2), 463–479.
2001 chapter
A Level Set-Boundary Element Method for Simulation of Dynamic Powder Consolidation of Metals
In Lecture Notes in Computer Science (Vol. 1988, pp. 527–534).
2001 journal article
A remark on jump conditions for the three-dimensional Navier-Stokes equations involving an immersed moving membrane
Applied Mathematics Letters, 14(2), 149–154.
2001 journal article
Level-set function approach to an inverse interface problem
Inverse Problems, 17(5), 1225–1242.
2001 journal article
Maximum principle preserving schemes for interface problems with discontinuous coefficients
SIAM Journal on Scientific Computing, 23(1), 339–361.
2001 journal article
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.
2001 journal article
The immersed interface method for the Navier-Stokes equations with singular forces
Journal of Computational Physics, 171(2), 822–842.
1999 journal article
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.
1999 journal article
Convergence analysis of the immersed interface method
IMA Journal of Numerical Analysis, 19(4), 583–608.
1999 journal article
Crack jump conditions for elliptic problems
Applied Mathematics Letters, 12(6), 81–88.
1999 journal article
Fast and accurate numerical approaches for Stefan problems and crystal growth
Numerical Heat Transfer. Part B, Fundamentals, 35(4), 461–484.
1999 journal article
The immersed finite volume element methods for the elliptic interface problems
Mathematics and Computers in Simulation, 50(1-4), 63–76.
1999 journal article
Types of reductive monoids
Journal of Algebra, 221(1), 102–116.
1998 journal article
A fast iterative algorithm for elliptic interface problems
SIAM Journal on Numerical Analysis, 35(1), 230–254.
1998 journal article
The immersed interface method using a finite element formulation
Applied Numerical Mathematics, 27(3), 253–267.
1997 journal article
A Hybrid Method for Moving Interface Problems with Application to the Hele–Shaw Flow
Journal of Computational Physics, 134(2), 236–252.
1996 journal article
A note on immersed interface method for three-dimensional elliptic equations
Computers & Mathematics with Applications, 31(3), 9–17.
1994 journal article
The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
SIAM Journal on Numerical Analysis, 31(4), 1019–1044.
book
Industrial Mathematics
In SIAM, USA.
book
Numerical Analysis and Its Applications
1997 - present
1994 - 1996