2020 journal article

How to obtain an accurate gradient for interface problems?

*Journal of Computational Physics*, *405*, 109070.

Source: ORCID

Added: November 1, 2019

2019 journal article

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

*NUMERICAL ALGORITHMS*, *80*(3), 709–740.

Sources: Web Of Science, ORCID

Added: April 2, 2019

2019 article

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

*INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING*.

Sources: Web Of Science, ORCID

Added: August 26, 2019

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.

Sources: Web Of Science, ORCID

Added: April 20, 2020

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).

Sources: Web Of Science, ORCID

Added: November 18, 2019

2019 journal article

Numerical Validations of the Tangent Linear Model for the Lorenz Equations

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

Sources: Web Of Science, ORCID

Added: August 5, 2019

2019 journal article

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

*JOURNAL OF CLEANER PRODUCTION*, *238*.

Sources: Web Of Science, ORCID

Added: October 14, 2019

2018 journal article

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

*Computers & Fluids*, *172*, 549–563.

Sources: NC State University Libraries, ORCID

Added: October 19, 2018

2018 journal article

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

*Applied Numerical Mathematics*, *130*, 112–130.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2018 journal article

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

*Computers & Fluids*, *167*, 384–399.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2018 journal article

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

*Applied Mathematics Letters*, *83*, 207–211.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2018 book

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

New York: Cambridge University Press.

Source: NC State University Libraries

Added: August 6, 2018

2018 journal article

ON MULTISCALE ADI METHODS FOR PARABOLIC PDEs WITH A DISCONTINUOUS COEFFICIENT

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

Sources: NC State University Libraries, ORCID

Added: January 7, 2019

2017 journal article

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

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

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.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2017 journal article

Accurate gradient computations at interfaces using finite element methods

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2017 journal article

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

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

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.

Source: NC State University Libraries

Added: August 6, 2018

2017 journal article

An augmented method for 4th order PDEs with discontinuous coefficients

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

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.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

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.

Sources: Crossref, ORCID

Added: February 19, 2020

2016 journal article

A new augmented immersed finite element method without using SVD interpolations

*Numerical Algorithms*, *71*(2), 395–416.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2016 journal article

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

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

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.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

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.

Source: NC State University Libraries

Added: August 6, 2018

2016 journal article

Augmented immersed finite element methods for some elliptic partial differential equations

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2016 journal article

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

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

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.

Source: NC State University Libraries

Added: August 6, 2018

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.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

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.

Source: NC State University Libraries

Added: August 6, 2018

2015 journal article

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

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

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.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

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.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2015 journal article

Effective matrix-free preconditioning for the augmented immersed interface method

*Journal of Computational Physics*, *303*, 295–312.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2015 journal article

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

*Journal of Computational Physics*, *298*, 305–319.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2015 journal article

Some new analysis results for a class of interface problems

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

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.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

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.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2014 journal article

A symmetric and consistent immersed finite element method for interface problems

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2014 journal article

Special issue on fluid structure interactions preface

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

Source: NC State University Libraries

Added: August 6, 2018

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.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2013 journal article

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

*Computers and Structures*, *122*, 249–258.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

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.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2013 journal article

Exploring accurate Poisson-Boltzmann methods for biomolecular simulations

*Computational and Theoretical Chemistry*, *1024*, 34–44.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2013 journal article

Numerical Poisson-Boltzmann model for continuum membrane systems

*Chemical Physics Letters*, *555*, 274–281.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2013 journal article

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

*Risk Analysis*, *33*(3), 469–479.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2012 journal article

A numerical method for solving elasticity equations with interfaces

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2012 journal article

An adaptive mesh refinement strategy for immersed boundary/interface methods

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2012 journal article

An augmented immersed interface method for moving structures with mass

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

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.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

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.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2012 journal article

Special issue on fluid motion driven by immersed structures preface

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

Source: NC State University Libraries

Added: August 6, 2018

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.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

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.

Source: NC State University Libraries

Added: August 6, 2018

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.

Source: NC State University Libraries

Added: August 6, 2018

2011 journal article

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

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

Source: NC State University Libraries

Added: August 6, 2018

2011 journal article

Numerical study of surfactant-laden drop-drop interactions

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2011 journal article

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

*Numerical Algorithms*, *57*(3), 405–423.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2010 journal article

An augmented method for free boundary problems with moving contact lines

*Computers & Fluids*, *39*(6), 1033–1040.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

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.

Source: NC State University Libraries

Added: August 6, 2018

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.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2009 journal article

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

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

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.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

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.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2009 conference paper

Analysis and computation for a fluid mixture model

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

Source: NC State University Libraries

Added: August 6, 2018

2009 book

Interface problems and methods in biological and physical flows

New Jersey: World Scientific.

Source: NC State University Libraries

Added: August 6, 2018

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.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

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.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

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.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

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.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2008 journal article

Mechanics of mesenchymal contribution to clefting force in branching morphogenesis

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2007 journal article

A finite difference method and analysis for 2D nonlinear Poisson-Boltzmann equations

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2007 journal article

A study of numerical methods for the level set approach

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2007 journal article

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

*Computers & Fluids*, *36*(3), 622–635.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

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.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

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.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2006 journal article

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

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

Source: NC State University Libraries

Added: August 6, 2018

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.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2006 journal article

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

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2006 book

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2005 journal article

A level-set method for interfacial flows with surfactant

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

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.

Source: NC State University Libraries

Added: August 6, 2018

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.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2004 journal article

An immersed finite element space and its approximation capability

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2004 journal article

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

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2003 journal article

An overview of the immersed interface method and its applications

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2003 journal article

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

*Numerische Mathematik*, *96*(1), 61–98.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2003 journal article

New formulations for interface problems in polar coordinates

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

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.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

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.

Source: NC State University Libraries

Added: August 6, 2018

2003 journal article

Three-dimensional elliptic solvers for interface problems and applications

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2002 journal article

Force and deformation on branching rudiments: Cleaving between hypotheses

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2002 journal article

Reactive autophobic spreading of drops

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2002 journal article

The immersed interface/multigrid methods for interface problems

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2001 chapter

A level set-boundary element method for simulation of dynamic powder consolidation of metals

In *Numerical analysis and its applications: Second international conference, NAA 2000, Rousse, Bulgaria, June 11-15, 2000: Revised papers* (Vol. 1988, pp. 527–534). Berlin; New York: Springer.

Source: NC State University Libraries

Added: August 6, 2018

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.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2001 journal article

Level-set function approach to an inverse interface problem

*Inverse Problems*, *17*(5), 1225–1242.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2001 journal article

Maximum principle preserving schemes for interface problems with discontinuous coefficients

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

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.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

2001 journal article

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

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

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.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

1999 journal article

Convergence analysis of the immersed interface method

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

1999 journal article

Crack jump conditions for elliptic problems

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

1999 journal article

Fast and accurate numerical approaches for Stefan problems and crystal growth

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

1999 journal article

The immersed finite volume element methods for the elliptic interface problems

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

1999 journal article

Types of reductive monoids

*Journal of Algebra*, *221*(1), 102–116.

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

1998 journal article

A fast iterative algorithm for elliptic interface problems

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018

1998 journal article

The immersed interface method using a finite element formulation

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

Sources: NC State University Libraries, ORCID

Added: August 6, 2018