2023 journal article

An efficient extrapolation multigrid method based on a HOC scheme on nonuniform rectilinear grids for solving 3D anisotropic convection-diffusion problems

*COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING*, *403*.

author keywords: Convection-diffusion equation; Completed Richardson extrapolation; Quintic Lagrange interpolation; High-order compact scheme; Cascadic multigrid

Sources: Web Of Science, ORCID

Added: January 30, 2023

2023 journal article

Higher Order Finite Element Methods for Some One-dimensional Boundary Value Problems

*Research Reports on Computer Science*, *2*(1), 15–27.

Source: ORCID

Added: January 16, 2023

2023 journal article

Higher Order Finite Element Methods for Some One-dimensional Boundary Value Problems

*Research Reports on Computer Science*.

Source: ORCID

Added: January 17, 2023

2023 journal article

Numerical analysis of a free boundary problem with non-local obstacles

*APPLIED MATHEMATICS LETTERS*, *135*.

author keywords: Obstacle-like minimization problem; Free boundary; SOR(omega) iteration

Sources: ORCID, Web Of Science

Added: August 30, 2022

2023 journal article

Numerical integration rules with improved accuracy close to discontinuities

*Mathematics and Computers in Simulation*.

Source: ORCID

Added: March 30, 2023

2022 article

A Variant Modified Skew-Normal Splitting Iterative Method for Non-Hermitian Positive Definite Linear Systems

Li, R., Yin, J.-F., & Li, Z.-L. (2022, February 16). *NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS*, Vol. 2.

author keywords: Non-Hermitian matrix; skew-normal splitting; precondition; complex linear system

Sources: Web Of Science, ORCID

Added: March 7, 2022

2022 journal article

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

*JOURNAL OF COMPUTATIONAL PHYSICS*, *449*.

author keywords: Diffusion equation; Discontinuous coefficients; Anisotropic coefficients; Richardson extrapolation; Finite volume method; Cell-centered multigrid method

Sources: ORCID, Web Of Science

Added: October 25, 2021

2022 journal article

A new parameter free partially penalized immersed finite element and the optimal convergence analysis

*NUMERISCHE MATHEMATIK*, *150*(4), 1035–1086.

author keywords: 65N15; 65N30; 35R05

Sources: Web Of Science, ORCID

Added: April 25, 2022

2022 journal article

A new patch up technique for elliptic partial differential equation with irregularities

*JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS*, *407*.

author keywords: Elliptic partial differential equation; Interface; Jump conditions; Cubic spline collocation; Irregularities; Patch up technique

Sources: Web Of Science, ORCID

Added: May 16, 2022

2022 journal article

AN L-8 SECOND ORDER CARTESIAN METHOD FOR 3D ANISOTROPIC INTERFACE PROBLEMS

*JOURNAL OF COMPUTATIONAL MATHEMATICS*, *40*(6), 882–912.

author keywords: Key veords; 3D anisotropic PDE; Cartesian meshes; Finite element method; Finite differ; ence method; Maximum preserving IIM; Convergence analysis

Sources: Web Of Science, ORCID

Added: December 5, 2022

2022 journal article

An immersed C R-P-0 element for Stokes interface problems and the optimal convergence analysis

*COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING*, *399*.

author keywords: Stokes equations; Interface; Immersed finite element; Unfitted mesh; Two-phase flow; Error estimates

Sources: Web Of Science, ORCID

Added: October 17, 2022

2021 journal article

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

*JOURNAL OF SCIENTIFIC COMPUTING*, *88*(3).

author keywords: Elliptic BVP; Interface problem; Irregular domain; High order compact Cartesian mesh method; IIM & augmented IIM; Discontinuous coefficients; Gradient; Helmholtz equation

Sources: ORCID, Web Of Science

Added: July 29, 2021

2021 article

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.

author keywords: Non-linear complementarity problems; Modulus-based Newton methods; P-matrix

Sources: Web Of Science, ORCID

Added: June 10, 2021

2021 journal article

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

*NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS*, *14*(3), 773–796.

author keywords: 3D elliptic interface problem; augmented IIM; fast Poisson solver; directional least squares interpolation

Sources: Web Of Science, ORCID

Added: July 6, 2021

2021 journal article

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

*JOURNAL OF COMPUTATIONAL PHYSICS*, *438*.

author keywords: Maxwell's equations; Yee's scheme; Interface problem; ADI method; Augmented immersed interface method; Scattering

Sources: ORCID, Web Of Science

Added: April 16, 2021

2021 book

An Introduction to Partial Differential Equations (with Maple)

Sources: Crossref, NC State University Libraries, ORCID

Added: December 5, 2020

2021 journal article

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

*APPLIED MATHEMATICS LETTERS*, *121*.

author keywords: Convection and diffusion PDEs; Integrating factor; 4th order compact scheme

Sources: ORCID, Web Of Science

Added: May 17, 2021

2021 journal article

Non-parallel hyperplanes ordinal regression machine

*KNOWLEDGE-BASED SYSTEMS*, *216*.

author keywords: Ordinal regression; Support vector machine; Twin support vector machine; Non-parallel hyperplanes ordinal regression machine

Sources: ORCID, Web Of Science

Added: November 10, 2020

2021 article

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.

author keywords: Incompressible magneto-hydrodynamics equations; Nonconforming finite element; Iterative method; Stability; Optimal error estimate

Sources: Web Of Science, ORCID

Added: November 23, 2021

2021 journal article

Partially penalized IFE methods and convergence analysis for elasticity interface problems

*JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS*, *382*.

author keywords: Elasticity interface problems; Immersed finite element; Discontinuous coefficients; Coercivity; Inf-sup condition; Error estimates

Sources: Web Of Science, ORCID

Added: September 14, 2020

2021 journal article

Partially penalized IFE methods and convergence analysis for elasticity interface problems

*Journal of Computational and Applied Mathematics*.

Source: ORCID

Added: March 2, 2021

2021 journal article

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

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

author keywords: Regression problem; support vector regression; quadratic kernel-free least squares support vector regression

Sources: Web Of Science, ORCID

Added: April 5, 2021

2021 journal article

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

*JOURNAL OF COMPUTATIONAL PHYSICS*, *431*.

author keywords: Surface and evolving surface PDEs; Local tangential lifting method; Moving interface on surface; Dendritic solidification; Front tracking method; Discrete delta function on surface

Sources: ORCID, Web Of Science

Added: January 20, 2021

2020 journal article

AN FE-FD METHOD FOR ANISOTROPIC ELLIPTIC INTERFACE PROBLEMS

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

author keywords: anisotropic elliptic interface problem; finite element and finite difference method; maximum principle preserving scheme; normal derivative computation; scaling technique; error analysis

Sources: Web Of Science, ORCID

Added: September 28, 2020

2020 journal article

How to obtain an accurate gradient for interface problems?

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

author keywords: Accuracy of derivatives; Elliptic interface problems; Discontinuous coefficient; Discrete Green functions; IIM

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.

author keywords: Elliptic interface problem; Accurate solution and gradient computation; Variable coefficient with discontinuities; Convergence proof; Discrete Green's function; Discrete elliptic maximum principle; Compact finite difference scheme

Sources: Web Of Science, ORCID

Added: April 2, 2019

2019 journal article

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

*INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING*, *120*(7), 901–917.

author keywords: adaptive strategy; recovery-based error estimator; streamline diffusion method; surface convection-diffusion-reaction equations; surface finite element method

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.

author keywords: Immersed boundary method; augmented approach; convergence; derivative computing

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).

author keywords: sustainable mode of transportation; bike-sharing system; public bicycle; complex network; network structure

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.

author keywords: Lorenz model; tangent linear model; nonlinear model; Monte Carlo

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*.

author keywords: Green travel; Public bicycle; Spatiotemporal characteristics; Clustering analysis; Visualization analysis

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.

author keywords: Incompressible Stokes equations; Interface problem; Discontinuous viscosity; Marker and cell scheme; Staggered mesh; Uzawa method; Immersed interface method; Finite difference method

Sources: Web Of Science, 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.

author keywords: Interface problem; Level set function; Source removal technique; Immersed interface

Sources: Web Of Science, 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.

author keywords: Navier-Stokes and Darcy coupling; Coupled fluid flow with porous media; Least squares augmented IIM; Fast Poisson/Helmholtz solver; Analytic solution for Navier-Stokes and; Darcy coupling; Interface relations

Sources: Web Of Science, 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.

author keywords: Stokes equations; Error analysis; Finite difference method; Immersed interface method; Divergence-free

Sources: Web Of Science, 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.

author keywords: ADI method; interface problems; discontinuous coefficient; multiscale; jump conditions; augmented variable; stability

Sources: Web Of Science, 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.

author keywords: Nonconforming immersed finite element; Elasticity interface problems; Cartesian grid

Sources: Web Of Science, 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.

author keywords: Fluid structure interactions; Darcy-Stokes-Brinkman equations; Stokes equations; Darcy flow; discontinuous coefficient; nonconforming rectangular element; interior penalty; infsup condition; error estimates

Sources: Web Of Science, 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.

author keywords: elliptic interface problems; gradient/flux computation; IFEM; mixed FE formulation; computational tube

Sources: Web Of Science, 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.

author keywords: elliptic interface problem; accurate gradient computation; variable coefficient with discontinuity; interface; M-matrix; convergence proof; discrete Green function

Sources: Web Of Science, ORCID

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.

author keywords: 4th order PDE; Discontinuous coefficient; Fast Poisson solver; Augmented immersed interface method; Schur complement; Natural jump conditions

Sources: Web Of Science, 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

New Conservative Finite Volume Element Schemes for the Modified Regularized Long Wave Equation

*ADVANCES IN APPLIED MATHEMATICS AND MECHANICS*, *9*(2), 250–271.

author keywords: Energy; momentum; mass; finite volume element method; MRLW equation

Sources: Web Of Science, ORCID

Added: August 6, 2018

2017 book

Numerical Solution of Differential Equations

In *Cambridge University Press*.

Source: ORCID

Added: January 1, 2021

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.

author keywords: IIM; Finite difference methods; Correction terms; Multiresolution schemes; Improved adaption to discontinuities; Signal processing

Sources: Crossref, ORCID

Added: February 19, 2020

2016 journal article

A Sparse Grid Stochastic Collocation Method for Elliptic Interface Problems with Random Input

*JOURNAL OF SCIENTIFIC COMPUTING*, *67*(1), 262–280.

author keywords: Sparse grids; Stochastic inputs; Interface; Immersed finite element; Smolyak construction

Sources: Web Of Science, ORCID

Added: August 6, 2018

2016 journal article

A new augmented immersed finite element method without using SVD interpolations

*NUMERICAL ALGORITHMS*, *71*(2), 395–416.

author keywords: Interface problem; Piecewise constant coefficient; Immersed finite element; Augmented immersed finite element method; Poisson equation on irregular domain; Fast poisson solver; Least squares interpolation using SVD

Sources: Web Of Science, 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.

author keywords: Stokes-Darcy fluid-structure interaction; augmented immersed interface method; fast Poisson solver; BJS interface condition; analytic solution of Stokes and Darcy coupling

Sources: Web Of Science, 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.

author keywords: level set function; singularity removal technique; irregular domain; interface problem; non-homogeneous jump condition; 35J60; 65N30; 65N15

Sources: Web Of Science, 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.

author keywords: Free discontinuity; free boundary; crack-tip; Mumford-Shah energy; augmented immersed interface method; fast/Poisson solver; irregular domain

Sources: Web Of Science, 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.

author keywords: Risk ranking; Pesticides; Dietary exposure; ADI

Sources: Web Of Science, 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.

author keywords: 65F10; 65N55; 65N30; Robin-Robin domain decomposition method; H(div)-elliptic problems; Raviart-Thomas finite element; convergence analysis; non-overlapping domain decomposition

Sources: Web Of Science, 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.

author keywords: Navier-Stokes Navier-Stokes equations; Finite difference approximation; Irregular domain; Open and traction boundary conditions; Local pressure boundary condition; Augmented immersed interface method (IIM)

Sources: Web Of Science, 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.

author keywords: Finite volume element method; Source removal technique; Interface problem; Jump conditions

Sources: Web Of Science, 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.

author keywords: Augmented immersed interface method; Schur complement system; GMRES; Matrix-free preconditioning; Hierarchically semiseparable structure; Adaptive randomized compression

Sources: Web Of Science, 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.

author keywords: PDE-constrained optimization; Variational discretization; Immersed finite element; Elliptic interface problem

Sources: Web Of Science, 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.

author keywords: immersed boundary (IB) method; immersed interface method (IIM); jump conditions; discontinuous coefficient; Dirac delta function; weak solution; boundary singularity; convergence of IB method; equivalent boundary conditions

Sources: Web Of Science, 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.

author keywords: Immersed interface method; Axis-symmetric interface problem; Discontinuous coefficients; Finite difference method; Level set method; Hele-Shaw flow

Sources: Web Of Science, 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.

author keywords: 3D immersed interface method; level-set method; insoluble surfactant; Stokes interfacial flow; drop deformation

Sources: Web Of Science, 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.

author keywords: Immersed finite element method; Interface problems; Cartesian mesh; Discontinuous coefficient; Symmetric and consistent weak form

Sources: Web Of Science, ORCID

Added: August 6, 2018

2014 journal article

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.

Sources: Crossref, ORCID

Added: March 21, 2021

2014 journal article

On convergence of the immersed boundary method for elliptic interface problems

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

Sources: Crossref, ORCID

Added: January 21, 2021

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.

author keywords: Fourier finite volume element method; Quasi-geostrophic equations on a sphere; Trial and test function spaces; Pole singularity

Sources: Web Of Science, ORCID

Added: August 6, 2018

2013 journal article

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

*COMPUTERS & STRUCTURES*, *122*, 249–258.

author keywords: Adaptive mesh refinement method; Immersed interface method; Stokes and Navier-Stokes equations; Surface tension; Bubble deformation; Level set method

Sources: Web Of Science, 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: Web Of Science, ORCID

Added: August 6, 2018

2013 journal article

Exploring accurate Poisson-Boltzmann methods for biomolecular simulations

*COMPUTATIONAL AND THEORETICAL CHEMISTRY*, *1024*, 34–44.

author keywords: Poisson-Boltzmann equation; Finite difference method; Immersed interface method; Continuum solvent models

Sources: Web Of Science, ORCID

Added: August 6, 2018

2013 journal article

Numerical Poisson-Boltzmann model for continuum membrane systems

*CHEMICAL PHYSICS LETTERS*, *555*, 274–281.

Sources: Web Of Science, 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.

author keywords: Autocorrelation; longitudinal data; mixed models; simulation; variance-covariance structure

Sources: Web Of Science, 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.

author keywords: Elasticity equations; non-body fitted mesh; finite element method; jump condition

Sources: Web Of Science, 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.

author keywords: Immersed interface method; augmented method; projection method; Navier-Stokes; moving interface; implicit scheme; fluid-structure

Sources: Web Of Science, 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.

author keywords: Adaptive mesh refinement; immersed boundary method; immersed interface method; elliptic interface problem; Cartesian grid method; level set representation; singular sources

Sources: Web Of Science, 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 AND MECHANICS*, *4*(6), 737–750.

author keywords: Collocation method; classical Holder space; system of singular integro-differential equation; Fejer points

Sources: Web Of Science, 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.

author keywords: Helmholtz equation; irregular domain; embedding method; elliptic interface problem; finite difference method; discrete maximum principle; level set function; immersed interface method; augmented IIM

Sources: Web Of Science, ORCID

Added: August 6, 2018

2012 book

SPECIAL ISSUE ON FLUID DYNAMICS, ANALYSIS AND NUMERICS

Source: ORCID

Added: January 1, 2021

2012 journal article

Simplified immersed interface methods for elliptic interface problems with straight interfaces

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

author keywords: conservative finite difference scheme; discontinuous coefficient; immersed interface method; interface problem; polar coordinates; Richardson extrapolation

Sources: Crossref, ORCID

Added: March 21, 2021

2012 book

Special Issue on Fluid Motion Driven by Immersed Structures

In *Global Sciences*. https://www.researchgate.net/publication/296762774_Special_Issue_on_Fluid_Motion_Driven_by_Immersed_Structures_Preface

Source: ORCID

Added: January 1, 2021

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 AND MECHANICS*, *4*(1), 21–35.

author keywords: Navier-Stokes equations; sensitivity analysis; flow past cylinder; embedding technique; immersed interface method; irregular domain; augmented system; projection method; fluid-solid interaction

Sources: Web Of Science, 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.

author keywords: Surfactants; drops; coalescence; surface tension; Marangoni effect; level-set method; immersed interface method; Stokes flow

Sources: Web Of Science, 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.

author keywords: Immersed interface method; Polar coordinates; Interface; Discontinuous coefficients; Finite difference method; Electro capacitance tomography; Forward problem

Sources: Web Of Science, 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.

author keywords: Moving contact line; Free boundary problem; Triple junction; One-phase flow; Navier-Stokes equations; Embedding technique; Immersed interface method; Irregular domain; Augmented method

Sources: Web Of Science, 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.

author keywords: Immersed boundary method; Moving boundary; Non-physical force oscillations; Smoothed discrete delta function

Sources: Web Of Science, 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.

author keywords: Navier-Stokes equations; Embedding technique; Immersed interface method; Irregular domain; Augmented system; Projection method; Level set representation

Sources: Web Of Science, 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: Web Of Science, 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.

author keywords: Domain decomposition; Mortar finite element method; Additive Schwarz method; Rotated Q(1) element

Sources: Web Of Science, 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

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

Sources: ORCID, Crossref

Added: January 1, 2021

2009 book

Interface problems and methods in biological and physical flows

New Jersey: World Scientific.

Ed(s): Z. B. C. Khoo & P. Lin

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.

author keywords: biharmonic equation; irregular domain; augmented method; immersed interface method; incompressible stokes flow

Sources: Web Of Science, 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 article

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

*COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING*, Vol. 197, pp. 2317–2328.

author keywords: Navier-Stokes equations; interface; discontinuous viscosity; immersed interface method; explicit jump immersed interface method; projection method

Sources: Web Of Science, 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.

author keywords: Incompressible viscous flows; Piecewise constant viscosity; Singular force; Immersed interface method; Projection method; Front tracking method

Sources: Web Of Science, ORCID

Added: August 6, 2018

2008 journal article

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

*SIAM JOURNAL ON NUMERICAL ANALYSIS*, *46*(1), 472–495.

author keywords: elliptic interface problems; nonhomogeneous jump conditions; immersed-interface finite-element method; level-set functions; error estimates

Sources: Web Of Science, 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: Web Of Science, 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.

author keywords: nonlinear Poisson-Boltzmann equation; exterior problem; immersed interface method; monotone iterative method

Sources: Web Of Science, ORCID, Crossref

Added: August 6, 2018

2007 article

A study of numerical methods for the level set approach

*APPLIED NUMERICAL MATHEMATICS*, Vol. 57, pp. 837–846.

Sources: Web Of Science, 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: Web Of Science, ORCID

Added: August 6, 2018

2007 journal article

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

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

Source: NC State University Libraries

Added: April 5, 2021

2007 journal article

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

*PAMM*, *7*(1), 1025401–1025402.

Sources: Crossref, ORCID

Added: February 24, 2020

2007 book

Moving Interface Problems and Applications in Fluid Dynamics

In *AMS Contemporary mathematics 466*. https://books.google.com/books/about/Moving_Interface_Problems_and_Applicatio.html?id=fMYbCAAAQBAJ

Source: ORCID

Added: January 1, 2021

2007 article

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

*APPLIED NUMERICAL MATHEMATICS*, Vol. 57, pp. 473–474.

Sources: Web Of Science, ORCID

Added: August 6, 2018

2007 book

Special Issue for the International Conference on Scientific Computing

https://www.sciencedirect.com/journal/applied-numerical-mathematics/vol/57/issue/5

Source: ORCID

Added: January 1, 2021

2006 journal article

A level-set method for interfacial flows with surfactant

*JOURNAL OF COMPUTATIONAL PHYSICS*, *212*(2), 590–616.

author keywords: incompressible stokes flow; interfaces; insoluble surfactant; Marangoni force; capillary force; level set method; immersed interface method

Sources: Web Of Science, 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

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

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

Source: NC State University Libraries

Added: April 5, 2021

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.

author keywords: arbitrary interface; fast 3D Poisson solver; immersed interface method; infinite domain; extension of jumps; spherical coordinates; level set function; artificial boundary condition

Sources: Web Of Science, 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.

author keywords: incompressible Stokes equations; interface; discontinuous viscosity; interface conditions; singular sources

Sources: Web Of Science, 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 chapter

Augmented Strategies for Interface and Irregular Domain Problems

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

Event: Third International Conference, Numerical Analysis and its Applications 2004 at Rousse, Bulgaria on June 29 - July 3, 2004

Sources: NC State University Libraries, Crossref, ORCID

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.

author keywords: fourth order finite difference schemes; elliptic and parabolic equations on irregular domains; immersed interface method

Sources: Web Of Science, ORCID

Added: August 6, 2018

2005 journal article

Immersed finite element for elasticity system with discontinuities

*AMS Contemporary Mathematics*, *383*, 285–298.

Source: NC State University Libraries

Added: December 28, 2021

2005 book

Numerical Analysis and Its Applications

Source: Crossref

Added: March 21, 2021

2004 journal article

An immersed finite element space and its approximation capability

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

author keywords: interface problems; immersed interface; finite element; error estimates

Sources: Web Of Science, ORCID, Crossref

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: Web Of Science, ORCID

Added: August 6, 2018

2003 journal article

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

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

Sources: Crossref, ORCID

Added: March 21, 2021

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

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

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

Sources: Crossref, ORCID

Added: March 21, 2021

2003 journal article

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

*NUMERISCHE MATHEMATIK*, *96*(1), 61–98.

Sources: Web Of Science, 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.

author keywords: interface problems; singular source; delta function; level set function; discontinuous coefficients; polar coordinates; immersed interface method; smooth extension; fast Poisson solver

Sources: Web Of Science, 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*(1-3), 253–266.

author keywords: non-linear interface problem; magneto-rheological fluid; maximum principal preserving scheme; immersed interface method; level set method; substitution method

Sources: Web Of Science, 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.

author keywords: 3D elliptic interface problem; irregular domain; discontinuous coefficient; discrete maximum preserving scheme; quadratic optimization; algebraic multigrid; shape identification; level set method

Sources: Web Of Science, 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: Web Of Science, ORCID

Added: August 6, 2018

2002 journal article

Reactive autophobic spreading of drops

*JOURNAL OF COMPUTATIONAL PHYSICS*, *183*(2), 335–366.

Sources: Web Of Science, 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.

author keywords: interface problems; diffusion and advection equation; multigrid method; discontinuous coefficients; quadratic optimization; discrete maximum principle

Sources: Web Of Science, ORCID

Added: August 6, 2018

2001 chapter

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).

Ed(s): J. L. Vulkov & P. Yalamov

Sources: NC State University Libraries, Crossref, ORCID

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.

author keywords: immersed boundary method; immersed interface method; jump conditions

Sources: Web Of Science, ORCID

Added: August 6, 2018

2001 book review

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,

Source: NC State University Libraries

Added: December 28, 2021

2001 journal article

Level-set function approach to an inverse interface problem

*INVERSE PROBLEMS*, *17*(5), 1225–1242.

Sources: Web Of Science, 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.

author keywords: elliptic interface problems; finite difference methods; discontinuous coefficients; singular source term; discrete maximum principle; quadratic optimization; multigrid methods

Sources: Web Of Science, ORCID

Added: August 6, 2018

2001 chapter

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.

Ed(s): M. Mu, Z. Shi, W. Xue & J. Zou

Event: Workshop on Scientific Computing at Hong Kong

Source: NC State University Libraries

Added: December 28, 2021

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.

author keywords: discontinuous and non-smooth solution; immersed interface method; interface; jump condition; Stokes equation; variable surface tension

Sources: Web Of Science, 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.

author keywords: Navier-Stokes equations; interface; discontinuous and nonsmooth solution; immersed interface method; immersed boundary method; projection method; level set method

Sources: Web Of Science, ORCID

Added: August 6, 2018

2000 book

Source: NC State University Libraries

Added: December 28, 2021

1999 journal article

A numerical method for solving heat equations involving interfaces

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

Event: Fourth Mississippi State Conference on Differential Equations and Computational Simulations, Conference 3

Source: NC State University Libraries

Added: December 28, 2021

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: Web Of Science, 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: Web Of Science, ORCID

Added: August 6, 2018

1999 journal article

Crack jump conditions for elliptic problems

*APPLIED MATHEMATICS LETTERS*, *12*(6), 81–88.

author keywords: jump conditions; transmission problem; elliptic crack problems

Sources: Web Of Science, 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: Web Of Science, ORCID

Added: August 6, 2018

1999 journal article

Numerical Study of Two Dimensional Electro-migration

*Journal of Computational Physics*, *152*, 281–304.

Source: NC State University Libraries

Added: December 28, 2021

1999 journal article

The immersed finite volume element methods for the elliptic interface problems

*MATHEMATICS AND COMPUTERS IN SIMULATION*, *50*(1-4), 63–76.

author keywords: finite volume; convergence; error estimate; interface problems

Sources: Web Of Science, 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.

author keywords: elliptic equation; discontinuous coefficients; immersed interface method; Cartesian grid; Schur complement; GMRES method; preconditioning

Sources: Web Of Science, ORCID

Added: August 6, 2018

1998 journal article

The immersed interface method using a finite element formulation

*APPLIED NUMERICAL MATHEMATICS*, *27*(3), 253–267.

author keywords: immersed interface method; finite element method; modified basis function; natural jump condition; error analysis

Sources: Web Of Science, ORCID

Added: August 6, 2018

1998 journal article

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

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

author keywords: mixed type system; discontinuous coefficients; Dirac delta function; finite difference; semi-implicit prediction-correction scheme; error analysis

Sources: Crossref, ORCID

Added: March 21, 2021

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.

Sources: Crossref, ORCID

Added: September 21, 2020

1997 journal article

An Inverse Problem in a Parabolic Equation

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

Event: Conference

Source: NC State University Libraries

Added: December 28, 2021

1997 journal article

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

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

Source: NC State University Libraries

Added: December 28, 2021

1997 journal article

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

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

author keywords: Stokes flow; creeping flow; interface tracking; discontinuous coefficients; immersed interface methods; Cartesian grids; bubbles

Sources: Crossref, ORCID

Added: March 21, 2021

1997 journal article

Immersed interface methods for moving interface problems

*Numerical Algorithms*, *14*, 269–293.

author keywords: immersed interface method; Stefan problem; moving interface; discontinuous coefficients; singular source term; immersed boundary method; Cartesian grid; heat conduction

Sources: Web Of Science, ORCID

Added: December 28, 2021

1996 journal article

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

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

author keywords: 3D elliptic equation; finite difference methods; irregular interface; discontinuous coefficients; singular source term; delta functions; Cartesian grid; immersed interface method

Sources: Crossref, ORCID

Added: September 21, 2020

1995 conference paper

Simulation of bubbles in creeping flow using the immersed interface method

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

Event: sixth international symposium on computational fluid dynamics at Lake Tahoe on September 4-8, 1995

Source: NC State University Libraries

Added: December 28, 2021

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.

author keywords: ELLIPTIC EQUATION; FINITE DIFFERENCE METHODS; IRREGULAR DOMAIN; INTERFACE; DISCONTINUOUS COEFFICIENTS; SINGULAR SOURCE TERM; DELTA FUNCTIONS

Sources: Crossref, ORCID

Added: September 21, 2020

1994 thesis

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

(PhD thesis). University of Washington.

Source: NC State University Libraries

Added: December 28, 2021

1993 conference paper

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.

Ed(s): W. Gautschi

Source: NC State University Libraries

Added: December 28, 2021

1990 journal article

Perturbation theorems of eigenvectors

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

Source: NC State University Libraries

Added: December 28, 2021

1989 journal article

Roundoff error analysis for polynomial interpolation

*Research and Review in Mathematics*, (2).

Source: NC State University Libraries

Added: December 28, 2021

1989 journal article

The uniform treatment for linear system — Algorithm and numerical stability

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

Source: NC State University Libraries

Added: December 28, 2021

1988 journal article

Optimal conjugate gradient method for solving arbitrary linear equations

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

Source: NC State University Libraries

Added: December 28, 2021

1987 journal article

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

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

Source: NC State University Libraries

Added: December 28, 2021

1987 journal article

An equivalent theorem on the numerical stability for an algorithm

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

Source: NC State University Libraries

Added: December 28, 2021

1985 journal article

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.

Source: NC State University Libraries

Added: December 28, 2021

book

Industrial Mathematics

In *SIAM, USA*.

Source: ORCID

Added: January 1, 2021

book

Numerical Analysis and Its Applications

https://link.springer.com/book/10.1007%2Fb106395

Source: ORCID

Added: January 1, 2021

1997 - present

1994 - 1996