Works (192)

Updated: June 8th, 2024 04:31

2024 journal article

A pressure Poisson equation-based second-order method for solving two-dimensional moving contact line problems with topological changes

COMPUTERS & FLUIDS, 269.

By: S. Chai*, Z. Li n, Z. Zhang* & Z. Zhang*

author keywords: Moving contact lines; Topological changes; Immersed interface method; Parametric finite element method; Pressure Poisson equation
Sources: Web Of Science, NC State University Libraries, ORCID
Added: January 2, 2024

2024 article

Coupled transformation methods and analysis for BVPs on infinite domains

Li, Z., & Pan, K. (2024, July). JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, Vol. 444.

By: Z. Li n & K. Pan*

author keywords: Infinity domains; Large domains; Transformation method; Discrete maximum principle; Convergence analysis; Polar coordinates
Sources: ORCID, Web Of Science, NC State University Libraries
Added: February 2, 2024

2024 journal article

Fully accurate approximation of piecewise smooth functions using corrected B-spline quasi-interpolants

COMPUTATIONAL & APPLIED MATHEMATICS, 43(4).

By: Z. Li n, K. Pan*, J. Ruiz* & D. Yanez*

author keywords: IIM; B-spline; Correction terms; Improved adaption to discontinuities; Signal processing
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities (OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: April 29, 2024

2024 journal article

High order compact augmented methods for Stokes equations with different boundary conditions

Computer Physics Communications.

By: K. Pan, J. Li & Z. Li*

Source: ORCID
Added: May 15, 2024

2024 article

New third-order convex splitting methods and analysis for the phase field crystal equation

Ye, Z., Zheng, Z., & Li, Z. (2024, February 28). NUMERICAL ALGORITHMS, Vol. 2.

By: Z. Ye*, Z. Zheng* & Z. Li n

author keywords: Phase field crystal equation; Convex splitting method; Third-order backward difference formula; Unique solvability; Energy stability
Sources: Web Of Science, NC State University Libraries
Added: March 18, 2024

2023 article

A CELL-CENTERED MULTIGRID SOLVER FOR THE FINITE VOLUME DISCRETIZATION OF ANISOTROPIC ELLIPTIC INTERFACE PROBLEMS ON IRREGULAR DOMAINS*

Pan, K., Wu, X., Hu, H., & Li, Z. (2023, December 14). JOURNAL OF COMPUTATIONAL MATHEMATICS, Vol. 12.

By: K. Pan, X. Wu, H. Hu & Z. Li*

author keywords: Elliptic interface problem; Discontinuous coefficients; Anisotropic coefficients; Cascadic multigrid method; Richardson extrapolation
Sources: Web Of Science, NC State University Libraries
Added: March 18, 2024

2023 article

A Stable FE-FD Method for Anisotropic Parabolic PDEs with Moving Interfaces

Dong, B., Li, Z., & Ruiz-Alvarez, J. (2023, July 10). COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION, Vol. 7.

By: B. Dong*, Z. Li n & J. Ruiz-Alvarez*

author keywords: Anisotropic parabolic interface problem; Hybrid finite element and finite difference (FE-FD) discretization; Modified Crank-Nicolson scheme
Sources: ORCID, Web Of Science, NC State University Libraries
Added: July 11, 2023

2023 journal article

Accurate derivatives approximations and applications to some elliptic PDEs using HOC methods

APPLIED MATHEMATICS AND COMPUTATION, 459.

By: J. Li*, Z. Li n & K. Pan*

author keywords: High order compact derivative computation; HOC schemes; Poisson/Helmholtz equation; Diffusion-advection equation; Stokes equations; Three Poisson equations approach
Sources: ORCID, Web Of Science, NC State University Libraries
Added: August 9, 2023

2023 journal article

Adapting Cubic Hermite Splines to the Presence of Singularities Through Correction Terms

JOURNAL OF SCIENTIFIC COMPUTING, 95(3).

author keywords: Splines; Adaption to singularities; Interpolation; Point-values; Computer aided design (modeling of curves)
Sources: Web Of Science, NC State University Libraries
Added: June 19, 2023

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.

By: S. Hu*, K. Pan, X. Wu, Y. Ge & Z. Li*

author keywords: Convection-diffusion equation; Completed Richardson extrapolation; Quintic Lagrange interpolation; High-order compact scheme; Cascadic multigrid
Sources: Web Of Science, NC State University Libraries
Added: January 30, 2023

2023 journal article

Analysis of nonconforming IFE methods and a new scheme for elliptic interface problems

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS, 57(4), 2041–2076.

By: H. Ji, F. Wang, J. Chen & Z. Li*

author keywords: Interface problem; Nonconforming; Immersed finite element; Unfitted mesh
TL;DR: This paper develops a new nonconforming IFE method with additional terms locally on interface edges which removes the limitation of the conventional partially penalized I FE method and derives the optimal approximation capabilities of both the Crouzeix-Raviart and the rotated-$Q_1 IFE spaces via a unified approach which can handle the case of variable coefficients easily. (via Semantic Scholar)
UN Sustainable Development Goal Categories
16. Peace, Justice and Strong Institutions (OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: July 24, 2023

2023 journal article

HIGH ORDER COMPACT SCHEMES FOR FLUX TYPE BCS

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 45(2), A646–A674.

By: Z. Li n & K. Pan*

author keywords: Poisson; Helmholtz; diffusion-advection; anisotropic equations; high order compact method; HOC method for flux BCs; discrete maximum principle
Sources: ORCID, Web Of Science, NC State University Libraries
Added: April 19, 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.

By: B. Dong, Z. Li & J. Ruiz-Álvarez

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.

By: B. Dong*, Z. Li n & J. Ruiz-Álvarez*

Source: ORCID
Added: January 17, 2023

2023 journal article

New Sixth-Order Compact Schemes for Poisson/Helmholtz Equations

NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 16(2), 393–409.

By: K. Pan, K. Fu, J. Li, H. Hu & Z. Li*

author keywords: Poisson equation; Helmholtz equation; sixth-order compact scheme; maximum principle; staggered grid
Sources: Web Of Science, NC State University Libraries
Added: May 22, 2023

2023 journal article

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

APPLIED MATHEMATICS LETTERS, 135.

By: Z. Li n & H. Mikayelyan*

author keywords: Obstacle-like minimization problem; Free boundary; SOR(omega) iteration
Sources: ORCID, Web Of Science, NC State University Libraries
Added: August 30, 2022

2023 journal article

Numerical integration rules with improved accuracy close to discontinuities

MATHEMATICS AND COMPUTERS IN SIMULATION, 210, 593–614.

author keywords: Accurate numerical integration formulas; Adaption to discontinuities; Definite integration; Adapted interpolation
UN Sustainable Development Goal Categories
13. Climate Action (Web of Science)
14. Life Below Water (Web of Science)
Sources: ORCID, Web Of Science, NC State University Libraries
Added: March 30, 2023

2023 article

Stable high order FD methods for interface and internal layer problems based on non-matching grids

Li, Z., Pan, K., & Ruiz-Alvarez, J. (2023, November 6). NUMERICAL ALGORITHMS, Vol. 11.

By: Z. Li n, K. Pan* & J. Ruiz-Alvarez*

author keywords: Interface problems; Internal layer problems; Non-matching grid; Discrete maximum principle; Hanging nodes
Sources: Web Of Science, NC State University Libraries, ORCID
Added: November 27, 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.

By: R. Li, J. Yin & Z. Li*

author keywords: Non-Hermitian matrix; skew-normal splitting; precondition; complex linear system
Sources: Web Of Science, NC State University Libraries
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.

By: K. Pan*, X. Wu*, H. Hu*, Y. Yu* & Z. Li n

author keywords: Diffusion equation; Discontinuous coefficients; Anisotropic coefficients; Richardson extrapolation; Finite volume method; Cell-centered multigrid method
TL;DR: A new approach for obtaining vertex values by interpolating the cell-centered ones, which avoids solving local linear system of equations even with arbitrary diffusion tensors, a new cascadic multigrid solver based on a prolongation operator, the newly developed explicit gradient transfer method, and a splitting extrapolation operator for solving 3D anisotropic diffusion equations with discontinuous coefficients. (via Semantic Scholar)
Sources: ORCID, Web Of Science, NC State University Libraries
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.

By: H. Ji*, F. Wang*, J. Chen* & Z. Li n

author keywords: 65N15; 65N30; 35R05
TL;DR: A lifting operator is introduced on interface edges to ensure the coercivity of the method without requiring an ad-hoc stabilization parameter and a new trace inequality which is necessary to prove the optimal convergence of immersed finite element methods is established on interface elements. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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.

By: S. Singh*, S. Singh* & Z. Li n

author keywords: Elliptic partial differential equation; Interface; Jump conditions; Cubic spline collocation; Irregularities; Patch up technique
Sources: Web Of Science, NC State University Libraries
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.

By: B. Dong n, X. Feng n & Z. Li n

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, NC State University Libraries
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.

By: H. Ji*, F. Wang*, J. Chen* & Z. Li n

author keywords: Stokes equations; Interface; Immersed finite element; Unfitted mesh; Two-phase flow; Error estimates
TL;DR: It is proved that the I FE basis functions are unisolvent on arbitrary interface elements and the IFE spaces have the optimal approximation capabilities, although the proof is challenging due to the coupling of the velocity and the pressure. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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).

By: K. Pan*, D. He* & Z. Li n

author keywords: Elliptic BVP; Interface problem; Irregular domain; High order compact Cartesian mesh method; IIM & augmented IIM; Discontinuous coefficients; Gradient; Helmholtz equation
TL;DR: An augmented third order compact finite difference method is further developed for elliptic interface problems with piecewise constant but discontinuous coefficients and the third order augmented method is applied to Poisson/Helmholtz equations on irregular domains with few changes along examples of Neumann, Robin, and Dirichlet boundary conditions. (via Semantic Scholar)
Sources: ORCID, Web Of Science, NC State University Libraries
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.

By: R. Li*, Z. Li n & J. Yin*

author keywords: Non-linear complementarity problems; Modulus-based Newton methods; P-matrix
Sources: Web Of Science, NC State University Libraries
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.

By: C. Zhang, Z. Li & X. Yue

author keywords: 3D elliptic interface problem; augmented IIM; fast Poisson solver; directional least squares interpolation
TL;DR: A new fast algorithm based on the augmented immersed interface method and a fast Poisson solver is proposed to solve three dimensional elliptic interface problems with a piecewise constant but discontinuous coefficient and can reduce the CPU time by 20-50%. (via Semantic Scholar)
UN Sustainable Development Goal Categories
7. Affordable and Clean Energy (OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: July 6, 2021

2021 journal article

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

JOURNAL OF COMPUTATIONAL PHYSICS, 438.

By: S. Deng*, Z. Li n & K. Pan*

author keywords: Maxwell's equations; Yee's scheme; Interface problem; ADI method; Augmented immersed interface method; Scattering
TL;DR: The ADI-YEE's scheme maintains the structure (the finite difference scheme with modified right-hand sides) as well as the accuracy and stability of Yee's scheme even with the presence of discontinuities. (via Semantic Scholar)
Sources: ORCID, Web Of Science, NC State University Libraries
Added: April 16, 2021

2021 book

An Introduction to Partial Differential Equations (with Maple)

By: Z. Li n & L. Norris n

Sources: Crossref, NC State University Libraries, NC State University Libraries
Added: December 5, 2020

2021 journal article

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

APPLIED MATHEMATICS LETTERS, 121.

By: F. Tong*, X. Feng* & Z. Li n

author keywords: Convection and diffusion PDEs; Integrating factor; 4th order compact scheme
TL;DR: Fourth order finite difference methods combined with an integrating factor strategy for steady convection and diffusion partial differential equations with variable coefficients in both 2D and 3D are proposed using uniform Cartesian grids. (via Semantic Scholar)
Sources: ORCID, Web Of Science, NC State University Libraries
Added: May 17, 2021

2021 journal article

Non-parallel hyperplanes ordinal regression machine

KNOWLEDGE-BASED SYSTEMS, 216.

By: H. Jiang n, Z. Yang* & Z. Li n

author keywords: Ordinal regression; Support vector machine; Twin support vector machine; Non-parallel hyperplanes ordinal regression machine
TL;DR: The results show that the approach NPHORM is comparable with the other SVM-based approaches, especially in real ordinal regression datasets, and outperforms the deep learning methods on MAE. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Sources: ORCID, Web Of Science, NC State University Libraries
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.

By: J. Xu*, H. Su* & Z. Li n

author keywords: Incompressible magneto-hydrodynamics equations; Nonconforming finite element; Iterative method; Stability; Optimal error estimate
Sources: Web Of Science, NC State University Libraries
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.

By: P. Huang* & Z. Li n

author keywords: Elasticity interface problems; Immersed finite element; Discontinuous coefficients; Coercivity; Inf-sup condition; Error estimates
TL;DR: Through verifying the inverse trace inequality on the interface edges, the optimal convergence in the energy norm are derived and a new test function is constructed to obtain the discrete inf-sup condition of the penalty-free nonsymmetric PPIFEM and is utilized in the proof of the optimal converge. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: September 14, 2020

2021 journal article

Partially penalized IFE methods and convergence analysis for elasticity interface problems

Journal of Computational and Applied Mathematics.

Zhilin Li

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.

By: J. Ye*, Z. Yang* & Z. Li n

author keywords: Regression problem; support vector regression; quadratic kernel-free least squares support vector regression
TL;DR: A novelkernel-free regressor, called quadratic hyper-surface kernel-free least squares support vector regression (QLSSVR), for some regression problems, which has better performance than other existing regression approaches in terms of regression criterion and CPU time. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Sources: Web Of Science, NC State University Libraries
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.

By: X. Xiao*, X. Feng* & Z. Li n

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, NC State University Libraries
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.

By: B. Dong, X. Feng & Z. Li*

author keywords: anisotropic elliptic interface problem; finite element and finite difference method; maximum principle preserving scheme; normal derivative computation; scaling technique; error analysis
TL;DR: Anisotropic elliptic interface problems are important but hard to solve either analytically or numerically, so there is limited literature on numerical methods based on structured meshes. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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
TL;DR: New strategies based on IIM are proposed for elliptic interface problems to compute the gradient at grid points both regular and irregular, and at the interface from each side of the interface, to validate the numerical methods and analysis. (via Semantic Scholar)
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.

By: X. Chen n, X. Feng* & Z. Li n

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
TL;DR: A direct method without using the augmented variable is proposed for elliptic interface problems with a variable coefficient that can have a finite jump across an interface. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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.

By: X. Xiao*, X. Feng* & Z. Li n

author keywords: adaptive strategy; recovery-based error estimator; streamline diffusion method; surface convection-diffusion-reaction equations; surface finite element method
TL;DR: Various numerical examples, including the convection‐dominated diffusion problems with large variations of solutions, nearly singular solutions, discontinuous sources, and internal layers on surfaces, are presented to demonstrate the efficacy and accuracy of the proposed adaptive mesh refinement method. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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.

By: Z. Li*, B. Dong, F. Tong & W. Wang

author keywords: Immersed boundary method; augmented approach; convergence; derivative computing
TL;DR: An immersed boundary-augmented method has been developed for linear elliptic boundary value problems on arbitrary domains with a Dirichlet boundary condition that inherits the simplicity, robustness, and first order convergence of the IB method but also provides asymptotic convergence of partial derivatives. (via Semantic Scholar)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities (OpenAlex)
Sources: Web Of Science, NC State University Libraries
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).

By: Y. Yao*, Y. Zhang, L. Tian*, N. Zhou*, Z. Li n & M. Wang*

author keywords: sustainable mode of transportation; bike-sharing system; public bicycle; complex network; network structure
TL;DR: The results showed that there were many stations with low usage of public bicycles, the average service coverage of the public bicycle system was consistent with the original intention of “the first and last mile”, and public bicycles could meet different travel needs. (via Semantic Scholar)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities (Web of Science; OpenAlex)
Sources: Web Of Science, NC State University Libraries
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.

By: T. Zhao, J. Zhang, Z. Li* & Z. Zhang

author keywords: Lorenz model; tangent linear model; nonlinear model; Monte Carlo
Sources: Web Of Science, NC State University Libraries
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.

By: Y. Yao*, X. Jiang* & Z. Li n

author keywords: Green travel; Public bicycle; Spatiotemporal characteristics; Clustering analysis; Visualization analysis
TL;DR: The results showed that public bicycles were mainly used for commuting or transferring, and social and economic activities around stations greatly influenced the use of public bicycles, however, the usage of the public bicycle system was still at a low level. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Sources: Web Of Science, NC State University Libraries
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.

By: X. Chen n, Z. Li n & J. Ruiz Alvarez*

author keywords: Incompressible Stokes equations; Interface problem; Discontinuous viscosity; Marker and cell scheme; Staggered mesh; Uzawa method; Immersed interface method; Finite difference method
TL;DR: A direct immersed interface method is proposed to solve two-phase incompressible Stokes equations with an interface and a piecewise constant viscosity on staggered grids that avoids the costs for introducing augmented variables and difficulties in solving them from the corresponding Schur complement system. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
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.

By: H. Ji*, J. Chen* & Z. Li n

author keywords: Interface problem; Level set function; Source removal technique; Immersed interface
TL;DR: A high-order finite element method based on unfitted meshes for solving a class of elliptic interface problems whose solution and its normal derivative have finite jumps across an interface is proposed in this paper. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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.

By: Z. Li n, M. Lai*, X. Peng* & Z. Zhang*

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
TL;DR: The proposed new idea in enforcing the divergence free condition at the interface from the fluid side has also been utilized to solve the Stokes and Darcy coupling equations and shown to outperform the original method. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
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.

By: R. Hu n & Z. Li n

author keywords: Stokes equations; Error analysis; Finite difference method; Immersed interface method; Divergence-free
TL;DR: Based on recent theoretical development, particularly the error analysis by Beale and Layton (2006), second order convergence has been shown for both pressure and velocity under some assumptions. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2018 book

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

New York: Cambridge University Press.

By: Z. Li, Q. Zhonghua & T. Tang

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.

By: Z. Li*, X. Chen* & Z. Zhang

author keywords: ADI method; interface problems; discontinuous coefficient; multiscale; jump conditions; augmented variable; stability
TL;DR: Alternating direction implicit (ADI) method is one of the most efficient methods in solving parabolic PDEs of initial and boundary value problems and it is challenging to develop efficient ADI methods. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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.

By: F. Qin*, J. Chen*, Z. Li n & M. Cai*

author keywords: Nonconforming immersed finite element; Elasticity interface problems; Cartesian grid
TL;DR: The proposed IFE method possesses optimal approximation property for both compressible and nearly incompressible problems and is robust with respect to the shape of the interface and its location relative to the domain and the underlying mesh. (via Semantic Scholar)
UN Sustainable Development Goal Categories
16. Peace, Justice and Strong Institutions (OpenAlex)
Sources: Web Of Science, NC State University Libraries
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.

By: P. Huang* & Z. Li n

author keywords: Fluid structure interactions; Darcy-Stokes-Brinkman equations; Stokes equations; Darcy flow; discontinuous coefficient; nonconforming rectangular element; interior penalty; infsup condition; error estimates
TL;DR: A nonconforming rectangular finite element method to solve a fluid structure interaction problem characterized by the Darcy-Stokes-Brinkman Equation with discontinuous coefficients across the interface of different structures with some distinguished advantages and features. (via Semantic Scholar)
UN Sustainable Development Goal Categories
16. Peace, Justice and Strong Institutions (OpenAlex)
Sources: Web Of Science, NC State University Libraries
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.

By: F. Qin*, Z. Wang n, Z. Ma* & Z. Li n

author keywords: elliptic interface problems; gradient/flux computation; IFEM; mixed FE formulation; computational tube
TL;DR: A rigorous one dimensional analysis is presented, which shows a second order convergence order for both the solution and the gradient in 1D, and super-convergence for the gradient at the interface for two dimensional problems. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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.

By: Z. Li*, H. Ji & X. Chen*

author keywords: elliptic interface problem; accurate gradient computation; variable coefficient with discontinuity; interface; M-matrix; convergence proof; discrete Green function
TL;DR: Numerical examples for general elliptic interface problems have confirmed the theoretical analysis and efficiency of the new augmented method and second order convergence for the solution and the gradient from each side of the interface has also been proved. (via Semantic Scholar)
Sources: Web Of Science, 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.

By: Z. Li n & F. Qin*

author keywords: 4th order PDE; Discontinuous coefficient; Fast Poisson solver; Augmented immersed interface method; Schur complement; Natural jump conditions
TL;DR: The proposed method is probably the first finite difference method for such an interface problem although the paper is partially motivated by the immersed finite element method. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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.

By: P. Angot & Z. Li

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.

By: J. Yan*, M. Lai*, Z. Li n & Z. Zhang*

author keywords: Energy; momentum; mass; finite volume element method; MRLW equation
UN Sustainable Development Goal Categories
14. Life Below Water (Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2017 book

Numerical Solution of Differential Equations

In Cambridge University Press.

By: Z. Li n, Z. Qiao* & T. Tang*

UN Sustainable Development Goal Categories
4. Quality Education (OpenAlex)
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.

By: S. Amat*, Z. Li n & J. Ruiz*

author keywords: IIM; Finite difference methods; Correction terms; Multiresolution schemes; Improved adaption to discontinuities; Signal processing
TL;DR: The aim is to develop an algorithm for function approximation with full accuracy that is capable to adapt to corners (kinks) and jump discontinuities, that uses a centered stencil and that does not use extrapolation. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Sources: Crossref, NC State University Libraries
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.

By: Q. Zhang*, Z. Li n & Z. Zhang*

author keywords: Sparse grids; Stochastic inputs; Interface; Immersed finite element; Smolyak construction
TL;DR: The numerical method consists of an immersed finite element discretization in the physical space and a Smolyak construction of the extreme of Chebyshev polynomials in the probability space, which leads to the solution of uncoupled deterministic problems as in the Monte Carlo method. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2016 journal article

A new augmented immersed finite element method without using SVD interpolations

NUMERICAL ALGORITHMS, 71(2), 395–416.

By: H. Ji*, J. Chen* & Z. Li n

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
TL;DR: A new augmented immersed finite element method (IFEM) that does not need the interpolations is proposed for elliptic interface problems that have a piecewise constant coefficient and is extended to Poisson equations on irregular domains with a Dirichlet boundary condition. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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.

By: Z. Li n

author keywords: Stokes-Darcy fluid-structure interaction; augmented immersed interface method; fast Poisson solver; BJS interface condition; analytic solution of Stokes and Darcy coupling
UN Sustainable Development Goal Categories
16. Peace, Justice and Strong Institutions (OpenAlex)
Sources: Web Of Science, NC State University Libraries
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.

By: S. Zhang & Z. Li

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.

By: H. Ji, J. Chen & Z. Li*

author keywords: level set function; singularity removal technique; irregular domain; interface problem; non-homogeneous jump condition; 35J60; 65N30; 65N15
TL;DR: Augmented immersed finite element methods are proposed to solve elliptic interface problems with non-homogeneous jump conditions using the singularity removal technique to solve Poisson equations on irregular domains. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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.

By: Z. Li* & H. Mikayelyan

author keywords: Free discontinuity; free boundary; crack-tip; Mumford-Shah energy; augmented immersed interface method; fast/Poisson solver; irregular domain
UN Sustainable Development Goal Categories
Sources: Web Of Science, NC State University Libraries
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.

By: X. Su, X. Feng & Z. Li

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.

By: L. Melnyk*, Z. Wang n, Z. Li n & J. Xue*

author keywords: Risk ranking; Pesticides; Dietary exposure; ADI
MeSH headings : Adolescent; Adult; Age Factors; Child; Child, Preschool; Environmental Exposure / adverse effects; Feeding Behavior; Food Contamination / analysis; Humans; Infant; Infant, Newborn; Middle Aged; Models, Statistical; Pesticides / adverse effects; Pesticides / analysis; Pesticides / classification; Stochastic Processes; Young Adult
TL;DR: The results indicated that the highest ranking pesticides were methamidophos and diazinon which exceeded 100% of the ADI which had a marked decrease from 1991-1999 to 2000-2011. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Sources: Web Of Science, NC State University Libraries
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.

By: L. Zhu, Z. Zhang & Z. Li

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.

By: Y. Zeng*, J. Chen* & Z. Li n

author keywords: 65F10; 65N55; 65N30; Robin-Robin domain decomposition method; H(div)-elliptic problems; Raviart-Thomas finite element; convergence analysis; non-overlapping domain decomposition
TL;DR: The convergence of the method is proved for both the continuous problem and the finite element approximation in a parallel Robin–Robin domain decomposition method for H(div)-elliptic problems. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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)
TL;DR: A new Navier-Stokes solver based on a finite difference approximation is proposed to solve incompressible flows on irregular domains with open, traction, and free boundary conditions, which can be applied to simulations of fluid structure interaction, implicit solvent model for biomolecular applications and other free boundary or interface problems. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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.

By: L. Zhu*, Z. Zhang* & Z. Li n

author keywords: Finite volume element method; Source removal technique; Interface problem; Jump conditions
TL;DR: An immersed finite volume element method is developed to solve 2D elliptic interface problems with a variable coefficient that has a finite jump across an interface. (via Semantic Scholar)
UN Sustainable Development Goal Categories
7. Affordable and Clean Energy (OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2015 journal article

Effective matrix-free preconditioning for the augmented immersed interface method

JOURNAL OF COMPUTATIONAL PHYSICS, 303, 295–312.

By: J. Xia*, Z. Li n & X. Ye*

author keywords: Augmented immersed interface method; Schur complement system; GMRES; Matrix-free preconditioning; Hierarchically semiseparable structure; Adaptive randomized compression
Sources: Web Of Science, NC State University Libraries
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.

By: Q. Zhang*, K. Ito n, Z. Li n & Z. Zhang*

author keywords: PDE-constrained optimization; Variational discretization; Immersed finite element; Elliptic interface problem
TL;DR: This paper presents a numerical method and analysis, based on the variational discretization concept, for optimal control problems governed by elliptic PDEs with interfaces, which uses a simple uniform mesh which is independent of the interface. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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.

By: Z. Li n, L. Wang*, E. Aspinwall*, R. Cooper*, P. Kuberry*, A. Sanders*, K. Zeng*

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
TL;DR: Some new results on the jump conditions of the solution across the interface are derived using the distribution theory and the theory of weak solutions and the proof of the convergency of the Immersed Boundary method is presented. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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.

By: J. Ruiz Alvarez* & Z. Li n

author keywords: Immersed interface method; Axis-symmetric interface problem; Discontinuous coefficients; Finite difference method; Level set method; Hele-Shaw flow
TL;DR: The immersed interface method (IIM) in axis-symmetric coordinates is developed for elliptic interface problems that have a discontinuous coefficient, solution or flux and is shown to be second order accurate in the infinity norm. (via Semantic Scholar)
UN Sustainable Development Goal Categories
13. Climate Action (Web of Science)
Sources: Web Of Science, NC State University Libraries
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.

By: J. Xu*, Y. Huang*, M. Lai* & Z. Li n

author keywords: 3D immersed interface method; level-set method; insoluble surfactant; Stokes interfacial flow; drop deformation
TL;DR: A novel rotational procedure is given to generate smooth local coordinate systems and make effective interpolation for quantities at the projection points on the interface in conjunction with the level-set techniques. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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.

By: H. Ji*, J. Chen* & Z. Li n

author keywords: Immersed finite element method; Interface problems; Cartesian mesh; Discontinuous coefficient; Symmetric and consistent weak form
Sources: Web Of Science, NC State University Libraries
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.

TL;DR: The initial efforts to formulate the physical concepts necessary for coupling the two mechanics and develop a 3D numerical algorithm to simulate the solvent fluid via the Navier-Stokes equation are reported. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
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.

By: Z. Li n

Sources: Crossref, NC State University Libraries
Added: January 21, 2021

2014 journal article

Special issue on fluid structure interactions preface

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

By: Z. Li

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.

By: Q. Wang*, Z. Zhang* & Z. Li n

author keywords: Fourier finite volume element method; Quasi-geostrophic equations on a sphere; Trial and test function spaces; Pole singularity
UN Sustainable Development Goal Categories
13. Climate Action (Web of Science)
Sources: Web Of Science, NC State University Libraries
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.

By: Z. Li n & P. Song n

author keywords: Adaptive mesh refinement method; Immersed interface method; Stokes and Navier-Stokes equations; Surface tension; Bubble deformation; Level set method
TL;DR: The AMR-IIM is validated for Stokes and Navier-Stokes equations with exact solutions, moving interfaces driven by the surface tension, and classical bubble deformation problems. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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.

MeSH headings : Algorithms; Computer Simulation; Models, Chemical; Models, Molecular; Proteins / chemistry; Small Molecule Libraries / chemistry; Solvents; Static Electricity; Thermodynamics
TL;DR: This study explored and evaluated a strategy based on the "induced surface charge" to eliminate the dielectric jump within the finite-difference discretization scheme and showed that the strategy is consistent with theory and the classical finite-Difference method on the tested systems. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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
TL;DR: A second-order finite-difference numerical method to solve the widely used Poisson-Boltzmann equation for electrostatic analyses of realistic bio-molecules is explored and found to deliver more accurate and better-converged grid potentials than the classical method on or nearby the molecular surface. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2013 journal article

Numerical Poisson-Boltzmann model for continuum membrane systems

CHEMICAL PHYSICS LETTERS, 555, 274–281.

By: W. Botello-Smith*, X. Liu*, Q. Cai*, Z. Li n, H. Zhao* & R. Luo*

TL;DR: This study developed a continuum membrane model utilizing a level set formulation under the numerical Poisson-Boltzmann framework within the AMBER molecular mechanics suite for applications such as protein-ligand binding affinity and docking pose predictions. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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.

By: P. Song n, J. Xue* & Z. Li n

author keywords: Autocorrelation; longitudinal data; mixed models; simulation; variance-covariance structure
MeSH headings : Analysis of Variance; Longitudinal Studies; Models, Theoretical
TL;DR: A new simulation method to generate longitudinal data with flexible numbers of subjects and days that generates values from numerous data sources and simulates continuous observed variables better than current data methods. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2012 journal article

A Numerical Method for Solving Elasticity Equations with Interfaces

COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 12(2), 595–612.

By: S. Hou*, Z. Li n, L. Wang* & W. Wang*

author keywords: Elasticity equations; non-body fitted mesh; finite element method; jump condition
TL;DR: An efficient non-traditional finite element method with non-body-fitting grids is proposed to solve elasticity equations with interfaces to choose the test function basis to be the standard finite element basis independent of the interface and the solution based to be piecewise linear satisfying the jump conditions across the interface. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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.

By: J. Ho, Z. Li* & S. Lubkin*

Contributors: J. Ho, Z. Li* & S. Lubkin*

author keywords: Immersed interface method; augmented method; projection method; Navier-Stokes; moving interface; implicit scheme; fluid-structure
TL;DR: An augmented immersed interface method for simulating the dynamics of a deformable structure with mass in an incompressible fluid and shows that the fluid-structure system has bi-stability: a stationary state for a smaller Reynolds number and an oscillatoryState for a larger Reynolds number. (via Semantic Scholar)
Sources: Web Of Science, 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.

By: Z. Li n & P. Song n

author keywords: Adaptive mesh refinement; immersed boundary method; immersed interface method; elliptic interface problem; Cartesian grid method; level set representation; singular sources
TL;DR: An adaptive mesh refinement strategy is proposed for the Immersed Boundary and Immersed Interface methods for two-dimensional elliptic interface problems involving singular sources by distributing the mesh more economically, therefore, reduce the size of the linear system of the equations. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2012 book

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

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

Zhilin Li

Ed(s): Z. Li

Source: NC State University Libraries
Added: April 5, 2021

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.

By: I. Caraus* & Z. Li n

author keywords: Collocation method; classical Holder space; system of singular integro-differential equation; Fejer points
Sources: Web Of Science, NC State University Libraries
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.

By: X. Wan* & Z. Li*

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
TL;DR: Two new finite difference methods are proposed for solving Helmholtz equations on irregular domains, or with interfaces, and a new maximum principle preserving finite difference method is developed. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2012 book

SPECIAL ISSUE ON FLUID DYNAMICS, ANALYSIS AND NUMERICS

Zhilin Li

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.

By: X. Feng* & Z. Li n

author keywords: conservative finite difference scheme; discontinuous coefficient; immersed interface method; interface problem; polar coordinates; Richardson extrapolation
TL;DR: This article proposes simplified immersed interface methods for elliptic partial/ordinary differential equations with discontinuous coefficients across interfaces that are few isolated points in 1D, and straight lines in 2D using a conservative second‐order finite difference scheme whose coefficient matrix is symmetric and definite. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
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

Zhilin Li

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-.

By: A. Layton, J. Stockie, Z. Li & H. Huang

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.

By: K. Ito n, Z. Li n & Z. Qiao*

author keywords: Navier-Stokes equations; sensitivity analysis; flow past cylinder; embedding technique; immersed interface method; irregular domain; augmented system; projection method; fluid-solid interaction
TL;DR: Numerical sensitivity analysis with respect to the Reynolds number can predict the critical Reynolds number at which the vortex shading begins to develop in the wake of the obstacle. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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.

By: H. Xie, Z. Li & Z. Qiao

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.

By: C. Wu, Z. Li & M. Lai

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.

By: X. Feng, Z. Li & Z. Qiao

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
UN Sustainable Development Goal Categories
Sources: Web Of Science, NC State University Libraries
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.

By: J. Ruiz Alvarez*, J. Chen* & Z. Li n

author keywords: Immersed interface method; Polar coordinates; Interface; Discontinuous coefficients; Finite difference method; Electro capacitance tomography; Forward problem
TL;DR: The algorithm and analysis here is one step forward in applying the IIM for 3D problems in axisymmetric situations or in the spherical coordinates and the application to the solution of the electric potential inside an ECT device. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2010 journal article

An augmented method for free boundary problems with moving contact lines

COMPUTERS & FLUIDS, 39(6), 1033–1040.

By: Z. Li n, M. Lai*, G. He* & H. Zhao*

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, NC State University Libraries
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.

By: Y. Gong & Z. Li

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.

By: X. Yang*, X. Zhang*, Z. Li n & G. He*

author keywords: Immersed boundary method; Moving boundary; Non-physical force oscillations; Smoothed discrete delta function
TL;DR: It has been shown that the smoothed discrete delta functions constructed in this paper have one-order higher derivative than the regular ones, which can effectively suppress the non-physical oscillations in the volume forces and improve the accuracy of the immersed boundary method with direct forcing in moving boundary simulations. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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.

By: K. Ito n, M. Lai* & Z. Li n

author keywords: Navier-Stokes equations; Embedding technique; Immersed interface method; Irregular domain; Augmented system; Projection method; Level set representation
TL;DR: An augmented method based on a Cartesian grid is proposed for the incompressible Navier-Stokes equations in irregular domains using the immersed interface method to achieve second order accuracy for the velocity. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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.

TL;DR: This work explored the ideas of enforcing interface conditions by the immerse interface method and of removing charge singularity to improve the finite-difference methods, showing significant improvement in both energies and forces. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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.

By: F. Wang*, J. Chen*, W. Xu* & Z. Li n

author keywords: Domain decomposition; Mortar finite element method; Additive Schwarz method; Rotated Q(1) element
TL;DR: It is shown that the proposed additive Schwarz preconditioner for the mortar-type rotated Q"1 finite element method for second order elliptic partial differential equations with piecewise but discontinuous coefficients has a quasi-optimal convergence behavior. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2009 conference paper

Analysis and computation for a fluid mixture model

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

By: Q. Jiang, Z. Li & S. Lubkin

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.

By: B. Khoo*, Z. Li n & P. Lin*

Ed(s): B. Khoo*, Z. Li n & P. Lin*

TL;DR: An Introduction to the Immersed Boundary and theImmersed Interface Methods Lecture Notes on Nonlinear Tumor Growth: Modeling and Simulation Progress in Modeling Pulsed Detonations Direct Numerical Simulations of Multiphase Flows. (via Semantic Scholar)
Sources: ORCID, Crossref, NC State University Libraries
Added: January 1, 2021

2009 book

Interface problems and methods in biological and physical flows

New Jersey: World Scientific.

Zhilin Li

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.

By: G. Chen n, Z. Li n & P. Lin*

author keywords: biharmonic equation; irregular domain; augmented method; immersed interface method; incompressible stokes flow
TL;DR: A fast second order accurate algorithm based on a finite difference discretization and a Cartesian grid and a new interpolation scheme to evaluate the residual of the Schur complement system is developed for two dimensional biharmonic equations on irregular domains with essential boundary conditions. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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.

By: H. Xie*, K. Ito*, Z. Li* & J. Toivanen

Sources: NC State University Libraries, NC State University Libraries
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.

By: V. Rutka* & Z. Li n

author keywords: Navier-Stokes equations; interface; discontinuous viscosity; immersed interface method; explicit jump immersed interface method; projection method
TL;DR: An explicit jump immersed interface method (EJIIM) for the incompressible Navier–Stokes equations with a discontinuous viscosity and singular forces along one or several interfaces in the solution domain to get a second-order finite difference discretization at the grid points near or on the interface. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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.

By: Z. Tan*, D. Le*, Z. Li n, K. Lim* & B. Khoo*

author keywords: Incompressible viscous flows; Piecewise constant viscosity; Singular force; Immersed interface method; Projection method; Front tracking method
TL;DR: This paper presents an implementation of the second-order accurate immersed interface method to simulate the motion of the flexible elastic membrane immersed in two viscous incompressible fluids with different viscosities, and introduces the velocity components at the membrane as two augmented unknown interface variables to decouple the originally coupled jump conditions for the velocity and pressure. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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.

By: Y. Gong*, B. Li & Z. Li*

author keywords: elliptic interface problems; nonhomogeneous jump conditions; immersed-interface finite-element method; level-set functions; error estimates
TL;DR: A class of new finite- element methods, called immersed-interface finite-element methods, is developed to solve elliptic interface problems with nonhomogeneous jump conditions to provide fast simulation of interface dynamics that does not require remeshing. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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.

By: X. Wan n, Z. Li n & S. Lubkin n

Contributors: X. Wan n, Z. Li n & S. Lubkin n

MeSH headings : Animals; Computer Simulation; Embryo, Mammalian; Epithelium / physiology; Extracellular Matrix / physiology; Kinetics; Mesoderm / cytology; Mesoderm / physiology; Models, Biological; Morphogenesis / physiology; Stress, Mechanical; Viscosity
TL;DR: A 3D model of the mechanics of clefting is developed, focusing in this paper solely on the potential role of mesenchyme-generated traction forces, and finds that mesenchymal traction forces are sufficient to generate a cleft of the correct size and morphology, in the correct time frame. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Sources: Web Of Science, 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.

By: Z. Li n, C. Pao n & Z. Qiao*

author keywords: nonlinear Poisson-Boltzmann equation; exterior problem; immersed interface method; monotone iterative method
TL;DR: A fast finite difference method based on the monotone iterative method and the fast Poisson solver on irregular domains for a 2D nonlinear Poisson–Boltzmann equation is proposed and analyzed and is efficient in terms of accuracy, speed, and flexibility in dealing with the geometry of the domain. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries, 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.

By: P. Gremaud n, C. Kuster n & Z. Li n

TL;DR: Two types of reinitialization methods are studied: a high order ''PDE'' approach and a second order Fast Marching method, with emphasis on the tube/narrow band implementation and accuracy considerations. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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.

By: Z. Li n, K. Ito n & M. Lai*

Sources: Web Of Science, NC State University Libraries
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.

By: Z. Li, S. Lubkin & X. Wan

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.

By: Z. Li n, M. Lai* & K. Ito n

Sources: Crossref, NC State University Libraries
Added: February 24, 2020

2007 book

Applied Numerical Mathematics for the International Conference on Scientific Computing

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

Zhilin Li

Ed(s): Z. Li

Source: NC State University Libraries
Added: April 5, 2021

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

Zhilin Li

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.

By: Z. Li n, Y. Song* & T. Tang*

Sources: Web Of Science, NC State University Libraries
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

Zhilin Li

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
TL;DR: The method couples a semi-implicit discretization for solving the surfactant transport equation recently developed by Xu and Zhao with the immersed interface method originally developed by LeVeque and Li, for the first time that the level-set method has been used to simulate fluid interfaces with surfactants. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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.

By: Z. Li, X. Wan, K. Ito & S. Lubkin

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.

By: Z. Li, Z. Qiao & T. Tang

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.

By: M. Lai, Z. Li* & X. Lin*

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, NC State University Libraries
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.

By: K. Ito* & Z. Li*

author keywords: incompressible Stokes equations; interface; discontinuous viscosity; interface conditions; singular sources
TL;DR: The interface conditions, or jump conditions, for the pressure and the velocity of the solution to the incompressible Stokes equations with a discontinuous viscosity and a singular source along an interface are derived in this work. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2006 book

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

By: Z. Li* & K. Ito*

Sources: NC State University Libraries, NC State University Libraries
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).

By: Z. Li n

Ed(s): Z. Li n, L. Vulkov & J. Wasniewski

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

TL;DR: The augmented strategies for interface problems and problems defined on irregular domains are reviewed in this paper to get faster algorithms, particularly, to take advantages of existing fast solvers. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries, 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.

By: K. Ito n, Z. Li* & Y. Kyei

author keywords: fourth order finite difference schemes; elliptic and parabolic equations on irregular domains; immersed interface method
TL;DR: Second and fourth order Cartesian grid based finite difference methods are proposed for elliptic and parabolic partial differential equations, and associated eigenvalue problems on irregular domains with general boundary conditions. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2005 journal article

Immersed finite element for elasticity system with discontinuities

AMS Contemporary Mathematics, 383, 285–298.

By: Z. Li & X. Yang

Source: NC State University Libraries
Added: December 28, 2021

2005 book

Numerical Analysis and Its Applications

Zhilin Li

Ed(s): Z. Li, L. Vulkov & J. Waśniewski

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

TL;DR: Uniform Convergence of a Monotone Iterative Method for a Nonlinear Reaction-Diffusion Problem and the Dynamics of Matrix Coupling with an Application to Krylov Methods are discussed. (via Semantic Scholar)
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.

By: Z. Li n, T. Lin*, Y. Lin* & R. Rogers*

author keywords: interface problems; immersed interface; finite element; error estimates
Sources: Web Of Science, NC State University Libraries, 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.

By: V. Zolotarevskii*, Z. Li* & I. Caraus n

Sources: Web Of Science, NC State University Libraries
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.

By: Z. Li* & C. Wang

TL;DR: A fast finite difference method is proposed to solve the incompressible Navier-Stokes equations defined on a general domain using the immersed interface method and the fast Poisson solver for general domains and the interpolation scheme for the boundary condition of the stream function. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
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.

By: Z. Li*

TL;DR: The immersed interface method for various problems is introduced, its recent advances and related software packages are discussed, and some of its applications are reviewed. (via Semantic Scholar)
Sources: NC State University Libraries, NC State University Libraries
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.

By: Z. Li n, X. Lin, M. Torres n & H. Zhao*

UN Sustainable Development Goal Categories
16. Peace, Justice and Strong Institutions (OpenAlex)
Sources: Crossref, NC State University Libraries
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.

By: Z. Li n, T. Lin* & X. Wu*

TL;DR: New finite element methods based on Cartesian triangulations are presented for two dimensional elliptic interface problems involving discontinuities in the coefficients, and these new methods can be used as finite difference methods. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2003 journal article

New formulations for interface problems in polar coordinates

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 25(1), 224–245.

By: Z. Li n, W. Wang*, I. Chern* & M. Lai

author keywords: interface problems; singular source; delta function; level set function; discontinuous coefficients; polar coordinates; immersed interface method; smooth extension; fast Poisson solver
TL;DR: A fast solver has been developed for the interface problems with a piecewise constant but a discontinuous coefficient using the new formulation in a polar coordinate system. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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.

By: K. Ito n & Z. Li n

author keywords: non-linear interface problem; magneto-rheological fluid; maximum principal preserving scheme; immersed interface method; level set method; substitution method
TL;DR: A finite difference method based on Cartesian grids and the maximum principle preserving immersed interface method is proposed for the nonlinear elliptic interface problems discussed in this paper and is nearly second order accurate in the infinity norm. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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.

By: X. Yang, B. Li & Z. Li

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.

By: S. Deng*, K. Ito n & Z. Li n

author keywords: 3D elliptic interface problem; irregular domain; discontinuous coefficient; discrete maximum preserving scheme; quadratic optimization; algebraic multigrid; shape identification; level set method
TL;DR: Two second-order accurate elliptic solvers using Cartesian grids are presented for three-dimensional interface problems in which the coefficients, the source term, the solution and its normal flux may be discontinuous across an interface. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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.

By: S. Lubkin* & Z. Li*

Contributors: S. Lubkin* & Z. Li*

MeSH headings : Animals; Cell Size / physiology; Computer Simulation; Elasticity; Epithelium / anatomy & histology; Epithelium / embryology; Epithelium / growth & development; Humans; Mechanotransduction, Cellular / physiology; Mesoderm / cytology; Mesoderm / physiology; Models, Biological; Morphogenesis / physiology; Rheology / methods; Stress, Mechanical; Surface Properties; Viscosity
TL;DR: It is proposed that a complete understanding of branching morphogenesis requires measurements of the mechanical aspects, and it is found that the surface tension, clefting force, and viscosity ratio of the two tissues have significant effects on the branching. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Sources: Web Of Science, NC State University Libraries, ORCID
Added: August 6, 2018

2002 report

Industrial Mathematics Modeling Workshop for Graduate Students Series

[CRSC Technical Reports].

Zhilin Li

Ed(s): P. Gremaud, Z. Li, R. Smith & H. Tran

Source: NC State University Libraries
Added: December 28, 2021

2002 journal article

Reactive autophobic spreading of drops

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

By: J. Hunter*, Z. Li n & H. Zhao*

Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2002 journal article

The immersed interface/multigrid methods for interface problems

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 24(2), 463–479.

By: L. Adams & Z. Li*

author keywords: interface problems; diffusion and advection equation; multigrid method; discontinuous coefficients; quadratic optimization; discrete maximum principle
TL;DR: The second order maximum principle preserving finite difference scheme for linear parabolic equations, using the Crank--Nicolson scheme to deal with the diffusion part and an explicit scheme for the first order derivatives is developed. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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).

By: Z. Li n & W. Cai*

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

TL;DR: The level set method is coupled with the boundary element method to simulate dynamic powder consolidation of metals based on linear elastostatics theory to simulations of dynamic powder aggregation of metals. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries, 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.

By: M. Lai* & Z. Li n

author keywords: immersed boundary method; immersed interface method; jump conditions
TL;DR: Jump conditions for the pressure, the velocity, and their normal derivatives across an immersed moving membrane in an incompressible fluid are derived and can be used to formulate the governing equations in an alternative form. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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,

By: Z. Li

Source: NC State University Libraries
Added: December 28, 2021

2001 report

Industrial Mathematics Modeling Workshop for Graduate Students Series

[CRSC Technical Reports].

Zhilin Li

Ed(s): P. Gremaud, Z. Li, R. Smith & H. Tran

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.

By: K. Ito n, K. Kunisch* & Z. Li n

Sources: Web Of Science, NC State University Libraries
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.

By: Z. Li* & K. Ito*

author keywords: elliptic interface problems; finite difference methods; discontinuous coefficients; singular source term; discrete maximum principle; quadratic optimization; multigrid methods
TL;DR: New finite difference methods using Cartesian grids are developed for elliptic interface problems with variable discontinuous coefficients, singular sources, and nonsmooth or even discontinuous solutions to satisfy the sign property of the discrete maximum principle using quadratic optimization techniques. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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.

By: Z. Li

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.

By: Z. Li n & . Lubkin n

Contributors: Z. Li n & S. Lubkin n

author keywords: discontinuous and non-smooth solution; immersed interface method; interface; jump condition; Stokes equation; variable surface tension
Sources: Web Of Science, 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.

By: Z. Li n & M. Lai n

author keywords: Navier-Stokes equations; interface; discontinuous and nonsmooth solution; immersed interface method; immersed boundary method; projection method; level set method
TL;DR: An immersed interface method for the incompressible Navier–Stokes equations with singular forces along one or several interfaces in the solution domain is proposed based on a second-order projection method with modifications only at grid points near or on the interface. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2000 book

Industrial Mathematics

Philadelphia: SIAM.

Zhilin Li

Ed(s): P. Gremaud, Z. Li, R. Smith & H. Tran

Source: NC State University Libraries
Added: December 28, 2021

2000 report

Industrial Mathematics Modeling Workshop for Graduate Students Series

[CRSC Technical Reports].

Zhilin Li

Ed(s): P. Gremaud, Z. Li, R. Smith & H. Tran

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.

By: Z. Li & Y. Shen

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.

By: Z. Li*, H. Zhao & H. Gao

UN Sustainable Development Goal Categories
10. Reduced Inequalities (OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

1999 journal article

Convergence analysis of the immersed interface method

IMA JOURNAL OF NUMERICAL ANALYSIS, 19(4), 583–608.

By: H. Huang & Z. Li

TL;DR: A rigorous error analysis is given for the immersed interface method (IIM) applied to elliptic problems with discontinuities and singularities, and second-order convergence of IIM is indicated by the analysis. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

1999 journal article

Crack jump conditions for elliptic problems

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

By: A. Wiegmann*, Z. Li n & R. LeVeque*

author keywords: jump conditions; transmission problem; elliptic crack problems
Sources: Web Of Science, NC State University Libraries
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.

By: Z. Li* & B. Soni

Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

1999 report

Industrial Mathematics Modeling Workshop for Graduate Students series

[CRSC Technical Reports].

Zhilin Li

Ed(s): P. Gremaud, Z. Li, R. Smith & H. Tran

Source: NC State University Libraries
Added: December 28, 2021

1999 journal article

Numerical Study of Two Dimensional Electro-migration

Journal of Computational Physics, 152, 281–304.

By: H. Gao, Z. Li & H. Zhao

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.

By: R. Ewing*, Z. Li n, T. Lin* & Y. Lin*

author keywords: finite volume; convergence; error estimate; interface problems
UN Sustainable Development Goal Categories
7. Affordable and Clean Energy (OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

1999 journal article

Types of reductive monoids

Journal of Algebra, 221(1), 102–116.

By: Z. Li* & M. Putcha n

Sources: NC State University Libraries, NC State University Libraries
Added: August 6, 2018

1998 journal article

A fast iterative algorithm for elliptic interface problems

SIAM JOURNAL ON NUMERICAL ANALYSIS, 35(1), 230–254.

By: Z. Li*

author keywords: elliptic equation; discontinuous coefficients; immersed interface method; Cartesian grid; Schur complement; GMRES method; preconditioning
TL;DR: The idea in this approach is to precondition the differential equation before applying the immersed interface method, and to take advantage of fast Poisson solvers on a rectangular region, an intermediate unknown function, the jump in the normal derivative across the interface, is introduced. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

1998 journal article

The immersed interface method using a finite element formulation

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

By: Z. Li n

author keywords: immersed interface method; finite element method; modified basis function; natural jump condition; error analysis
Sources: Web Of Science, NC State University Libraries
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.

By: Z. Li n, D. Wang* & J. Zou*

author keywords: mixed type system; discontinuous coefficients; Dirac delta function; finite difference; semi-implicit prediction-correction scheme; error analysis
Sources: Crossref, NC State University Libraries
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.

By: T. Hou*, Z. Li*, S. Osher* & H. Zhao*

TL;DR: This method combines the advantage of the two approaches and gives a second-order Eulerian discretization for interface problems and is applied to Hele?Shaw flow, an unstable flow involving two fluids with very different viscosity. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: September 21, 2020

1997 journal article

An Inverse Problem in a Parabolic Equation

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

By: Z. Li & K. Zheng

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.

By: J. Heine, Z. Li & D. McTigue

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.

By: R. LeVeque & Z. Li*

author keywords: Stokes flow; creeping flow; interface tracking; discontinuous coefficients; immersed interface methods; Cartesian grids; bubbles
TL;DR: A second-order accurate interface tracking method for the solution of incompressible Stokes flow problems with moving interfaces on a uniform Cartesian grid is presented and an implicit quasi-Newton method is developed that allows reasonable time steps to be used. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: March 21, 2021

1997 journal article

Immersed interface methods for moving interface problems

Numerical Algorithms, 14, 269–293.

By: Z. Li*

author keywords: immersed interface method; Stefan problem; moving interface; discontinuous coefficients; singular source term; immersed boundary method; Cartesian grid; heat conduction
TL;DR: The Crank-Nicolson difference scheme with modifications near the interface is used to solve for the solution u(x,t) and the interface α (t) simultaneously and second order accuracy on uniform grids is confirmed both for the solutions and the position of the interface. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
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.

By: Z. Li*

author keywords: 3D elliptic equation; finite difference methods; irregular interface; discontinuous coefficients; singular source term; delta functions; Cartesian grid; immersed interface method
Sources: Crossref, NC State University Libraries
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.

By: R. LeVeque & Z. Li

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.

By: R. LeVeque & Z. Li*

author keywords: ELLIPTIC EQUATION; FINITE DIFFERENCE METHODS; IRREGULAR DOMAIN; INTERFACE; DISCONTINUOUS COEFFICIENTS; SINGULAR SOURCE TERM; DELTA FUNCTIONS
Sources: Crossref, NC State University Libraries
Added: September 21, 2020

1994 thesis

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

(PhD thesis). University of Washington.

By: Z. Li

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.

By: Z. Li & A. Mayo

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.

By: K. Huang & Z. Li

Source: NC State University Libraries
Added: December 28, 2021

1989 journal article

Roundoff error analysis for polynomial interpolation

Research and Review in Mathematics, (2).

By: K. Huang & Z. Li

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).

By: Z. Li

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.

By: Z. Li

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.

By: Z. Li

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.

By: K. Huang & Z. Li

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.

By: K. Huang & Z. Li

Source: NC State University Libraries
Added: December 28, 2021

book

Industrial Mathematics

In SIAM, USA.

Zhilin Li

Source: ORCID
Added: January 1, 2021

book

Numerical Analysis and Its Applications

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

Zhilin Li

Source: ORCID
Added: January 1, 2021

Employment

Updated: January 1st, 2021 10:23

1997 - present

North Carolina State University Raleigh, NC, US
Professor Mathematics

1994 - 1996

University of California, Los Angeles CA, CA, US
CAM Assistant professor Mathematics

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