Research Interests
1. Numerical analysis and scientific computation,
2. Applied mathematics and mathematical biology.
Past and current Research Projects
1. Electrostatics, Coulomb field, and the
Poisson–Boltzmann equation
2. The Poisson–Nernst–Planck model
3. Particle trajectory crossing in two-phase
flows
4. Computation of semi-classical approximation
of the Schrodinger equation, multi-valued solutions to the Euler-Poisson
equation and high frequency wave propagation
Publications
·
J. Ding, Z.
Wang and S. Zhou, Energy dissipative and positivity preserving schemes for
large convection ion transport with steric and
solvation effects, J. Comput. Phys., 2023,
488(2):112206.
·
H. Liu, Z. Wang, P. Yin and H. Yu,
Positivity-preserving third order DG schemes for Poisson--Nernst--Planck
equations, J. Comput. Phys., 2022, 110777
·
S. Roudenko, Z. Wang, and K. Yang,
Dynamics of solutions in the generalized Benjamin-Ono equation: A numerical
study, J. Comput. Phys., 445(2021), 110570
·
J. Ding, Z. Wang and S. Zhou,
Structure-preserving and efficient numerical methods for ion transport, J. Comput.
Phys., 418(2020), 109597
·
J. Ding, Z. Wang and S. Zhou, Positivity
Preserving Finite Difference Methods for Poisson--Nernst--Planck Equations with
Steric Interactions: Application to Slit-Shaped Nanopore Conductance, J. Comput.
Phys., 397(2019), 108864.
·
Y. Qian, Z. Wang and S. Zhou, A
conservative, free energy dissipating, and positivity preserving finite
difference scheme for multi-dimensional nonlocal Fokker-Planck equation, J. Comput. Phys., 386(2019), 22-36.
·
F. Siddiqua, Z. Wang and S. Zhou, A
Modified Poisson--Nernst--Planck Model with Excluded Volume Effect: Theory and
Numerical Implementation, Commun. Math. Sci., 16(2018), no. 1, 251-271.
·
J. Ding, H. Sun, Z. Wang and S. Zhou,
Computational study on hysteresis of ion channels: multiple solutions to
steady-state Poisson--Nernst--Planck equations, Commun. Comput. Phys., 23 (2018), 1549-1572.
·
C. Li, R. Qin, J. Ming and Z. Wang, A
discontinuous Galerkin method for stochastic
Cahn-Hilliard equations,
Comput.
Math. Appl., 75(2018), no. 6, 2100-2114.
·
H. Liu and Z. Wang, A free energy
satisfying discontinuous Galerkin method for one-dimensional
Poisson--Nernst--Planck systems, J. Comput. Phys., 328(2017), 413--437.
·
Z. Dong and Z. Wang, Variational
inference of linear regression with nonzero prior means, Communications in
Statistics - Simulation and Computation, 45 (2016), 2241-2248
·
H. Liu and Z. Wang, Entropy satisfying
Discontinuous Galerkin methods for Nonlinear
Fokker-Planck equations, J. Sci. Comput., 62 (2015),
no. 3, 803--830
·
H. Liu and Z. Wang, A free energy
satisfying finite difference method for Poisson–Nernst–Planck equations, J. Comput. Phys. 268 (2014), 363--376
Z. Wang, J. Che, L.T. Cheng,J. Dzubiella, B. Li and A.
McCammon, Level-set variational implicit solvation modeling of
Biomolecules with the Coulomb-field
approximation, J. Chem. Theory Comput.8,
386 (2012)
·
Z. Wang, J. Che, L.-T. Cheng, J. Dzubiella, B. Li, and J.
McCammon, Level-set variational implicit-solvent modeling of
biomolecules with the Coulomb-field approximation, J. Chem. Theory Comput., 8 (2012), 386-397.
·
S. Zhou, Z. Wang and B. Li, Mean-field
description of ionic size effects with nonuniform ionic sizes: A numerical approach, Phys. Rev.
E 84, 021901 (2011)
·
H. Liu, Z. Wang and F. Rodney, A level
set approach for dilute fluid-particle flows, J. Comput.
Phys. 230 (2011), no. 4, 920–936
·
L.-T. Cheng, B. Li,
Z. Wang, Level-set minimization of potential controlled Hadwiger
valuations for molecular solvation, J. Comput. Phys.,
229 (2010), 8497--8510
·
B. Li, B. Lu, Z. Wang and A. McCammon,
Solutions to a model Poisson-Nernst-Planck system and the determination of
reaction rates, Physica A 389 (2010), 1329--1345
·
P. Setny, Z.
Wang, L.-T. Cheng, B. Li, J.A. McCammon, J. Dzubiella,
Dewetting-controlled binding of ligands to
hydrophobic pockets, Physical Review Letters 103 (2009),
no.18, 187801
Note: This
article was also selected for republication in the Nov 1, 2009 issue of Virtual
J. of Biological Physics Research.
·
L.-T. Cheng, Z. Wang, P. Setny, J. Dzubiella, B. Li and A.
McCammon, Interfaces and hydrophobic interactions in receptor-ligand systems: A
level-set variational implicit solvent approach, J.
Chem. Phys., 131 (2009), no.14, 144102
Note: This
article was also selected for republication in the Oct. 15, 2009 issue of
Virtual J. of Biological Physics Research.
·
H. Liu and Z. Wang, A Bloch band based
level set method for computing the semiclassical
limit in Schroedinger equations, J. Comput. Phys. 228 (2009), no. 9, 3326--3344.
·
H. Liu and Z. Wang, Superposition of
multi-valued solutions in high frequency wave dynamics, J. Sci. Comput. 35 (2008), no. 2-3, 192--218.
·
H. Liu and Z. Wang, A field space-based
level set method for computing multi-valued solutions to 1D Euler-Poisson
equations, Journal of Computational Physics, 2007
(225), 591--614
·
H. Liu and Z. Wang, Computing
multi-valued velocity and electrical fields for 1d Euler-Poisson
equations. Applied Numerical Mathematics, 57 (2007), 821--836
Presentations and Posters
* A free energy satisfying finite difference method for
Poisson-Nernst-Planck equations, KI-NET Summer School, May 4, 2014, Iowa State University
* AMS Spring central sectional
meeting, April 27—28, 2013, Ames, IA
* Workshop on kinetic PDEs:
Analysis and Computation, April 25—26, 2013, Iowa State University
* RIW Workshop on kinetic theory
and molecular modeling Oct. 20-21, 2012, Iowa State University
* Solutions to a model Poisson-Nernst-Planck system and the
determination of reaction rates, Oct. 19, 2012, Mathematics, Iowa State
University
* The 9th AIMS conference on
Dynamics Systems, Differential Equations and Applications, July 1—7, 2012,
Orlando, FL
* Delopments
of level set method in high frequency wave propagation, FIU Department of
Mathematics and Statistics, 2011
* A Level Set Approach for Dilute
Non-Collisional Fluid-Particle flows, 2011 Spring AMS Central Section Meeting,
Iowa City, IA, March 18-20, 2011
* A Level-Set Variational Implicit-Solvent
Approach to Biomolecular Solvation, International Research Workshop, Zhejiang
University, Hangzhou, China, Sept. 11, 2009
* A Bloch Band Based Level Set Method for
Computing the Semiclassical Limit of Schroedinger,
Kinetic FRG Young Researchers Workshop, March 5, 2009
* A Level-Set Variational Implicit-Solvent
Approach to Hydrophobic Interactions UCSD Informal Seminars on Mathematics and
Biochemistry-Biophysics, Jan 27, 2009
*
Solutions to a Model Poisson-Nernst-Planck System and the Determination
of Reaction Rates, Informal Seminars on Mathematics and
Biochemistry-Biophysics, Department of Mathematics, UCSD, Nov, 2008
* A Field Space-Based Level Set Method for
Computing Multi-Valued Solutions to 1D Euler-Poisson Equations, Conference on
Analysis of Partial Differential Equations (PD07), Mesa, Az., December 10-12,
2007
* Superposition of Multi-valued Solutions in
High Frequency Wave Dynamics, CAM seminar, Department of Mathematics, Iowa
State University, Ames, IA. October 8, 2007
* Application of Level Set Method to 1D
Euler-Poisson Equations, CAM seminar, Department of Mathematics, Iowa State
University, Ames, IA. October 30, 2006
* Level set
formulation and computation of multi-valued solutions to 1D Euler-Poisson
equations, Iowa Section MAA Meeting, Iowa State University, Ames, IA. April 7,
2006
* Computation of Multi-Valued Solutions in
High Frequency Wave Dynamics. Computational and Mathematical Aspects
of Materials and Fluids, Iowa State University, April 13, 2007
* Computing
Multi-valued Velocity and Electrical Fields in Euler-Poisson Equations.
Workshop on Computational Methods and Applied PDEs(CMAPDE05),
Mathematics Department, Iowa State University, Ames, IA, November 5, 2005