Publication
Publication
The purpose of computation is insight, not numbers ------ Richard Hamming
The purpose of computation is insight, not numbers ------ Richard Hamming
Yanan Zhu, Naimin Zhang, and Zhen Chao %, Two Block Splitting Iteration Methods for Solving Complex Symmetric Linear Systems from Complex Helmholtz Equation. Mathematics, 2024, 12(12), 1888; https://doi.org/10.3390/math12121888 (registering DOI).
Hwi Lee, Zhen Chao%, Harris Cobb, Dexuan Xie, Yingjie Liu, A PNP ion channel deep learning solver with local neural network and finite element input data. Machine Learning: Science and Technology, 2024.
Zhen Chao*, Weihua Geng, and Robert Krasny, Integral equation method for the 1D steady-state Poisson-Nernst-Planck equations. Journal of Computational Electronics, 2023, https://doi.org/10.1007/s10825-023-02092-y.
Zhen Chao#, Cong He, and Jingchun Chen, Dispersive Estimates for Kinetic Transport Equation in Modulation Spaces. Filomat, 481 (2023) 9587-9593.
Dexuan Xie and Zhen Chao%, A Poisson-Nernst-Planck single ion channel model and its effective finite element solver. Journal of Computational Physics, 481 (2023) 112043. [download PDF]
Zhen Chao#, Sheng Gui, Benzhuo Lu, and Dexuan Xie, Efficient Generation of Membrane and Solvent Tetrahedral Meshes for Finite Element Ion Channel Calculation, International Journal of Numerical Analysis and Modeling, April 2022.
Zhen Chao# and Dexuan Xie, An Improved Poisson-Nernst-Planck Ion Channel Model and Numerical Studies on Effects of Boundary Conditions, Membrane Charges, and Bulk Concentrations, Journal of Computational Chemistry, 2021,[download PDF]. This paper was featured on the cover of the journal [cover page].
Dexuan Xie and Zhen Chao%. A Finite Element Iterative Solver for an Improved PNP Ion Channel Model by Neumann Boundary Condition and Membrane Surface Charge, Journal of Computational Physics, 423 (2020), 109915. [download PDF]
Zhen Chao#, Dexuan Xie, and Ahmed Sameh. Preconditioners for nonsymmetric indefinite linear systems. Journal of Computational and Applied Mathematics, 367 (2020) 112436. [download PDF]
Yunying Huang, Zhen Chao%, and Guoliang Chen. Spectral properties of the matrix splitting preconditioners for generalized saddle point problems. Journal of Computational and Applied Mathematics, 332 (2018) 1-12.
Zhen Chao*, Guoliang Chen, and Ye Guo. On the semi-convergence of regularized HSS iteration methods for singular saddle point problems. Computers and Mathematics with Applications, 76 (2018) 438-450.
Zhen Chao*, Kai Wang, Chao Zhu and Yanling Zhu. Almost Sure and Moment Exponential Stability of Regime-Switching Jump Diffusions. SIAM Journal on Control and Optimization, 55 (2017) 3458-3488.
Zhen Chao* and Guoliang Chen. A generalized modified HSS method for singular complex symmetric linear systems. Numerical Algorithms, 73 (2016) 77-89.
Zhen Chao* and Guoliang Chen. A generalized preconditioned parameterized inexact Uzawa method for singular saddle point problems, Applied Mathematics and Computation, 284 (2016) 219-225.
Zhen Chao* and Guoliang Chen. A note on semi-convergence of generalized parameterized inexact Uzawa method for singular saddle point problems. Numerical Algorithms, 68 (2015) 95-105.
Zhen Chao* and Guoliang Chen. Semi-convergence analysis of the Uzawa-SOR methods for singular saddle point problems. Applied Mathematics Letters, 35 (2014) 52–57.
Zhen Chao*, Naimin Zhang, and Guoliang Chen. Brief derivation for optimal iteration parameters in the GSOR method. Communication on Applied Mathematics and Computation, 28 (2014) 134–139.
Zhen Chao*, Naimin Zhang, and Yunzeng Lu. Optimal parameters of the generalized symmetric SOR method for augmented systems. Journal of Computational and Applied Mathematics, 266 (2014) 52–60.
Zhen Chao* and Naimin Zhang. A generalized preconditioned HSS method for singular saddle point problems. Numerical Algorithms, 66 (2014) 203–211.
Zhen Chao*, Naimin Zhang, and Pan Shen. Convergence of p-regular splitting iterative methods for non-hermitian positive semidefinite linear systems. International Journal of Computer Mathematics, 90(2013) 630–640.
Zhen Chao* and Naimin Zhang, Some convergence conditions for P-regular splitting for solving non-Hermitian linear systems, 2012 International Conference on Computational Problem-Solving (ICCP), 2012.
*corresponding author, #first author, % main contribution