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成果及论文

代码和软件

  1. LAMMPS-RBE: Random batch Ewald is a fast algorithm for electrostatic interactions in molecular dynamics simulations.  A brief introduction of this algorithm can be found at link. The CPU version of the package is now available for tests at the πcluster.

  2. HSMA3D and HSMA2D: Harmonic surface mapping algorithm for electrostatic interaction in MD simulations of particle systems of 3D periodicity (HSMA3D) or doubly periodic slit with dielectric interfaces along one direction (HSMA2D).
  3. HybridMD: MD package for simulating nanoparticle self-assembly. It is based on a novel hybrid ICM/moment method for fast and accurate calculation of the Poisson’s equation with closely-packed dielectric spheres and ions.
  4. VPMR: Matlab code for SOE and SOG approximations using de la Vallée-Poussin sums – based model reduction.  C++ version developed by Theodore Chang from HU Berlin, Julia version developed by Xuanzhao Gao from HKUST. See also: VP-WBT, a kernel-independent SOE/SOG approximation software with high precision and the nearly optimal convergence rate.
  5. RBMD:  Random batch molecular dynamics package for simulating atomic systems.


部分发表论文

预印本

  1. A divergence-free projection method for quasiperiodic photonic crystals in three dimensions, Z. Gao, Z. Xu and Z. Yang, arXiv:2409.05528
  2. Real 2D galvanostatic model (R2D): Encoding physicochemical heterogeneity into full battery, Z. T. Sun, S. Chen, T. Zhao, Y. Guo, Z. Xu, S. Zhou and S. H. Bo, submitted.
  3. A fast spectral sum-of-Gaussians method for electrostatic summation in quasi-2D systems, X. Gao, S. Jiang, J. Liang, Z. Xu and Q. Zhou, arXiv:2412.04595
  4. MscaleFNO: Multi-scale Fourier neural operator learning for oscillatory function spaces, Z. You, Z. Xu and W. Cai, arXiv:2412.20183
  5. VGPT-PINN: Viscosity-enhanced Generative Pre-Trained Physics Informed Neural Networks for parameterized nonlinear conversation laws, Y. Ji, Y. Chen and Z. Xu, arXiv:2501.01587
  6. Low dimensional current densities in incommensurate 3D moiré lattice, Z. Gao, V. V. Konotop, R. Peng, Z. Xu, Z. Yang and F. Ye, submitted.
  7. Machine-learning interatomic potentials for long-range systems, Y. Ji, J. Liang and Z. Xu, arXiv:2502.04668
  8. Weighted balanced truncation method for approximating kernel functions by exponentials, Y. Lin, Z. Xu, Y. Zhang and Q. Zhou, arXiv:2503.03183
  9. A second-order accurate, original energy dissipative numerical scheme for chemotaxis and its convergence analysis, J. Ding, C. Wang and S. Zhou, Preprint.
  10. Structure-preserving numerical methods for disease transmission with chemotaxis of singular sensitivity, J. Ding, Z. Xu and S. Zhou, Preprint.
  11. Shape optimization of supercapacitor electrodes to maximize charge storage, J. Li, S. Zhou and S. Zhu, Preprint.
  12. Entropy increasing numerical methods for prediction of reversible and irreversible heating in supercapacitors, J. Ding, X. Ji and S. Zhou, Preprint.
  13. Finite-difference approximations and local algorithms for the Poisson and Poisson-Boltzmann electrostatics, B. Li, Q. Yin and S. Zhou, Preprint.

2025年

  1. Hierarchical interpolative factorization for self Green's function in 3D modified Poisson-Boltzmann equations, Y. Tu, Z. Xu and H. Yang, Commun. Appl. Math. Comput., 7(2025), 536-561. In CAMC focused issue in memory of Professor Zhong-Ci Shi.
  2. Reduced projection method for photonic moiré lattices, Z. Gao, Z. Xu, and Z. Yang, J. Sci. Comput., 102(2025), 8.
  3. Comment on `Pressure of Coulomb systems with volume-dependent long-range potentials', L. Li, J. Liang and Z. Xu, J. Phys. A: Math. Theor., 58(2025), 088001.
  4. RBMD: A molecular dynamics package enabling to simulate 10 million all-atom particles in a single graphics processing unit, W. Gao et al., Comm. Compu. Phys., in press. arXiv:2407.09315
  5. Fast algorithms for quasi-2D Coulomb systems, Z. Gan, X. Gao, J. Liang and Z. Xu, J. Comput. Phys., 524(2025), 113733.
  6. Random batch sum-of-Gaussians algorithm for molecular dynamics simulations of Yukawa systems in three dimensions, C. Chen, J. Liang and Z. Xu, J. Comput. Phys., 531(2025), 113922.
  7. Error estimate of the u-series method for molecular dynamics simulations, J. Liang, Z. Xu and Q. Zhou, Appl. Comput. Harmon. Anal., 77(2025) 101.
  8. Random batch Ewald method for dielectrically confined Coulomb systems, Z. Gan, X. Gao, J. Liang and Z. Xu, SIAM J. Sci. Comput., in press. arXiv:2405.06333


2024年

  1. Dielectric polymer grafted electrodes enhanced aqueous supercapacitors, S. Dong et al., Nano Research, 17(2024), 1525-1534.
  2. Energy stable scheme for random batch molecular dynamics, J. Liang, Z. Xu and Y. Zhao, J. Chem. Phys., 160(2024), 034101.
  3. Local structure-preserving relaxation method for equilibrium of charged systems on unstrctured meshes, Z. Qiao, Z. Xu, Q. Yin and S. Zhou, SIAM J. Sci. Comput., 46(2024), A2248-2269.
  4. TGPT-PINN: Nonlinear model reduction with transformed GPT-PINNs, Y. Chen, Y. Ji A. Narayan and Z. Xu, Comput. Meth. Appl. Mech. Energ., 430(2024), 117198.
  5. 基于随机分批埃瓦尔德算法的分子动力学模拟异构加速，吕奇正等，2024年全国高性能计算学术年会大会论文集(CCF HPC China 2024), pp. 257-264
  6. MCMS-RBM: Multi-component multi-state reduced basis method toward rapid generation of phase diagrams for the Lifshitz-Petrich model, Y. Ji, L. Ji, Y. Chen and Z. Xu, SIAM J. Sci. Comput., 46(2024), B785-805.
  7. Variance-reduced random batch Langevin dynamics, Z. Xu, Y. Zhao and Q. Zhou, J. Chem. Phys., 161, 244110(2024).
  8. Second-order, positive, and unconditional energy dissipative scheme for modified Poisson-Nernst-Planck equations, J. Ding and S. Zhou, J. Comput. Phys., 510(2024), 113094.

2023年

  1. Structure-preserving numerical method for Maxwell-Ampère Nernst-Planck model, Z. Qiao, Z. Xu, Q. Yin and S. Zhou, J. Comput. Phys., 475(2023), 111845. arXiv:2204.11743

  2. Molecular insights into temperature oscillation of electric double-layer capacitors in charging-discharging cycles, T. Zhao, S. Zhou, Z. Xu and S. Zhao, J. Power Sources, 559(2023), 232596. SSRN.4258982

  3. Dielectric-electrolyte supercapacitors, S. Dong, W. Gao, K. Shi, Q. Kang, Z. Xu, J. Yuan, Y. Zhu, H. Li, J. Chen, P. Jiang, G. Wu, Q. Wei, J. Qiu, X. Qian and X. Huang, Cell Reports Physical Science, 4(2023), 101284

  4. A Maxwell-Ampère Nernst-Planck framework for modeling charge dynamics, Z. Qiao, Z. Xu, Q. Yin and S. Zhou, SIAM J. Appl. Math., 83(2023), 374-393. arXiv: 2202.07366

  5. Asymptotic analysis on charging dynamics for stack-electrode model of supercapacitors, L. Ji, Z. Xu and S. Zhou, Proc. Royal Soc. A, 479(2023), 20230044. arXiv: 2212.02214

  6. Random batch sum-of-Gaussians method for molecular dynamics simulations of particle systems, J. Liang, Z. Xu and Q. Zhou, SIAM J. Sci. Comput., 45(2023), B591-B617. arXiv: 2205.13824

  7. An asymptotic-preserving and energy-conserving particle-in-cell method for Vlasov-Maxwell equations, L. Ji, Z. Yang, Z. Li, D. Wu, S. Jin and Z. Xu, J. Math. Phys., 64(2023), 063503. In Special Collection: Cascades of Scales: Applications and Mathematical Methodologies. arXiv: 2209.08227

  8. Microscopic energy storage mechanism of dielectric polymer-coated supercapacitors, W. Gao, T. Zhao, S. Dong, X. Huang and Z. Xu, J. Energy Storage, 72(2023), 108174. arXiv:2302.09499

  9. A screening condition imposed stochastic approximation for long-ranged electrostatic correlations, W. Gao, Z. Hu and Z. Xu, J. Chem. Theory Comput., 19(2023), 4822-4827.

  10. How thermal effect regulates cyclic voltammetry of supercapacitors, T. Zhao, S. Zhao, S. Zhou and Z. Xu, ACS Energy Lett., 8(2023), 3365-3372. Journal Cover Article. arXiv:2305.18713

  11. Pythagoras superposition principle for localized eigenstates of two-dimensional moiré lattices, Z. Gao, Z. Xu, Z. Yang and F. Ye, Phy. Rev. A, 108(2023), 013513. arXiv:2306.02035

  12. An energy-conserving Fourier particle-in-cell method with asymptotic-preserving preconditioner for Vlasov-Ampère system with exact curl-free constraint, Z. Li, Z. Xu and Z. Yang, J. Comput. Phys., 495(2023), 112569. arXiv:2211.10070

  13. Convergence analysis of structure-preserving numerical methods based on Slotboom transformation for the Poisson-Nernst-Planck equations, J. Ding, C. Wang and S. Zhou, Commun. Math. Sci., 21(2), 459-484, 2023.
  14. Convergence analysis on a structure-preserving numerical numerical scheme for the Poisson-Nernst-Planck-Cahn-Hilliard system, Q. Yin, C. Wang and S. Zhou, CSIAM Trans. Appl. Math., 4(2), 345-380, 2023.
  15. Energy dissipative and positivity preserving schemes for large-convection ion transport with steric and solvation effects, J. Ding, Z. Wang and S. Zhou, J. Comput. Phys., 488(2023), 112206.
  16. Fast Newton iterative method for local steric Poisson-Boltzmann theories in biomolecular solvation, W. Dou, M. Chen and S. Zhou, Comput. Phys. Commun., 291(2023), 108808.
  17. A second order accurate numerical method for the Poisson-Nernst-Planck system in the energetic variational formulation, C. Liu, C. Wang, S. M. Wise, X. Yue and S. Zhou, J. Sci. Comput., 97:23, 2023.


2022年

  1. Superscalability of the random batch Ewald method, J. Liang, P. Tan, Y. Zhao, L. Li, S. Jin, L. Hong and Z. Xu, J. Chem. Phys.,  156 (2022), 014114. arXiv: 2106.05494

  2. HSMA: An O(N) electrostatics package implemented in LAMMPS, J. Liang, J. Yuan and Z. Xu, Comput. Phys. Commun., 276(2022), 108332. arXiv: 2104.05260. Code

  3. Improved random batch Ewald method in molecular dynamics simulations, J. Liang, Z. Xu and Y. Zhao, J. Phys. Chem. A, in press. arXiv: 2204:13595

  4. C. Liu, C. Wang, S. M. Wise, X. Yue, and S. Zhou, A second order accurate numerical method for the Poisson-Nernst-Planck system in the energetic variational formulation, Submitted, 2022

  5.  A kernel-independent sum-of-exponentials method, Z. Gao, J. Liang and Z. Xu, J. Sci. Comput., 93(2022), Article Number: 40. arXiv: 2012.13477. Code


2021年

  1. Linear-scaling selected inversion based on hierarchical interpolative factorization for self Green’s function for modified Poisson-Boltzmann equation in two dimensions, Y. Tu, Q. Pang, H. Yang and Z. Xu, J. Comput. Phys., 461 (2022), 110893. arXiv: 2105.09200

  2. Ion transport in electrolytes of dielectric nanodevices, M. Ma, Z. Xu and L. Zhang, Phys. Rev. E, 104 (2021), 035307

  3. The theoretical model, method and applications of scattering photon burst counting based on objective scanning technique, C. Dong, Q. Wang, Z. Xu, L. Deng, T. Zhang, B. Lu, Q. Wang, and J. Ren, Anal. Chem., 93 (2021), 12556-12564

  4. Bo Wang, Zhiguo Yang, Li-Lian Wang, Shidong Jiang, On time-domain NRBC for Maxwell‘s equations and its application in electromagnetic invisibility cloaks. Journal of Scientific Computing, 86 (2), 1-34, 2021

  5. Zhiguo Yang, Li-Lian Wang, Yang Gao, A truly exact perfect absorbing layer for time-harmonic acoustic wave scattering problems. SIAM Journal of Scientific Computing, 43 (2), A1027-A1061, 2021.

  6. B. Li, Z. Zhang, and S. Zhou, The Calculus of Boundary Variations and the Dielectric Boundary Force in the Poisson--Boltzmann Theory for Molecular Solvation, To appear in J. Nonlinear Sci., 2021.

  7. S. Zhou, Y. Zhang, L. Cheng, and B. Li, Prediction of multiple dry-wet transition pathways with a mesoscale variational approach, To appear in J. Chem. Phys., 2021.

  8. An EIM-degradation free reduced basis method via over collocation and residual hyper reduction-based error estimation, Y. Chen, S. Gottlieb, L. Ji and Y. Maday, to be published at J. Comput. Phys., arXiv:2101.05902

  9. Modified Poisson-Nernst-Planck model with Coulomb and hard-sphere correlations, M. Ma, Z. Xu and L. Zhang, to be published at SIAM J. Appl. Math.. arXiv: 2002.07489

  10. A random batch Ewald method for particle systems with Coulomb interactions, S. Jin, L. Li, Z. Xu and Y. Zhao, to be published at SIAM J. Sci. Comput.. arXiv: 2010.01559

  11. A kernel-independent sum-of-Gaussians method by de la Vallée-Poussin sums, J. Liang, Z. Gao and Z. Xu, to be published at Adv. Appl. Math. Mech.. arXiv: 2010.05192, Code

  12. L1-based reduced over-collocation and hyper reduction for steady state and time-dependent nonlinear equations, Y. Chen, L. Ji, A. Narayan and Z. Xu, J. Sci. Comput. 87(2021), 10. arXiv: 2009.04812

  13. A high-accurate fast Poisson solver based on harmonic surface mapping algorithm, J. Liang, P. Liu and Z. Xu, Commun. Comput. Phys., 30 (2021), 210-226.

  14. C. Liu, C. Wang, S. M. Wise, X. Yue, and S. Zhou, A positivity-preserving, energy stable and convergent numerical scheme for the Poisson--Nernst--Planck system, Math. Comput. , In Press, 2021.

  15. Y. Qian, C. Wang, and S. Zhou, A Positive and Energy Stable Numerical Scheme for the Poisson--Nernst--Planck--Cahn--Hilliard Equations with Steric Interactions, J. Comput. Phys. , 426, 109908, 2021.

  16. C. Duan, W. Chen, C. Liu, X. Yue, and S. Zhou, Structure-Preserving Numerical Methods for Nonlinear Fokker--Planck Equations with Nonlocal Interactions by an Energetic Variational Approach, SIAM J. Sci. Comput. , 43(1), B82-B107, 2021.


2020年

  1. Harmonic surface mapping algorithm for molecular dynamics simulations of particle systems with planar dielectric interfaces, J. Liang, J. Yuan, E. Luijten and Z. Xu, J. Chem. Phys., 152 (2020), 134109.

  2. A random-batch Monte Carlo method for many-body systems with singular kernels, L. Li, Z. Xu and Y. Zhao, SIAM J. Sci. Comput., 42 (2020), A1486–A1509. arXiv: 2003.06554

  3. Effects of kinetic dielectric decrement on ion diffusion and capacitance in electrochemical systems, L. Qing, J. Lei, T. Zhao, G. Qiu, M. Ma, Z. Xu and S. Zhao, Langmuir, 36 (2020), 4055-4064.

  4. J. Ding, H. Sun, and S. Zhou, Hysteresis and Linear Stability Analysis on Multiple Steady-State Solutions to the Poisson--Nernst--Planck equations with Steric Interactions: A Numerical Approach, Phys. Rev. E , 102, 053301, 2020.

  5. J. Ding, Z. Wang, and S. Zhou, Structure-Preserving and Efficient Numerical Methods for Ion Transport, J. Comput. Phys. , 418, 109597, 2020.

  6.  Yanxia Qian, Zhiguo Yang, Suchuan Dong,  gPAV-based unconditionally energy-stable schemes for the Cahn-Hilliard equation: stability and error analysis. Computer Methods in Applied Mechanical Engineering,Vol.372,113444,2020.                                              

  7. Fukeng Huang, Jie Shen, Zhiguo Yang (corr), A highly efficient and accurate new scalar auxiliary variable approach for gradient flows. SIAM Journal of Scientific Computing, Vol. 42(4), A2514-A2536, 2020.

  8. Lianlei Lin, Naxian Ni, Zhiguo Yang, Suchuan Dong, An energy-stable scheme for incompressible Navier-Stokes equations with periodically updated coefficient matrix. Journal of Computational Physics, Vol. 418, 109624 , 2020.

  9. Zhiguo Yang, Suchuan Dong, A roadmap for discretely energy-stable schemes for dissipative systems based on a generalized auxiliary variable with guaranteed positivity. Journal of Computational Physics, Vol. 404, 109-121, 2020.


2019年

  1. Efficient dynamic simulations of charged dielectric colloids through a novel hybrid method, Z. Gan, Z. Wang, S. Jiang, Z. Xu and E. Luijten, J. Chem. Phys., 151, 024112 (2019). This paper has been selected the 2019 Editors’ Choice Collection.

  2. A reduced basis method for the nonlinear Poisson-Boltzmann equation, L. Ji, Y. Chen and Z. Xu, Adv. Appl. Math. Mech., 11 (2019), pp. 1200-1218. arXiv: 1808.09392

  3. S. Zhou, R. G. Weiss, L. Cheng, J. Dzubiella, J. A. McCammon, and B. Li, Variational implicit-solvent predictions of the dry-wet transition pathways for ligand-receptor binding and unbinding kinetics, Proc. Natl Acad. Sci. USA (PNAS) , 116(30), 14989-14994, 2019.

  4. 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, 108864, 2019.

  5. X. Ji and S. Zhou, Variational Approach to Concentration Dependent Dielectrics with the Bruggeman Model: Theory and Numerics, Commun. Math. Sci. , 17(7), 1949-1974, 2019.

  6. 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, 22-36, 2019.

  7. J. Ding, C. Wang, and S. Zhou, Optimal rate convergence analysis of a second order numerical scheme for the Poisson--Nernst--Planck system, Numer. Math.: Theory, Methods and Appl. , 12, 607-626, 2019.

  8. Zhiguo Yang, Suchuan Dong, An unconditionaly energy-stable scheme based on an implicit energy variable for incompressible two-phase flows of different densities involving only precomputable coefficient matrices. Journal of Computational Physics, Vol. 393,  229--257, 2019.

  9. Lianlei Lin, Zhiguo Yang, Suchuan Dong, Numerical approximation of incompressible Navier-Stokes equations based on an auxiliary energy variable. Journal of Computational Physics, Vol. 388, 1--22, 2019.

  10. Naxian Ni, Zhiguo Yang, Suchuan Dong, Energy-stable boundary conditions based on a quadratic form: applications to outflow/open-boundary problems in incompressible flows. Journal of Computational Physics, Vol. 391, 179--215, 2019.

  11. Zhiguo Yang, Lianlei Lin, Suchuan Dong, A family of second-order energy-stable schemes for Cahn–Hilliard type equations.  Journal of Computational Physics, Vol. 383, 24--54, 2019.