Publications

Submitted:

  1. Z. Cai, Y, Kuang, and H. K. Tan, Regularization of complex Langevin method.
  2. G. Wang and Z. Cai, Differential equation based path integral for system-bath dynamics.
  3. Z. Cai, J. Hu, Y. Kuang, and B. Lin, An entropic method for discrete systems with Gibbs entropy.
  4. H. Zhan, Z. Cai, and G. Hu, The Wigner function of ground state and one-dimensional numerics.
  5. Z. Cai and Y. Wang, Numerical solver for the Boltzmann equation with self-adaptive collision operators.
  6. Z. Cai, J. Lu, and S. Yang, Numerical analysis for inchworm Monte Carlo method: Sign problem and error growth.

Published:

  1. Z. Cai, Moment method as a numerical solver: Challenge from shock structure problems, Journal of Computational Physics, 444: 110593, 2021.
  2. S. Yang, Z. Cai, and J. Lu, Inclusion-exclusion principle for open quantum systems with Bosonic bath, New Journal of Physics, 23: 063049, 2021.
  3. Z. Cai, X. Dong, and Y. Kuang, On the validity of complex Langevin method for path integral computations, SIAM Journal on Scientific Computing, 43(1): A685–A719, 2021.
  4. J. Cao and Z. Cai, Numerical Analysis of a High-Order Scheme for Nonlinear Fractional Differential Equations with Uniform Accuracy, Numerical Mathematics: Theory, Methods and Applications, 14(1): 71–112, 2021.
  5. Z. Hu, S. Yang, and Z. Cai, Flows between parallel plates: Analytical solutions of regularized 13-moment equations for inverse-power-law models, Physics of Fluids, 32(12): 122027, 2020.
  6. B. Lin, C. Zhuang, Z. Cai, R. Zeng, and W. Bao, Accurate and Efficient Calculation of Photoionization in Streamer Discharges Using the Fast Multipole Method, Plasma Sources Science and Technology, 29(12): 125010, 2020.
  7. Z. Cai, J. Lu, and S. Yang, Inchworm Monte Carlo Method for Open Quantum Systems, Communications in Pure and Applied Mathematics, 73(11): 2430–2472, 2020.
  8. Z. Hu and Z. Cai, Burnett Spectral Method for High-Speed Rarefied Gas Flows, SIAM Journal on Scientific Computing, 42(5): B1193–B1226, 2020.
  9. X. Dong, Z. Cai, and Y. Di, Alternating Descent Method for Gauge Cooling of Complex Langevin Simulations, Physical Review D, 102: 054518, 2020.
  10. Z. Cai and Y. Wang, Regularized 13-Moment Equations for Inverse Power Law Models, Journal of Fluid Mechanics, 894: A12, 2020.
  11. Z. Cai, Y. Di, and X. Dong, How does Gauge Cooling Stabilize Complex Langevin?, Communications in Computational Physics, 27(5): 1344–1377, 2020.
  12. Z. Cai, Y. Fan, and Y. Wang, Burnett Spectral Method for the Spatially Homogeneous Boltzmann Equation, Computers & Fluids, 200: 104456, 2020.
  13. Z. Hu, Z. Cai, and Y. Wang, Numerical Simulation of Microflows Using Hermite Spectral Methods, SIAM Journal on Scientific Computing, 42(1): B105–B134, 2020.
  14. B. Lin, C. Zhuang, Z. Cai, R. Zeng, and W. Bao, An Efficient and Accurate MPI-based Parallel Simulator for Streamer Discharges in Three Dimensions, Journal of Computational Physics, 401: 109026, 2020.
  15. Z. Cai and M. Torrilhon, On the Holway-Weiss Debate: Convergence of the Grad-Moment-Expansion in Kinetic Gas Theory, Physics of Fluids, 31: 126105, 2019.
  16. Y. Wang and Z. Cai, Approximation of the Boltzmann Collision Operator Based on Hermite Spectral Method, Journal of Computational Physics, 397: 108815, 2019.
  17. Z. Cai and Y. Wang, Suppression of Recurrence in the Hermite-Spectral Method for Transport Equations, SIAM Journal on Numerical Analysis, 56(5), 3144–3168, 2019.
  18. Z. Cai, Y. Fan, and L. Ying, An Entropic Fourier Method for the Boltzmann Equation, SIAM Journal on Scientific Computing, 40(5), A2858–A2882, 2018.
  19. Z. Cai and J. Lu, A Surface Hopping Gaussian Beam Method for High-Dimensional Transport Systems, SIAM Journal on Scientific Computing, 40(5), B1277–B1301, 2018.
  20. Z. Cai and J. Lu, A Quantum Kinetic Monte Carlo Method for Quantum Many-body Spin Dynamics, SIAM Journal on Scientific Computing, 40: B706–B722, 2018.
  21. Z. Cai and M. Torrilhon, Numerical Simulation of Microflows Using Moment Methods with Linearized Collision Operator, Journal of Scientific Computing, 74: 336–374, 2018.
  22. Z. Cai, Y. Fan, Z. Hu, R. Li, and H. Wang, The Development and Application of the Moment Method in the Gas Kinetic Theory, Scientia Sinica Informationis, 46: 1465–1488, 2016.
  23. Z. Cai, Y. Fan, and R. Li, A Framework on Moment Model Reduction for Kinetic Equation, SIAM Journal on Applied Mathematics, 75: 2001–2023, 2015.
  24. Z. Cai and M. Torrilhon, Approximation of the Linearized Boltzmann Collision Operator for Hard-Sphere and Inverse-Power-Law Models, Journal of Computational Physics, 295: 617–643, 2015.
  25. Z. Cai and R. Li, The NRxx Method for Polyatomic Gases, Journal of Computational Physics, 267: 63–91, 2014.
  26. Z. Cai, Y. Fan and R. Li, Globally Hyperbolic Regularization of Grad’s Moment System, Communications in Pure and Applied Mathematics, 67: 464–518, 2014.
  27. Z. Cai, Y. Fan, and R. Li, On Hyperbolicity of 13-Moment System, Kinetic and Related Models, 7(3): 415–432, 2014.
  28. Z. Cai, Y. Fan, R. Li, and Z. Qiao, Dimension-Reduced Hyperbolic Moment Method for the Boltzmann Equation with BGK-Type Collision, Communications in Computational Physics, 15(5): 1368–1406, 2014.
  29. Z. Cai, Y. Fan, R. Li, T. Lu, and W. Yao, Quantum Hydrodynamic Model of Density Functional Theory, Journal of Mathematical Chemistry, 51(7): 1747–1771, 2013.
  30. Z. Cai, R. Li, and Z. Qiao, Globally Hyperbolic Regularized Moment Method with Applications to Microflow Simulation, Computers & Fluids, 81: 95–109, 2013.
  31. Z. Cai, R. Li, and Y. Wang, Solving Vlasov Equations Using NRxx Method, SIAM Journal on Scientific Computing, 35(6): A2807–A2831, 2013.
  32. Z. Cai, Y. Fan, and R. Li, Globally Hyperbolic Regularization of Grad’s Moment System in One Dimensional Space, Communications in Mathematical Sciences, 11(2): 547–571, 2013.
  33. Z. Cai, Y. Fan, R. Li, T. Lu, and Y. Wang, Quantum Hydrodynamic Model by Moment Closure of Wigner Equation, Journal of Mathematical Physics, 53(10): 103503, 2012.
  34. Z. Cai, R. Li, and Z. Qiao, NRxx Simulation of Microflows with Shakhov Model, SIAM Journal on Scientific Computing, 34(1): A339–A369, 2012.
  35. Z. Cai, R. Li, and Y. Wang, An Efficient NRxx Method for Boltzmann-BGK Equation, Journal of Scientific Computing, 50(1): 103–119, 2012.
  36. Z. Cai, R. Li, and Y. Wang, Numerical Regularized Moment Method for High Mach Number Flow, Communications in Computational Physics, 11(5): 1415–1438, 2012.
  37. Z. Cai and R. Li, Numerical Regularized Moment Method of Arbitrary Order for Boltzmann-BGK Equation, SIAM Journal on Scientific Computing, 32(5): 2875–2907, 2010.
  38. Z. Cai and R. Li, An h-Adaptive Mesh Method for Boltzmann-BGK/Hydrodynamics Coupling, Journal of Computational Physics, 229(5): 1661–1680, 2010.