Juntao Huang

I am currently a visiting assistant professor in the Department of Mathematics at Michigan State University (East Lansing, Michigan, US).


Address: Department of Mathematics, Michigan State University, 619 Red Cedar Road, East Lansing, MI 48824

Office: C227 Wells Hall

Email: huangj75@msu.edu

Education:

  • Ph.D. in Applied Mathematics, Tsinghua University, China, September 2013 - July 2018.

Advisor: Prof. Wen-An Yong.

  • B.S. in Mathematics, Department of Mathematical Science, Tsinghua University, China, September 2010 - July 2013.
  • B.E. in Engineering Mechanics, School of Aerospace, Tsinghua University, China, September 2009 - July 2013.

Professional Experience:

  • Visiting Assistant Professor, Department of Mathematics, Michigan State University, September 2018 - present.
  • Visiting scholar, Beijing Computational Science Research Center (CSRC), May 2019 - July 2019.
  • Visiting Ph.D. student, Division of Applied Mathematics, Brown University, September 2015 - September 2016.

Mentor: Prof. Chi-Wang Shu.

Research Interests:

  • Sparse grid methods for high-dimensional PDEs.
  • High-order schemes (Discontinuous Galerkin, WENO) for hyperbolic systems with stiff source terms.
  • Boundary treatment of kinetic models.

Publications:

See my Google Scholar

Preprints:

  1. J. Huang and Y. Cheng. An adaptive multiresolution discontinuous Galerkin method with artificial viscosity for scalar hyperbolic conservation laws in multidimensions, arXiv preprint arXiv:1906.00829, 2019, submitted. [link]
  2. W. Zhao, J. Huang and W.-A. Yong. Lattice Boltzmann method for stochastic convection-diffusion equations, submitted.
  3. W. Zhao and J. Huang. Boundary treatment of implicit-explicit Runge-Kutta method for hyperbolic systems with source terms, arXiv preprint arXiv:1908.01027, 2019, submitted. [link]

Publications in Refereed Journals:

  1. W. Zhao, J. Huang and W.-A. Yong. Boundary conditions for kinetic theory based models I: lattice Boltzmann models, Multiscale Modeling and Simulation, 17(2), 854-872, 2019. [link]
  2. J. Huang, W. Zhao and C.-W. Shu. A third-order unconditionally positivity-preserving scheme for production-destruction equations with applications to non-equilibrium flows, Journal of Scientific Computing, 79, 1015-1056, 2019. [link]
  3. J. Huang and C.-W. Shu. Positivity-preserving time discretizations for production-destruction equations with applications to non-equilibrium flows, Journal of Scientific Computing, 78, 1811-1839, 2019. [link]
  4. J. Huang and C.-W. Shu. Bound-preserving modified exponential Runge-Kutta discontinuous Galerkin methods for scalar hyperbolic equations with stiff source terms, Journal of Computational Physics, 361, 111-135, 2018. [link]
  5. J. Huang and C.-W. Shu. A second-order asymptotic-preserving and positivity-preserving discontinuous Galerkin scheme for the Kerr-Debye model, Mathematical Models and Methods in Applied Sciences, 27 (03), 549-579, 2017. [link]
  6. J. Huang and C.-W. Shu. Error estimates to smooth solutions of semi-discrete discontinuous Galerkin methods with quadrature rules for scalar conservation laws, Numerical Methods for Partial Differential Equations, 33 (2), 467-488, 2017. [link]
  7. Z.-X. Hu, J. Huang, W.-X. Huang and G.-X. Cui. Second-order curved interface treatments of the lattice Boltzmann method for convection-diffusion equations with conjugate interfacial conditions, Computers and Fluids, 144, 60-73, 2017. [link]
  8. Z. Hu, J. Huang and W.-A. Yong. Lattice Boltzmann method for convection-diffusion equations with general interfacial conditions, Physical Review E, 93(4), 043320, 2016.[link]
  9. J. Huang, Z. Hu and W.-A. Yong. Second-order curved boundary treatments of the lattice Boltzmann method for convection-diffusion equations, Journal of Computational Physics, 310, 26-44, 2016. [link]
  10. J. Huang, L. Hong and W.-A. Yong. Generalization of the Kullback-Leibler divergence in the Tsallis statistics, Journal of Mathematical Analysis and Applications, 436(1), 501-512, 2016. [link]
  11. J. Huang and W.-A. Yong. Boundary conditions of the lattice Boltzmann method for convection-diffusion equations, Journal of Computational Physics, 300, 70-91, 2015. [link]
  12. J. Huang, H. Wu and W.-A. Yong. On initial conditions for the lattice Boltzmann method, Communications in Computational Physics, 18(2), 450-468, 2015. [link]
  13. J. Huang, L. Zhang, W.-A. Yong and M. Wang. On complex boundary conditions of the lattice Boltzmann method for the diffusion equations, Applied Mathematics and Mechanics (Chinese Edition), 35(3), 305-312, 2014. [link]

Teaching:

Current Course:

  • Instructor: MTH 124 (2 sections), Survey of Calculus I, Michigan State University, Spring 2020.

Past Courses:

  • Instructor: MTH 124, Survey of Calculus I, Michigan State University, Fall 2019.
  • Instructor: MTH 124 (3 sections), Survey of Calculus I, Michigan State University, Spring 2019.
  • Teaching Assistant: Linear Algebra I, Tsinghua University, China, Fall 2016, Spring 2018.
  • Teaching Assistant: Calculus II, Tsinghua University, China, Spring 2014, Spring 2015, Spring 2017.
  • Teaching Assistant: Functional Analysis I, Tsinghua University, China, Fall 2014.
  • Teaching Assistant: Methods of Mathematical Physics, Tsinghua University, China, Fall 2013.