Myself

Left: Me; Right: Gilbert Strang; At SIAM AN18, Portland OR

 

 

 

 

Current Teaching
Research interests

 

My current research interests include numerical analysis for partial differential equations with nature of multiple scales or highly-oscillatory heterogeneities. Such partial differential equations (Darcy, Stokes, Brinkman, etc) are studied for many applications (such as flows in porous media). The main technique (that I mainly used) for solving these problems is generalized multiscale finite element method (GMsFEM). There are many others multiscale methods in the community (such as localized orthogonal decomposition, gamblet, variational multisacle methods, heterogeneous multisacle methods, etc). Temporal discertization for such partial differential equations could also be studied. I am also interested in studying the (energy-driven/goal-oriented) adaptive algorithms for multiscale PDEs. As techniques of machine learning are being very mature, these can be utilized when designing computational multiscale methods. If there are enough space and time in the margin, I would also like to study high-performance computing in the future.
Publications
  1. E. Chung, S. Pollock and S.-M. Pun. Goal-oriented adaptivity of mixed GMsFEM for flows in heterogeneous media. Computer Methods in Applied Mechanics and Engineering, 323 (2017), pp.151-173.
  2. E. Chung, S.-M. Pun and Z. Zhang. An adaptive dynamically low-dimensional approximation method for multiscale stochastic diffusion equations. Journal of Computational and Applied Mathematics, 393 (2019), pp.302-313.
  3. R. Altmann, E. Chung, R. Maier, D. Peterseim and S.-M. Pun. Computational multiscale methods for linear heterogeneous poroelasticity. Journal of Computational Mathematics 38 (1) 2020, 41-57.
  4. E. Chung, S. Pollock and S.-M. Pun. Online basis construction for goal-oriented adaptivity in the GMsFEM. Journal of Computational Physics, 393 (2019), pp.59-73.
  5. S. Fu, R. Altmann, E. Chung, R. Maier, D. Peterseim and S.-M. Pun. Computational multiscale methods for linear heterogeneous poroelasticity with high contrast. Journal of Computational Physics, 395 (2019), pp.286-297.
  6. E. Chung and S.-M. Pun. Online adaptive basis enrichment for mixed CEM-GMsFEM. Multiscale Modeling & Simulation 17 (4) 2019, 1103-1122.
  7. E. Chung and S.-M. Pun. Computational multiscale methods for first-order wave equation using CEM-GMsFEM. Journal of Computational Physics 409, 109359, 2020.
  8. E. Chung, J. Hu, and S.-M. Pun. Convergence of the CEM-GMsFEM for Stokes flows in heterogeneous perforated domains. Journal of Computational and Applied Mathematics (2021), 113327.
  9. E. Chung, W.-T. Leung, S.-M. Pun, and Z.-C. Zhang. A multi-stage deep learning based algorithm for multiscale model reduction. Journal of Computational and Applied Mathematics (2021), 113506.
  10. B. Chetverushkin, E. Chung, Y. Efendiev, S.-M. Pun, and Z.-C. Zhang. Computational multiscale methods for quasi-gas dynamic equations. Journal of Computational Physics (2021), 110352.
  11. Y. Efendiev, S.-M. Pun, and and P. N. Vabishchevich. Temporal splitting algorithms for non-stationary multiscale problems. Journal of Computational Physics (2021), 110375.
  12. S. W. Cheung, E. Chung, Y. Efendiev, W.-T. Leung, and S.-M. Pun. Iterative Oversampling Technique for Constraint Energy Minimizing Generalized Multiscale Finite Element Method in the Mixed Formulation. Applied Mathematics and Computation 415, 126622, 2021.
  13. X. Su and S.-M. Pun. A multiscale method for the heterogeneous Signorini Problem. Journal of Computational and Applied Mathematics (2022), 114160.
  14. E. Chung, Y. Efendiev, S.-M. Pun, and Z.-C. Zhang. Computational multiscale methods for parabolic wave approximations in heterogeneous media. Applied Mathematics and Computation 425, 127044, 2022.
  15. E. Chung, Y. Efendiev, W.-T. Leung, S.-M. Pun, and Z.-C. Zhang. Multi-agent Reinforcement Learning Accelerated MCMC on Multiscale Inversion Problem. arXiv preprint arXiv.2011.08954, 2020.
  16. S.-M. Pun and S. W. Cheung. Online Adaptive Algorithm for Constraint Energy Minimizing Generalized Multiscale Discontinuous Galerkin Method. arXiv preprint arXiv.2103.02677, 2021.
  17. J. Hu, W.-T. Leung, E. Chung, Y. Efendiev, and S.-M. Pun. Space-time non-local multi-continua upscaling for parabolic equations with moving channelized media. arXiv preprint arXiv.2106.12010, 2021.
  18. Y. Efendiev, W.-T. Leung, W. Li, S.-M. Pun, and P. N. Vabishchevich. Nonlocal transport equations in multiscale media. Modeling, dememorization, and discretizations. arXiv preprint arXiv.2204.00554, 2022.

Past Teaching
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