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Courses
Fall 2024: MA/CS-51400 Numerical Analysis
Academic Background
- Post-Doc, Applied Mathematics, Brown University, 2004.
- Ph.D., Mechanical Engineering, State University of New York at
Buffalo, 2001.
- M.S., Physics, Zhejiang University (China), 1995.
- B.S., Aerospace Engineering, National University of Defense
Technology (China), 1992.
Research
- High-order numerical methods and time integration
algorithms for fluids- and solids-related phenomena.
- Neural network-based numerical methods, data-driven
scientific computing, mathematical and scientific machine learning.
- Computational partial differential equations, computational
methods.
- Computational fluid dynamics, computational mechanics.
- Physically and thermodynamically consistent modeling.
- Fluid interfaces, free surfaces, and contact line dynamics.
- Two-phase and multiphase flows, and interactions
with wall surfaces.
- Open boundary problems, open boundary conditions and
related problems
- Turbulent pattern formation.
- Bio-fluids and bio-structural simulations.
- Flow-structure interaction, vortex-induced vibrations.
- Turbulence at high Reynolds numbers in complex geometries.
- High performance computing, parallel computing.
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Representative Publications
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S. Dong & Y. Wang. A method for computing inverse parametric PDE problems with
random-weight neural networks. Journal of Computational Physics,
489, 112263, 2023. [PDF]
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S. Dong & J. Yang. Numerical approximation of partial differential equations
by a variable projection method with artificial neural networks.
Computer Methods in Applied Mechanics and Engineering, 398, 115284, 2022.
[PDF]
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S. Dong & J. Yang. On computing the hyperparameter of extreme learning machines:
Algorithm and application to computational PDEs, and comparison with
classical and high-order finite elements. Journal of Computational Physics,
463, 111290, 2022. [PDF]
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S. Dong & Z. Li. Local extreme learning machines and domain decomposition for solving
linear and nonlinear partial differential equations. Computer Methods in
Applied Mechanics and Engineering, 387, 114129, 2021. [PDF]
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S. Dong & N. Ni. A method for representing periodic functions and
enforcing exactly periodic boundary conditions with deep neural networks.
Journal of Computational Physics, 435, 110242, 2021.
[PDF]
extended list of publications ... |
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