Bo Dong
University of Massachusetts-Dartmouth, MA·Mathematics & Statistics
Many physical systems, from water waves to quantum particles, obey equations that conserve certain quantities, such as energy or mass. Others produce waves that oscillate extremely rapidly.
- Fields
Mathematics & Statistics
Computer Science
Physics
- Topics
numerical analysis
discontinuous Galerkin methods
hybridizable discontinuous Galerkin
- Grants
- 1 known grant, through May 2027
What they work on
- Analyze a new conservative discontinuous Galerkin (DG) method that preserves conserved quantities through implicit penalty parameters, applied to the Korteweg-de Vries equation for shallow-water waves.
- Extend implicit-penalty conservative DG methods to coupled and two-dimensional wave models, including the Hirota-Satsuma, Schrödinger-KdV, abcd-Boussinesq, Zakharov-Kuznetsov and Kadomtsev-Petviashvili equations.
- Design, analyze and implement hybridizable DG methods with multiscale non-polynomial basis functions that capture highly oscillatory Schrödinger equation solutions on coarse meshes.
More about the research
Computer simulations of these systems often slowly lose the conserved quantities over long runs. They can also need impractically fine grids to capture fast oscillations. This project develops new numerical methods for partial differential equations (PDEs), the equations describing how quantities change in space and time, that address both problems.
Why it matters
More accurate and stable long-time simulations could benefit fluid dynamics, nonlinear optics, plasma physics and Bose-Einstein condensate research. Efficient methods for highly oscillatory quantum wave equations could support quantum mechanics studies and the design of ultrafast, low-power nanoscale electronic devices.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Yiran Wang
University of Alabama, AL·Mathematics & Statistics
Develop hybrid reduced order models in which neural networks add basis functions to precomputed multiscale ones, guided by stable Petrov-Galerkin formulations and residual-based error indicators.
Georg Stadler
New York University, NY·Mathematics & Statistics
Develop lifted Newton methods that move severely nonlinear PDE systems into a higher-dimensional space and apply nonlinear transformations before linearization, a form of nonlinear preconditioning.
Haomin Zhou
Georgia Institute of Technology, GA·Mathematics & Statistics
Establish parameterized Wasserstein sub-manifolds, which represent evolving probability distributions through a neural network's parameters via a push-forward map and pullback metric, and develop their mathematical foundations.
The school
University of Massachusetts-Dartmouth: 2 labs on PI Pages, $42M a year on research, 30 research doctorates a year.
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