293 citations · 1.2k across the 39 of their papers we have counts for
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math.NA2021★ 3 cited
Geometric Quasilinearization Framework for Analysis and Design of Bound-Preserving Schemes
Kailiang Wu, Chi-Wang Shu
Solutions to many partial differential equations satisfy certain bounds or constraints. For example, the density and pressure are positive for equations of fluid dynamics, and in t…
cs.LG2021★ 4 cited
Deep Neural Network Modeling of Unknown Partial Differential Equations in Nodal Space
Zhen Chen, Victor Churchill, Kailiang Wu +1
We present a numerical framework for deep neural network (DNN) modeling of unknown time-dependent partial differential equations (PDE) using their trajectory data. Unlike the recen…
math.NA2021
Minimum Principle on Specific Entropy and High-Order Accurate Invariant Region Preserving Numerical Methods for Relativistic Hydrodynamics
Kailiang Wu
This paper explores Tadmor's minimum entropy principle for the relativistic hydrodynamics (RHD) equations and incorporates this principle into the design of robust high-order disco…