3 papers
math.AP2024
The 3D Euler equations with inflow, outflow and vorticity boundary conditions
Gung-Min Gie, James P. Kelliher, Anna L. Mazzucato
The 3D incompressible Euler equations in a bounded domain are most often supplemented with impermeable boundary conditions, which constrain the fluid to neither enter nor leave the…
math.NA2024
Singular layer PINN methods for Burgers' equation
Teng-Yuan Chang, Gung-Min Gie, Youngjoon Hong +1
In this article, we present a new learning method called sl-PINN to tackle the one-dimensional viscous Burgers problem at a small viscosity, which results in a singular interior la…
math.NA2024
Singular Layer Physics-Informed Neural Network Method for Convection-Dominated Boundary Layer Problems in Two Dimensions
Gung-Min Gie, Youngjoon Hong, Chang-Yeol Jung +1
This research explores neural network-based numerical approximation of two-dimensional convection-dominated singularly perturbed problems on square, circular, and elliptic domains.…