2 papers
physics.comp-ph2025
Surrogate-based multilevel Monte Carlo methods for uncertainty quantification in the Grad-Shafranov free boundary problem
Howard Elman, Jiaxing Liang, Tonatiuh Sánchez-Vizuet
We explore a hybrid technique to quantify the variability in the numerical solutions to a free boundary problem associated with magnetic equilibrium in axisymmetric fusion reactors…
math.NA2024
Transformed Physics-Informed Neural Networks for The Convection-Diffusion Equation
Jiajing Guan, Howard Elman
Singularly perturbed problems are known to have solutions with steep boundary layers that are hard to resolve numerically. Traditional numerical methods, such as Finite Difference…