3 papers
math.NA2025
PODNO: Proper Orthogonal Decomposition Neural Operators
Zilan Cheng, Zhongjian Wang, Li-Lian Wang +1
In this paper, we introduce Proper Orthogonal Decomposition Neural Operators (PODNO) for solving partial differential equations (PDEs) dominated by high-frequency components. Build…
math.NA2021
New efficient time-stepping schemes for the anisotropic phase-field dendritic crystal growth model
Minghui Li, Mejdi Azaiez, Chuanju Xu
In this paper, we propose and analyze a first-order and a second-order time-stepping schemes for the anisotropic phase-field dendritic crystal growth model. The proposed schemes ar…
physics.comp-ph2019
A cure for instabilities due to advection-dominance in POD solution to advection-diffusion-reaction equations
Mejdi Azaïez, Tomás Chacón Rebollo, Samuele Rubino
In this paper, we propose to improve the stabilized POD-ROM introduced by S. Rubino in [37] to deal with the numerical simulation of advection-dominated advection-diffusion-reactio…