4 papers
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…
An efficient numerical method for the anisotropic phase field dendritic crystal growth model
Yayu Guo, Mejdi Azaiez, Chuanju Xu
In this paper, we propose and analyze an efficient numerical method for the anisotropic phase field dendritic crystal growth model, which is challenging because we are facing the n…
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…
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…