From the 2 of 11 linked papers with an AI index.
11 papers
A Convex Splitting Spectral Method for the Phase Field Crystal Equation: Energy Stability, Computational Stability Maps, and Three-Dimensional GPU Simulations
Saulo Orizaga, Peimeng Yin, Deep Choudhuri
The paper introduces a Fourier spectral method based on convex splitting for the phase field crystal equation that is unconditionally energy stable, conserves mass, and can be effi…
A linear, fully decoupled, and unconditionally energy-stable SAV-FEM for the Cahn--Hilliard--Navier--Stokes model
Jinting Yang, Nianyu Yi, Peimeng Yin
The paper presents a linear, fully decoupled finite element scheme using a single scalar auxiliary variable that is unconditionally energy‑stable for the Cahn–Hilliard–Navier–Stoke…
Neural network-enhanced -adaptive finite element algorithm for parabolic equations
Jiaxiong Hao, Yunqing Huang, Nianyu Yi +1
In this paper, we propose a novel -adaptive finite element method, enhanced by neural networks, for parabolic equations. The main challenge of the conventional -adaptive fin…
Unconditional energy stable hybrid IEQ-FEMs for the Cahn-Hilliard-Navier-Stokes equations
Yaoyao Chen, Dongqian Li, Yin Yang +1
We investigate two unconditionally energy stable invariant energy quadratization (IEQ) finite element methods (FEMs) [Chen et al. Numerical Algorithms, DOI: 10.1007/s11075-024-0191…
A fully decoupled and structure-preserving relaxation Crank--Nicolson finite element method for Gross--Pitaevskii--Poisson model
Dongqian Li, Huini Liu, Yin Yang +1
We propose a fully decoupled, structure-preserving relaxation Crank--Nicolson finite element method (FEM) for the coupled Gross--Pitaevskii--Poisson (GPP) system modeling ultracold…
Towards finite element methods for fourth-order elliptic equation. Part I: general boundary conditions
Xihao Zhang, Hengguang Li, Nianyu Yi +1
This paper is part of a series developing finite element methods for fourth-order elliptic equations on polygonal domains. Here, we investigate how boundary conditions influe…