From the 1 of 12 linked papers with an AI index.
12 papers
An Order-One Lower Bound on the Error of Scalable Generalized Multiscale Finite Element Space Constructions
Changqing Ye
The paper shows that any deterministic, locally supported multiscale finite element construction with fixed support and coefficient‑information radii cannot achieve uniform converg…
Matrix-Free FFT-HSS Preconditioning for Periodic Landau-Lifshitz-Gilbert Saddle-Point Systems
Hang Qi, Changqing Ye, Xiaofei Guan
In this paper, a matrix-free Hermitian/skew-Hermitian splitting (HSS) preconditioner is proposed for periodic Landau--Lifshitz--Gilbert (LLG) saddle-point systems. The main contrib…
Multiscale modeling for problems with high contrast heterogeneous coefficients by the CEM-GMsFEM
Eric T. Chung, Yalchin Efendiev, Xingguang Jin +2
This review paper provides a comprehensive overview of the Constrained Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) for solving elliptic PDEs charact…
Multiscale Methods for wave propagation in materials with sign-changing coefficients
Eric T. Chung, Patrick Ciarlet, Xingguang Jin +1
From a mathematical perspective, the extraordinary properties of metamaterials are often reflected in the coefficients of the governing partial differential equations (PDEs). These…
Multiscale modeling for a class of high-contrast heterogeneous sign-changing problems
Eric T. Chung, Patrick Ciarlet, Xingguang Jin +1
The mathematical formulation of sign-changing problems involves a linear second-order partial differential equation in the divergence form, where the coefficient can assume positiv…
Efficient Multiscale Methods for Highly Heterogeneous Spatial Network Models
Yingjie Zhou, Xiang Zhong, Changqing Ye +1
Modeling complex spatial networks with multiscale heterogeneity poses significant mathematical and computational challenges. Lacking explicit PDE discretizations and facing excessi…