12 papers
MsFEM-Inspired CNNs with Transfer Learning for Multiscale Model Reduction
Xuehan Zhang, Lijian Jiang, Eric T. Chung
Deep learning-based surrogate models have been extensively developed for efficiently approximating multiscale systems with random input fields. However, most existing approaches re…
Multiscale Modeling for Time-harmonic Maxwell equations with impedance boundary conditions in highly heterogeneous media
Xiang Zhong, Eric T. Chung, Xingguang Jin
Modeling time-harmonic Maxwell problems in heterogeneous media presents significant mathematical and computational challenges. Due to the inherent non-elliptic structure and non-co…
Iterative Contact-resolving Hybrid Methods for Multiscale Contact Mechanics
Eric T. Chung, Hyea Hyun Kim, Xiang Zhong
Modeling contact mechanics with high contrast coefficients presents significant mathematical and computational challenges, especially in achieving strongly symmetric stress approxi…
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 contact problem with high-contrast heterogeneous coefficients with primary-dual formulation
Zishang Li, Changqing Ye, Eric T. Chung
In this paper, we propose a novel iterative multiscale framework for solving high-contrast contact problems of Signorini type. The method integrates the constrained energy minimizi…
A locking free multiscale method for linear elasticity in stress-displacement formulation with high contrast coefficients
Eric T. Chung, Changqing Ye, Xiang Zhong
Achieving strongly symmetric stress approximations for linear elasticity problems in high-contrast media poses a significant computational challenge. Conventional methods often str…
Efficient numerical method for the Schrödinger equation with high-contrast potentials
Xingguang Jin, Liu Liu, Xiang Zhong +1
In this paper, we study the Schrödinger equation in the semiclassical regime and with multiscale potential function. We develop the so-called constraint energy minimization general…
Constraint Energy Minimizing Generalized Multiscale Finite Element Method for Convection Diffusion Equations with Inhomogeneous Boundary Conditions
Po Chai Wong, Eric T. Chung, Changqing Ye +1
In this paper, we develop the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) for convection-diffusion equations with inhomogeneous Dirichlet…
Robust Multiscale Methods for Helmholtz equations in high contrast heterogeneous media
Xingguang Jin, Changqing Ye, Eric T. Chung
In this paper, we provide the constraint energy minimization generalized multiscale finite element method (CEM-GMsFEM) to solve Helmholtz equations in heterogeneous medium. This no…
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…
An iterative constraint energy minimizing generalized multiscale finite element method for contact problem
Zishang Li, Changqing Ye, Eric T. Chung
This work presents an Iterative Constraint Energy Minimizing Generalized Multiscale Finite Element Method (ICEM-GMsFEM) for solving the contact problem with high contrast coefficie…
A second-order exponential integration constraint energy minimizing generalized multiscale method for parabolic problems
Leonardo A. Poveda, Juan Galvis, Eric Chung
This paper investigates an efficient exponential integrator generalized multiscale finite element method for solving a class of time-evolving partial differential equations in boun…