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20172026
most citedConvergence Rate of Multiscale Finite Element Method for Various Boundary Problems

8 citations · 12 across the 10 of their papers we have counts for

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math.NA2026

High-Order Multi-Scale Method and Its Convergence Analysis for Nonlinear Thermo-Electro-Mechanical Coupling Problems of Composite Structures

Hao Dong

This study proposes a high-order multi-scale method tailored for time-dependent nonlinear thermo-electro-mechanical coupling problems of composite structures with highly spatial he…

math.NA2026

Higher-Order Multiscale Computational Method for Multi-Continuum Problems in Highly Heterogeneous Media

Hao Dong, Jiayuan Peng, Jian Huang

This paper presents a high-accuracy higher-order multiscale method for solving multi-continuum problems in in highly heterogeneous media. First, microscopic unit cell functions are…

math.NA2025

Higher-order multiscale method and its convergence analysis for nonlinear thermo-electric coupling problems of composite structures

Hao Dong, Zongze Yang, Yufeng Nie

This paper proposes a higher-order multiscale computational method for nonlinear thermo-electric coupling problems of composite structures, which possess temperature-dependent mate…

math.NA2023

Statistical higher-order multi-scale method for nonlinear thermo-mechanical simulation of random composite materials with temperature-dependent properties

Hao Dong, Junzhi Cui

Stochastic multi-scale modeling and simulation for nonlinear thermo-mechanical problems of composite materials with complicated random microstructures remains a challenging issue.…

math.NA2023

Higher-order multi-scale method for high-accuracy nonlinear thermo-mechanical simulation of heterogeneous shells

Hao Dong, Xiaofei Guan, Yufeng Nie

In the present work, we consider multi-scale computation and convergence for nonlinear time-dependent thermo-mechanical equations of inhomogeneous shells possessing temperature-dep…

math.NA2023

Higher-order multi-scale deep Ritz method for multi-scale problems of authentic composite materials

Jiale Linghu, Hao Dong, Junzhi Cui +1

The direct deep learning simulation for multi-scale problems remains a challenging issue. In this work, a novel higher-order multi-scale deep Ritz method (HOMS-DRM) is developed fo…

math.NA2019★ 8 cited

Convergence Rate of Multiscale Finite Element Method for Various Boundary Problems

Changqing Ye, Hao Dong, Junzhi Cui

In this paper, we examine the effectiveness of classic multiscale finite element method (MsFEM) (Hou and Wu, 1997; Hou et al., 1999) for mixed Dirichlet-Neumann, Robin and hemivari…

math.NA2019★ 4 cited

A First-order Two-scale Analysis for Contact Problems with Small Periodic Configurations

Changqing Ye, Junzhi Cui

This paper is devoted to studying a type of contact problems modeled by hemivariational inequalities with small periodic coefficients appearing in PDEs, and the PDEs we considered…

math.NA2017

Multiscale computational method for heat conduction problems of composite structures with diverse periodic configurations in different subdomains

Hao Dong, Junzhi Cui, Yufeng Nie +1

This study develops a novel multiscale computational method for heat conduction problems of composite structures with diverse periodic configurations in different subdomains. First…