Work

Heterogeneous Multiscale Methods for Fourth-Order Singular Perturbations

Year: 2025

Type: article

Abstract: . We develop a numerical homogenization method for fourth-order singular perturbation problems within the framework of heterogeneous multiscale methods. These problems arise from heterogeneous strain gradient elasticity and elasticity models for structured materials. We establish an error estimate for the homogenized solution applicable to general media and derive an explicit convergence for the locally periodic media with the fine-scale [Formula: see text]. For cell problems of size [Formula: see text], the classical resonance error [Formula: see text] can be eliminated due to the dominance of the higher-order operator. Despite the occurrence of boundary layer effects, discretization errors do not necessarily deteriorate for general boundary conditions. Numerical simulations corroborate these theoretical findings.

Source: Multiscale Modeling and Simulation

DOI: 10.1137/24m1686218

Authors: Yulei Liao, Pingbing Ming

Institutions: National University of Singapore, Chinese Academy of Sciences, Academy of Mathematics and Systems Science, University of Chinese Academy of Sciences

Language: English

Topic: Advanced Mathematical Modeling in Engineering

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Awards: G2082367026, 应变梯度弹性模型多尺度建模与计算方法研究