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arXiv · 2301.13145

Accurate and efficient multiscale simulation of a heterogeneous elastic beam via computation on small sparse patches

A. J. Roberts·Thien Tran-Duc·J. E. Bunder·Yannis Kevrekidis
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Abstract

Modern `smart' materials have complex microscale structure, often with unknown macroscale closure. The Equation-Free Patch Scheme empowers us to non-intrusively, efficiently, and accurately simulate over large scales through computations on only small well-separated patches of the microscale system. Here the microscale system is a solid beam of random heterogeneous elasticity. The continuing challenge is to compute the given physics on just the microscale patches, and couple the patches across un-simulated macroscale space, in order to establish efficiency, accuracy, consistency, and stability on the macroscale. Dynamical systems theory supports the scheme. This research program is to develop a systematic non-intrusive approach, both computationally and analytically proven, to model and compute accurately macroscale system levels of general complex physical and engineering systems.

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A. J. Roberts, Thien Tran-Duc, J. E. Bunder, Yannis Kevrekidis. 2023-01-20. Accurate and efficient multiscale simulation of a heterogeneous elastic beam via computation on small sparse patches. https://arxiv.org/abs/2301.13145

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