Analysis of a Predictor-Corrector Method for Computationally Efficient\n Modeling of Surface Effects in 1D

2016/05/18 by Andrew Binder, Binder, Andrew J., Mitchell Luskin +3
Engineering · #65Z05 (Primary) #70C20 (Secondary) #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1605.05750

openalex publication_date 2016/05/18 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

The regular Cauchy--Born method is a useful and efficient tool for analyzing\nbulk properties of materials in the absence of defects. However, the method\nnormally fails to capture surface effects, which are essential to determining\nmaterial properties at small length scales. In this paper, we present a\ncorrector method that improves upon the prediction for material behavior from\nthe Cauchy--Born method over a small boundary layer at the surface of a 1D\nmaterial by capturing the missed surface effects. We justify the separation of\nthe problem into a bulk response and a localized surface correction by\nestablishing an error estimate, which vanishes in the long wavelength limit.\n

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