Goal-oriented Atomistic-Continuum Adaptivity for the Quasicontinuum Approximation

2007/07/31 by Marcel Arndt, Arndt, Marcel, Mitchell Luskin +1
Computer Science · Engineering · Materials Science · #65Z05 #70C20 #70G75 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Microstructure and mechanical properties #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.0708.0025

openalex publication_date 2007/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We give a goal-oriented a posteriori error estimator for the atomistic-continuum modeling error in the quasicontinuum method, and we use this estimator to design an adaptive algorithm to compute a quantity of interest to a given tolerance by using a nearly minimal number of atomistic degrees of freedom. We present computational results that demonstrate the effectiveness of our algorithm for a periodic array of dislocations described by a Frenkel-Kontorova type model.

Citations

• Error Estimation and Atomistic-Continuum Adaptivity for the Quasicontinuum Approximation of a Frenkel-Kontorova Model

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