Goal-oriented Atomistic-Continuum Adaptivity for the Quasicontinuum Approximation

Goal-oriented Atomistic-continuum Adaptivity for the Quasicontinuum Approximation

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 algorit...

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

We propose and analyze a goal-oriented a posteriori error estimator for the atomisticcontinuum modeling error in the quasicontinuum method. Based on this error estimator, we develop an algorithm which adaptively determines the atomistic and continuum regions to compute a quantity of interest to within a given tolerance. We apply the algorithm to the computation of the structure of a crystallogr...

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to appear in Multiscale Modeling and Simulation ERROR ESTIMATION AND ATOMISTIC-CONTINUUM ADAPTIVITY FOR THE QUASICONTINUUM APPROXIMATION OF A FRENKEL-KONTOROVA MODEL

We propose and analyze a goal-oriented a posteriori error estimator for the atomisticcontinuum modeling error in the quasicontinuum method. Based on this error estimator, we develop an algorithm which adaptively determines the atomistic and continuum regions to compute a quantity of interest to within a given tolerance. We apply the algorithm to the computation of the structure of a crystallogr...

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Goal-oriented Atomistic-Continuum Adaptivity for the Quasicontinuum Approximation

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