Geodesic
On assessing the accuracy of defect free energy computations
Dobson, Matthew1  ; Duong, Manh Hong2  ; Ortner, Christoph2 
1 Department of Mathematics and Statistics, UMass Amherst, 710 N Pleasant Street, Amherst, MA 01003, USA
2 Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 4, pp. 1315-1352

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We develop a rigorous error analysis for coarse-graining of defect-formation free energy. For a one-dimensional constrained atomistic system, we establish the thermodynamic limit of the defect-formation free energy and obtain explicitly the rate of convergence. We then construct a sequence of coarse-grained energies with the same rate but significantly reduced computational cost. We illustrate our analytical results through explicit computations for the case of harmonic potentials and through numerical simulations.

Reçu le :
Accepté le :
DOI : 10.1051/m2an/2017052
Classification : 65G99, 74E15, 74S60
Keywords: Defect formation free energy, finite temperature, material defects, Cauchy–Born rule

Dobson, Matthew 1 ; Duong, Manh Hong 2 ; Ortner, Christoph 2

1 Department of Mathematics and Statistics, UMass Amherst, 710 N Pleasant Street, Amherst, MA 01003, USA
2 Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK 
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Dobson, Matthew; Duong, Manh Hong; Ortner, Christoph. On assessing the accuracy of defect free energy computations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 4, pp. 1315-1352. doi: 10.1051/m2an/2017052

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