A Posteriori Error Estimate and Adaptive Mesh Refinement Algorithm for Atomistic/Continuum Coupling with Finite Range Interactions in Two Dimensions

Liao, Mingjie

doi:10.4208/cicp.oa-2018-0169

Cited by 6 publications

(9 citation statements)

References 34 publications

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“…5 where such an assumption holds. A more general numerical approach may need to combine ideas such as stress based error indicator from adaptive atomistic/continuum coupling method [31,20], and will be investigated in our future work. Remark 4.2.…”

Section: Adaptive Qm/mm Algorithmsmentioning

confidence: 99%

“…But the main purpose of this paper is to develop an analytical framework for adaptive QM/MM computation, and justify it numerically by some prototypical examples, such as the single vacancy and two separated vacancies in Section 5 where such an assumption holds. A more general numerical approach may need to combine ideas such as stress based error indicator from adaptive atomistic/continuum coupling method [31,20], and will be investigated in our future work. Remark 4.2.…”

Section: Adaptive Qm/mm Algorithmsmentioning

confidence: 99%

“…In fact, recent developments in a similar field, atomistic/continuum coupling methods for crystalline defects (see, e.g. [1,2,23,26,28,29,31,20]) have provided valuable insights also on the study of QM/MM methods.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Adaptive QM/MM coupling for crystalline defects

Chen

Liao

Wang

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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QM (quantum mechenics) and MM (molecular mechenics) coupling methods are widely used in simulations of crystalline defects. In this paper, we construct a residual based a posteriori error indicator for QM/MM coupling approximations. We prove the reliability of the error indicator (upper bound of the true approximation error) and develop some sampling techniques for its efficient calculation. Based on the error indicator and Dörfler marking strategy, we design an adaptive QM/MM algorithm for crystalline defects and demonstrate the efficiency with some numerical experiments.keywords. qm/mm coupling, a posteriori error estimate, adaptive algorithm, crystal defects AMS subject classifications.

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Section: Adaptive Qm/mm Algorithmsmentioning

confidence: 99%

Section: Adaptive Qm/mm Algorithmsmentioning

confidence: 99%

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Adaptive QM/MM coupling for crystalline defects

Chen

Liao

Wang

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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“…A natural extension of the FBC method is to include adaptive refinement techniques to evolve the atomistic domain in case the equilibrium position of a dislocation lies outside the prechosen boundaries [27]. In this context, an alternative option would be to use the coupled atomistic/discrete dislocations (CADD) method [2,20,9] in which the atomistic domain is coupled to a discrete dislocation dynamics domain.…”

Section: Further Improvements and Extensionsmentioning

confidence: 99%

Efficient flexible boundary conditions for long dislocations

Hodapp

2021

Preprint

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We present a novel efficient implementation of the flexible boundary condition (FBC) method, initially proposed by Sinclair et al., for large single-periodic problems. Efficiency is primarily achieved by constructing a hierarchical matrix (H -matrix) representation of the periodic Green matrix, reducing the complexity for updating the boundary conditions of the atomistic problem from quadratic to almost linear in the number of pad atoms. In addition, our implementation is supported by various other tools from numerical analysis, such as a residual-based transformation of the boundary conditions to accelerate the convergence. We assess the method for a dislocation bow-out problem and compare its performance with the state-of-the-art method for this class of problems, the periodic array of dislocations (PAD) method. The main result of our analysis is that the FBC method is up to two orders of magnitude more efficient than the PAD method in terms of the required number of per-atom force computations when both methods give similar accuracy. This opens new prospects for large-scale atomistic simulations-without having to worry about spurious image effects that plague classical boundary conditions.

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“…Using a weighted 2 -norm on the QM/MM force error leads to a simple and practical scheme, but makes it impossible to guarantee lower bounds on the error, which is important to guarantee the efficiency of the algorithm. There have also been investigations of related a posteriori error estimates for atomistic/continuum (A/C) coupling methods, which share many similarities [2,33,37,42,31,43,48,28,49].…”

Section: Introductionmentioning

confidence: 99%

A Posteriori Error Estimates for Adaptive QM/MM Coupling Methods

Wang¹,

Chen²,

Liao³

et al. 2020

Preprint

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Hybrid quantum/molecular mechanics models (QM/MM methods) are widely used in material and molecular simulations when MM models do not provide sufficient accuracy but pure QM models are computationally prohibitive. Adaptive QM/MM coupling methods feature on-the-fly classification of atoms during the simulation, allowing the QM and MM subsystems to be updated as needed. In this work, we propose such an adaptive QM/MM method for material defect simulations based on a new residual based a posteriori error estimator, which provides both lower and upper bounds for the true error. We validate the analysis and illustrate the effectiveness of the new scheme on numerical simulations for material defects.

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A Posteriori Error Estimate and Adaptive Mesh Refinement Algorithm for Atomistic/Continuum Coupling with Finite Range Interactions in Two Dimensions

Cited by 6 publications

References 34 publications

Adaptive QM/MM coupling for crystalline defects

Adaptive QM/MM coupling for crystalline defects

Efficient flexible boundary conditions for long dislocations

A Posteriori Error Estimates for Adaptive QM/MM Coupling Methods

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