Minimizing Boundary Reflections in Coupled-Domain Simulations

Cai, Wei; Koning, Maurice de; Bulatov, Vasily V.; Yip, Sidney

doi:10.1103/physrevlett.85.3213

Cited by 209 publications

(169 citation statements)

References 18 publications

(23 reference statements)

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“…However, these approaches differ in the way the time history kernel function Θ is derived. For instance, Cai et al [76] computed Θ from several MD simulations. E and Huang [77,78] have computed analytically the kernel coefficients by minimizing the reflection coefficients at each wavenumber.…”

Section: State Of the Art Of Multiscale Methodsmentioning

confidence: 99%

MD/FE Multiscale Modeling of Contact

Ramisetti

Anciaux

Molinari

2014

Fundamentals of Friction and Wear on the Nanoscale

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Limitations of single scale approaches to study the complex physics involved in friction have motivated the development of multiscale models. We review the state-of-the-art multiscale models that have been developed up to date. These have been successfully applied to a variety of physical problems, but that were limited, in most cases, to zero Kelvin studies. We illustrate some of the technical challenges involved with simulating a frictional sliding problem, which by nature generates a large amount of heat. These challenges can be overcome by a proper usage of spatial filters, which we combine to a direct finite-temperature multiscale approach coupling molecular dynamics with finite elements. The basic building block relies on the proper definition of a scale transfer operator using the least square minimization and spatial filtering. Then, the restitution force from the generalized Langevin equation is modified to perform a two-way thermal coupling between the two models. Numerical examples are shown to illustrate the proposed coupling formulation.

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Section: State Of the Art Of Multiscale Methodsmentioning

confidence: 99%

MD/FE Multiscale Modeling of Contact

Ramisetti

Anciaux

Molinari

2014

Fundamentals of Friction and Wear on the Nanoscale

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“…Then if we set f = E[ρ] + g, it is clear from (7) that f satisfies (1). Moreover, taking the moments of (7) and using (6) gives ∂ t mg = 0. Since these moments are zero at t = 0 due to the initial data, then mg = 0 at anytime, and hence mf = mE[ρ] = ρ.…”

Section: Microscopic Upscaling and Macroscopic Downscalingmentioning

confidence: 99%

“…Then we use the definition of the equilibrium flux vector F (ρ) given in the proposition and relation (3) and (5) to find (6). Relation (7) is directly derived from (4) and (1).…”

Section: Microscopic Upscaling and Macroscopic Downscalingmentioning

confidence: 99%

Diffusion approximation

Gass¹,

Harris²

2001

Encyclopedia of Operations Research and Management Science

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Abstract.This paper presents a general methodology to design macroscopic fluid models that take into account localized kinetic upscaling effects. The fluid models are solved in the whole domain together with a localized kinetic upscaling that corrects the fluid model wherever it is necessary. This upscaling is obtained by solving a kinetic equation on the non-equilibrium part of the distribution function. This equation is solved only locally and is related to the fluid equation through a downscaling effect. The method does not need to find an interface condition as do usual domain decomposition methods to match fluid and kinetic representations. We show our approach applies to problems that have a hydrodynamic time scale as well as to problems with diffusion time scale. Simple numerical schemes are proposed to discretized our models, and several numerical examples are used to validate the method.

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“…However, general situations involving heterogeneous strain fields and high defect densities, as opposed to isolated defects, are usually not considered. Furthermore, increasing evidence supports the idea that concurrent simulations at finite temperature in which a statistical (quantum mechanical) or discrete (molecular) domain is interfaced with a continuum domain presents profound obstacles to computer method development [37][38][39][40]. Although the present investigation is restricted to quasi-static isothermal conditions, it is noteworthy that self-consistent hierarchical approaches provide a means of preserving statistical ensembles of atomic motions in the continuum domain, such as at a finite element quadrature point, through the use of unit cell-based averaging.…”

Section: Introductionmentioning

confidence: 99%

Multiscale Modeling of Point and Line Defects in Cubic Lattices

Chung

Clayton

2007

Int J Mult Comp Eng

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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. REPORT DATE (DD-MM-YYYY) March 2008 REPORT TYPE Reprint DATES COVERED (From SPONSOR/MONITOR'S ACRONYM(S) 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) SPONSOR/MONITOR'S REPORT NUMBER(S) DISTRIBUTION/AVAILABILITY STATEMENTApproved for public release; distribution is unlimited. SUPPLEMENTARY NOTESA reprint from the International Journal for Multiscale Computational Engineering, vol. 5, nos. 3 and 4, pp. 203-226, 2007. 14. ABSTRACT A multilength scale method based on asymptotic expansion homogenization (AEH) is developed to compute minimum energy configurations of ensembles of atoms at the fine length scale and the corresponding mechanical response of the material at the coarse length scale. This multiscale theory explicitly captures heterogeneity in microscopic atomic motion in crystalline materials, attributed, for example, to the presence of various point and line lattice defects. The formulation accounts for large deformations of nominally hyperelastic, monocrystalline solids. Unit cell calculations are performed to determine minimum energy configurations of ensembles of atoms of body-centered cubic tungsten in the presence of periodic arrays of vacancies and screw dislocations of line orientations [111] or [100]. Results of the theory and numerical implementation are verified versus molecular statics calculations based on conjugate gradient minimization (CGM) and are also compared with predictions from the local Cauchy-Born rule. For vacancy defects, the AEH method predicts the lowest system energy among the three methods, while computed energies are comparable between AEH and CGM for screw dislocations. Computed strain energies and defect energies (e.g., energies arising from local internal stresses and strains near defects) are used to construct and evaluate continuum energy functions for defective crystals parameterized via the vacancy density, the dislocation density tensor, and the generally incompatible lattice deformation gradient. For crystals with vacancies, a defect energy increasing linearly with vacancy density and applied elastic deformation is suggested, while for crystals with screw d...

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Minimizing Boundary Reflections in Coupled-Domain Simulations

Cited by 209 publications

References 18 publications

MD/FE Multiscale Modeling of Contact

MD/FE Multiscale Modeling of Contact

Diffusion approximation

Multiscale Modeling of Point and Line Defects in Cubic Lattices

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