Filters for Improvement of Multiscale Data from Atomistic Simulations

Gardner, David J.; Reynolds, Daniel R.

doi:10.1137/15M1053785

Title: Filters for Improvement of Multiscale Data from Atomistic Simulations

Abstract

Multiscale computational models strive to produce accurate and efficient numerical simulations of systems involving interactions across multiple spatial and temporal scales that typically differ by several orders of magnitude. Some such models utilize a hybrid continuum-atomistic approach combining continuum approximations with first-principles-based atomistic models to capture multiscale behavior. By following the heterogeneous multiscale method framework for developing multiscale computational models, unknown continuum scale data can be computed from an atomistic model. Concurrently coupling the two models requires performing numerous atomistic simulations which can dominate the computational cost of the method. Furthermore, when the resulting continuum data is noisy due to sampling error, stochasticity in the model, or randomness in the initial conditions, filtering can result in significant accuracy gains in the computed multiscale data without increasing the size or duration of the atomistic simulations. In this work, we demonstrate the effectiveness of spectral filtering for increasing the accuracy of noisy multiscale data obtained from atomistic simulations. Moreover, we present a robust and automatic method for closely approximating the optimum level of filtering in the case of additive white noise. By improving the accuracy of this filtered simulation data, it leads to a dramatic computational savings by allowing for shorter andmore »« less

Authors:

Gardner, David J. ^[1]; Reynolds, Daniel R. ^[2]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
Southern Methodist Univ., Dallas, TX (United States). Dept. of Mathematics

Publication Date:: Thu Jan 05 00:00:00 EST 2017

Research Org.:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

OSTI Identifier:: 1368025

Report Number(s):: LLNL-JRNL-678665
Journal ID: ISSN 1540-3459

Grant/Contract Number:: AC52-07NA27344

Resource Type:: Accepted Manuscript

Journal Name:: Multiscale Modeling & Simulation

Additional Journal Information:: Journal Volume: 15; Journal Issue: 1; Journal ID: ISSN 1540-3459

Publisher:: SIAM

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; heterogeneous multiscale method; filtering; hybrid continuum-atomistic simulations

Citation Formats


                    Gardner, David J., and Reynolds, Daniel R. Filters for Improvement of Multiscale Data from Atomistic Simulations.  United States: N. p., 2017. 
Web.  doi:10.1137/15M1053785.

Copy to clipboard


                    Gardner, David J., & Reynolds, Daniel R. Filters for Improvement of Multiscale Data from Atomistic Simulations.  United States.  https://doi.org/10.1137/15M1053785

Copy to clipboard


                    Gardner, David J., and Reynolds, Daniel R. Thu .  
"Filters for Improvement of Multiscale Data from Atomistic Simulations".  United States.  https://doi.org/10.1137/15M1053785.  https://www.osti.gov/servlets/purl/1368025.

Copy to clipboard


                    
@article{osti_1368025,

  title        = {Filters for Improvement of Multiscale Data from Atomistic Simulations},

  author       = {Gardner, David J. and Reynolds, Daniel R.},

  abstractNote = {Multiscale computational models strive to produce accurate and efficient numerical simulations of systems involving interactions across multiple spatial and temporal scales that typically differ by several orders of magnitude. Some such models utilize a hybrid continuum-atomistic approach combining continuum approximations with first-principles-based atomistic models to capture multiscale behavior. By following the heterogeneous multiscale method framework for developing multiscale computational models, unknown continuum scale data can be computed from an atomistic model. Concurrently coupling the two models requires performing numerous atomistic simulations which can dominate the computational cost of the method. Furthermore, when the resulting continuum data is noisy due to sampling error, stochasticity in the model, or randomness in the initial conditions, filtering can result in significant accuracy gains in the computed multiscale data without increasing the size or duration of the atomistic simulations. In this work, we demonstrate the effectiveness of spectral filtering for increasing the accuracy of noisy multiscale data obtained from atomistic simulations. Moreover, we present a robust and automatic method for closely approximating the optimum level of filtering in the case of additive white noise. By improving the accuracy of this filtered simulation data, it leads to a dramatic computational savings by allowing for shorter and smaller atomistic simulations to achieve the same desired multiscale simulation precision.},

  doi          = {10.1137/15M1053785},

  journal      = {Multiscale Modeling & Simulation},

  number       = 1,

  volume       = 15,

  place        = {United States},

  year         = {Thu Jan 05 00:00:00 EST 2017},

  month        = {Thu Jan 05 00:00:00 EST 2017}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1137/15M1053785

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 1 work

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Molecular dynamics with coupling to an external bath
journal, October 1984

Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.
The Journal of Chemical Physics, Vol. 81, Issue 8
DOI: 10.1063/1.448118

Stochastic Problems in Physics and Astronomy
journal, January 1943

Chandrasekhar, S.
Reviews of Modern Physics, Vol. 15, Issue 1
DOI: 10.1103/RevModPhys.15.1

The Heterognous Multiscale Methods
journal, January 2003

E., Weinan; Engquist, Bjorn
Communications in Mathematical Sciences, Vol. 1, Issue 1
DOI: 10.4310/CMS.2003.v1.n1.a8

Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen
journal, January 1905

Einstein, A.
Annalen der Physik, Vol. 322, Issue 8
DOI: 10.1002/andp.19053220806

Multiscale Local Polynomial Smoothing in a Lifted Pyramid for Non-Equispaced Data
journal, February 2013

Jansen, Maarten
IEEE Transactions on Signal Processing, Vol. 61, Issue 3
DOI: 10.1109/TSP.2012.2225059

Equation-Free, Coarse-Grained Multiscale Computation: Enabling Mocroscopic Simulators to Perform System-Level Analysis
journal, January 2003

Gear, C. William; Hyman, James M.; Kevrekidid, Panagiotis G.
Communications in Mathematical Sciences, Vol. 1, Issue 4
DOI: 10.4310/CMS.2003.v1.n4.a5

Multiscale modeling of the dynamics of solids at finite temperature
journal, July 2005

Li, Xiantao; E., Weinan
Journal of the Mechanics and Physics of Solids, Vol. 53, Issue 7
DOI: 10.1016/j.jmps.2005.01.008

Concurrent coupling of atomistic and continuum models at finite temperature
journal, January 2011

Mathew, N.; Picu, R. C.; Bloomfield, M.
Computer Methods in Applied Mechanics and Engineering, Vol. 200, Issue 5-8
DOI: 10.1016/j.cma.2010.09.018

Fast Parallel Algorithms for Short-Range Molecular Dynamics
journal, March 1995

Plimpton, Steve
Journal of Computational Physics, Vol. 117, Issue 1
DOI: 10.1006/jcph.1995.1039

Heterogeneous multiscale method for the modeling of complex fluids and micro-fluidics
journal, March 2005

Ren, Weiqing; E., Weinan
Journal of Computational Physics, Vol. 204, Issue 1
DOI: 10.1016/j.jcp.2004.10.001

Multi-scale plasma simulation by the interlocking of magnetohydrodynamic model and particle-in-cell kinetic model
journal, December 2007

Sugiyama, Tooru; Kusano, Kanya
Journal of Computational Physics, Vol. 227, Issue 2
DOI: 10.1016/j.jcp.2007.09.011

On the Theory of the Brownian Motion
journal, September 1930

Uhlenbeck, G. E.; Ornstein, L. S.
Physical Review, Vol. 36, Issue 5
DOI: 10.1103/PhysRev.36.823

The local microscale problem in the multiscale modeling of strongly heterogeneous media: Effects of boundary conditions and cell size
journal, March 2007

Yue, Xingye; Weinan, E.
Journal of Computational Physics, Vol. 222, Issue 2, p. 556-572
DOI: 10.1016/j.jcp.2006.07.034

Similar Records in DOE PAGES and OSTI.GOV collections:

Multiscale Modeling of Dissipation and Failure in MEMS Resonators

Conference Rudd, R

This work studies multiscale phenomena in silicon micro-resonators which comprise the mechanical components of next-generation Micro-Electro-Mechanical Systems (MEMS). Unlike their larger relatives, the behavior of these sub-micron MEMS is not described well by conventional continuum models and finite elements, but it is determined appreciably by the interplay between physics at the Angstrom, nanometer and micron scales. As device sizes are reduced below the micron scale, atomistic processes cause systematic deviations from the behavior predicted by conventional continuum elastic theory. [1] These processes cause anomalous surface effects in the resonator frequency and quality factor--even for single crystal devices with clean surfacesmore »« less
Full Text Available
First principles-based multiscale atomistic methods for input into first principles nonequilibrium transport across interfaces

Journal Article Cheng, Tao ; Jaramillo-Botero, Andres ; An, Qi ; ... - Proceedings of the National Academy of Sciences of the United States of America

This issue of PNAS features “nonequilibrium transport and mixing across interfaces,” with several papers describing the nonequilibrium coupling of transport at interfaces, including mesoscopic and macroscopic dynamics in fluids, plasma, and other materials over scales from microscale to celestial. Most such descriptions describe the materials in terms of the density and equations of state rather than specific atomic structures and chemical processes. It is at interfacial boundaries where such atomistic information is most relevant. However, there is not yet a practical way to couple these phenomena with the atomistic description of chemistry. The starting point for including such information ismore »« less
Cited by 5
https://doi.org/10.1073/pnas.1800035115

Full Text Available
Concurrent atomistic-continuum modeling of crystalline materials

Journal Article Chen, Youping ; Shabanov, Sergei ; McDowell, David L. - Journal of Applied Physics

In the work reported here, we present a concurrent atomistic-continuum (CAC) method for modeling and simulation of crystalline materials. The CAC formulation extends the Irving-Kirkwood procedure for deriving transport equations and fluxes for homogenized molecular systems to that for polyatomic crystalline materials by employing a concurrent two-level description of the structure and dynamics of crystals. A multiscale representation of conservation laws is formulated, as a direct consequence of Newton's second law, in terms of instantaneous expressions of unit cell-averaged quantities using the mathematical theory of distributions. Finite element (FE) solutions to the conservation equations, as well as fluxes and temperaturemore »« less
Cited by 30
https://doi.org/10.1063/1.5099653

Full Text Available
Fluid simulations with atomistic resolution: a hybrid multiscale method with field-wise coupling

Journal Article Borg, Matthew K. ; Lockerby, Duncan A., E-mail: duncan.lockerby@warwick.ac.uk ; Reese, Jason M., E-mail: jason.reese@strath.ac.uk - Journal of Computational Physics

We present a new hybrid method for simulating dense fluid systems that exhibit multiscale behaviour, in particular, systems in which a Navier–Stokes model may not be valid in parts of the computational domain. We apply molecular dynamics as a local microscopic refinement for correcting the Navier–Stokes constitutive approximation in the bulk of the domain, as well as providing a direct measurement of velocity slip at bounding surfaces. Our hybrid approach differs from existing techniques, such as the heterogeneous multiscale method (HMM), in some fundamental respects. In our method, the individual molecular solvers, which provide information to the macro model, aremore »« less
https://doi.org/10.1016/J.JCP.2013.08.022
Mathematical and Numerical Analyses of Peridynamics for Multiscale Materials Modeling

Technical Report Du, Qiang

The rational design of materials, the development of accurate and efficient material simulation algorithms, and the determination of the response of materials to environments and loads occurring in practice all require an understanding of mechanics at disparate spatial and temporal scales. The project addresses mathematical and numerical analyses for material problems for which relevant scales range from those usually treated by molecular dynamics all the way up to those most often treated by classical elasticity. The prevalent approach towards developing a multiscale material model couples two or more well known models, e.g., molecular dynamics and classical elasticity, each of whichmore »« less
https://doi.org/10.2172/1163672

Full Text Available

Similar Records

Title: Filters for Improvement of Multiscale Data from Atomistic Simulations

Abstract

Citation Formats

Molecular dynamics with coupling to an external bath journal, October 1984

Stochastic Problems in Physics and Astronomy journal, January 1943

The Heterognous Multiscale Methods journal, January 2003

Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen journal, January 1905

Multiscale Local Polynomial Smoothing in a Lifted Pyramid for Non-Equispaced Data journal, February 2013

Equation-Free, Coarse-Grained Multiscale Computation: Enabling Mocroscopic Simulators to Perform System-Level Analysis journal, January 2003

Multiscale modeling of the dynamics of solids at finite temperature journal, July 2005

Concurrent coupling of atomistic and continuum models at finite temperature journal, January 2011

Fast Parallel Algorithms for Short-Range Molecular Dynamics journal, March 1995

Heterogeneous multiscale method for the modeling of complex fluids and micro-fluidics journal, March 2005

Multi-scale plasma simulation by the interlocking of magnetohydrodynamic model and particle-in-cell kinetic model journal, December 2007

On the Theory of the Brownian Motion journal, September 1930

The local microscale problem in the multiscale modeling of strongly heterogeneous media: Effects of boundary conditions and cell size journal, March 2007

Molecular dynamics with coupling to an external bath
journal, October 1984

Stochastic Problems in Physics and Astronomy
journal, January 1943

The Heterognous Multiscale Methods
journal, January 2003

Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen
journal, January 1905

Multiscale Local Polynomial Smoothing in a Lifted Pyramid for Non-Equispaced Data
journal, February 2013

Equation-Free, Coarse-Grained Multiscale Computation: Enabling Mocroscopic Simulators to Perform System-Level Analysis
journal, January 2003

Multiscale modeling of the dynamics of solids at finite temperature
journal, July 2005

Concurrent coupling of atomistic and continuum models at finite temperature
journal, January 2011

Fast Parallel Algorithms for Short-Range Molecular Dynamics
journal, March 1995

Heterogeneous multiscale method for the modeling of complex fluids and micro-fluidics
journal, March 2005

Multi-scale plasma simulation by the interlocking of magnetohydrodynamic model and particle-in-cell kinetic model
journal, December 2007

On the Theory of the Brownian Motion
journal, September 1930

The local microscale problem in the multiscale modeling of strongly heterogeneous media: Effects of boundary conditions and cell size
journal, March 2007