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Domain Decomposition Methods for Multiscale Modeling

  • Xin BianEmail author
  • Matej Praprotnik
Living reference work entry

Abstract

Domain decomposition methods (DDM), which originate from the Schwarz alternating method to solve elliptic partial different equations, are largely extended and prove to have increasing influences on multiscale modeling of materials. We discuss some of the important extensions of the DDM in the fields of multiscale modeling for soft materials such as simple and complex fluids. To this end, we typically model the fluids in two or more levels of detail, which exploits the computational efficiency of the coarse model and physical accuracy of the fine description. For simple fluids, we take a continuum perspective to couple the molecular dynamics (MD) and Navier-Stokes equations by matching the state variables and/or fluxes across the hybrid interface. For complex fluids, we take a discrete perspective to encompass the complex structure of the molecules and couple the MD with coarse-grained MD by interpolating the forces between the two levels of descriptions.

Notes

Acknowledgements

Xin Bian acknowledges Prof. George Em Karniadakis, who led him to the research field of DDM for multiscale modeling. During his postdoctoral period, Xin benefited enormously from discussions with Prof. Karniadakis and his group. Xin Bian is also grateful for the discussions and full support from Prof. Nikolaus A. Adams, without whom the completeness of this work is impossible. Matej Praprotnik would like to thank Rafael Delgado-Buscalioni, Kurt Kremer, Luigi Delle Site, Jens H. Walther, and Petros Koumoutsakos for discussions and collaboration on this topic. He also acknowledges financial support from the Slovenian Research Agency (research core funding No. P1-0002 and the project J1-7435).

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Chair of Aerodynamics and Fluid Mechanics, Department of Mechanical EngineeringTechnical University of MunichGarching bei MünchenGermany
  2. 2.Laboratory for Molecular ModelingNational Institute of ChemistryLjubljanaSlovenia
  3. 3.Department of Physics, Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia

Section editors and affiliations

  • Ming Dao
    • 1
  • George E Karniadakis
    • 2
  1. 1.Department of Materials Science and EngineeringMassachusetts Institute of TechnologyCambridgeUnited States
  2. 2.Division of Applied MathematicsBrown UniversityProvidenceUSA

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