In engineering, mathematics, physics, meteorology and computer science, multiscale modeling (Steinhauser 2008) or multiscale mathematics is the field of solving problems which have important features at multiple scales of time and/or space. Important problems include scale linking (Baeurle 2009, de Pablo 2011, Knizhnik 2002, Adamson 2007). Horstemeyer 2009 presented historical review of the different disciplines (solid mechanics, numerical methods, mathematics, physics, and materials science) for solid materials related to multiscale materials modeling. Martin Karplus, Michael Levitt, Arieh Warshel were awarded a Nobel Prize in Chemistry for the development of a multiscale model method using both classical and quantum mechanical theory which were used to model large complex chemical systems and reactions.
In physics and chemistry, multiscale modeling is aimed to calculation of material properties or system behavior on one level using information or models from different levels. On each level particular approaches are used for description of a system. The following levels are usually distinguished: level of quantum mechanical models (information about electrons is included), level of molecular dynamics models (information about individual atoms is included), mesoscale or nano level (information about groups of atoms and molecules is included), level of continuum models, level of device models. Each level addresses a phenomenon over a specific window of length and time. Multiscale modeling is particularly important in integrated computational materials engineering since it allows to predict material properties or system behavior based on knowledge of the atomistic structure and properties of elementary processes.
In operations research, multiscale modeling addresses challenges for decision makers which come from multiscale phenomena across organizational, temporal and spatial scales. This theory fuses decision theory and multiscale mathematics and is referred to as multiscale decision-making. Multiscale decision-making draws upon the analogies between physical systems and complex man-made systems.
In meteorology, multiscale modeling is the modeling of interaction between weather systems of different spatial and temporal scales that produces the weather that we experience. The most challenging task is to model the way through which the weather systems interact as models cannot see beyond the limit of the model grid size. In other words, to run an atmospheric model that is having a grid size (very small ~ ) which can see each possible cloud structure for the whole globe is computationally very expensive. On the other hand, a computationally feasible 500 mGlobal climate model (GCM, with grid size ~ , cannot see the smaller cloud systems. So we need to come to a balance point so that the model becomes computationally feasible and at the same time we do not lose much information, with the help of making some rational guesses, a process called Parametrization. 100 km
Besides the many specific applications, one area of research is methods for the accurate and efficient solution of multiscale modeling problems. The primary areas of mathematical and algorithmic development include:
- Analytical modeling
- Center manifold and slow manifold theory
- Continuum modeling
- Discrete modeling
- Network-based modeling
- Statistical modeling
- Computational mechanics
- Equation-free modeling
- Integrated computational materials engineering
- Multiresolution analysis
- Space mapping
- Steinhauser, M. O. (2008). Multiscale Modeling of Fluids and Solids - Theory and Applications. ISBN 978-3540751168.
- Baeurle, S. A. (2008). "Multiscale modeling of polymer materials using field-theoretic methodologies: A survey about recent developments". Journal of Mathematical Chemistry 46 (2): 363. doi:10.1007/s10910-008-9467-3.
- De Pablo, Juan J. (2011). "Coarse-Grained Simulations of Macromolecules: From DNA to Nanocomposites". Annual Review of Physical Chemistry 62: 555–74. doi:10.1146/annurev-physchem-032210-103458. PMID 21219152.
- Knizhnik, A.A.; Bagaturyants, A.A.; Belov, I.V.; Potapkin, B.V.; Korkin, A.A. (2002). "An integrated kinetic Monte Carlo molecular dynamics approach for film growth modeling and simulation: ZrO2 deposition on Si surface". Computational Materials Science 24: 128. doi:10.1016/S0927-0256(02)00174-X.
- Adamson, S.; Astapenko, V.; Chernysheva, I.; Chorkov, V.; Deminsky, M.; Demchenko, G.; Demura, A.; Demyanov, A.; et al. (2007). "Multiscale multiphysics nonempirical approach to calculation of light emission properties of chemically active nonequilibrium plasma: Application to Ar GaI3 system". Journal of Physics D: Applied Physics 40 (13): 3857. Bibcode:2007JPhD...40.3857A. doi:10.1088/0022-3727/40/13/S06.
- Horstemeyer, M. F. (2009). "Multiscale Modeling: A Review". In Leszczyński, Jerzy; Shukla, Manoj K. Practical Aspects of Computational Chemistry: Methods, Concepts and Applications. pp. 87–135. ISBN 978-90-481-2687-3.
- Rawson, Shelley D.; Margetts, Lee; Wong, Jason K. F.; Cartmell, Sarah H. (2014-05-20). "Sutured tendon repair; a multi-scale finite element model". Biomechanics and Modeling in Mechanobiology 14 (1): 123–133. doi:10.1007/s10237-014-0593-5. ISSN 1617-7959. PMC 4282689. PMID 24840732.
- Shterenlikht, A.; Margetts, L. (2015-05-08). "Three-dimensional cellular automata modelling of cleavage propagation across crystal boundaries in polycrystalline microstructures". Proc. R. Soc. A 471 (2177): 20150039. doi:10.1098/rspa.2015.0039. ISSN 1364-5021.
- Multiscale Modeling of Materials (MMM-Tools) Project at Dr. Martin Steinhauser's group at the Fraunhofer-Institute for High-Speed Dynamics, Ernst-Mach-Institut, EMI, at Freiburg, Germany. Since 2013, M.O. Steinhauser is associated at the University of Basel, Switzerland.
- Multiscale Modeling Group: Institute of Physical & Theoretical Chemistry, University of Regensburg, Regensburg, Germany
- Hosseini, SA; Shah, N (2009). "Multiscale modelling of hydrothermal biomass pretreatment for chip size optimization". Bioresource technology 100 (9): 2621–8. doi:10.1016/j.biortech.2008.11.030. PMID 19136256.
- Multiscale Materials Modeling: Fourth International Conference, Tallahassee, FL, USA
- Multiscale Modeling Tools for Protein Structure Prediction and Protein Folding Simulations, Warsaw, Poland
- Tao, Wei-Kuo; Chern, Jiun-Dar; Atlas, Robert; Randall, David; Khairoutdinov, Marat; Li, Jui-Lin; Waliser, Duane E.; Hou, Arthur; et al. (2009). "A Multiscale Modeling System: Developments, Applications, and Critical Issues". Bulletin of the American Meteorological Society 90 (4): 515. Bibcode:2009BAMS...90..515T. doi:10.1175/2008BAMS2542.1.
- Multiscale modeling for Materials Engineering: Set-up of quantitative micromechanical models
- Multiscale Material Modelling on High Performance Computer Architectures, MMM@HPC project
- Modeling Materials: Continuum, Atomistic and Multiscale Techniques (E. B. Tadmor and R. E. Miller, Cambridge University Press, 2011)
- Kremers, Enrique; De Durana, Jose Maria Gonzalez; Barambones, Oscar; Viejo, Pablo; Lewal, Norbert (2011). "Agent-Based Simulation of Wind Farm Generation at Multiple Time Scales". In Suvire, Gastón Orlando. Wind Farm: Impact in Power System and Alternatives to Improve the Integration. pp. 313–30. doi:10.5772/16531. ISBN 978-953-307-467-2.
- An Introduction to Computational Multiphysics II: Theoretical Background Part I Harvard University video series
- SIAM Journal of Multiscale Modeling and Simulation
- International Journal for Multiscale Computational Engineering
- Department of Energy Summer School on Multiscale Mathematics and High Performance Computing