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Printed October 2007
A Mathematical Framework for
Multiscale Science and Engineering:
the Variational Multiscale Method and
Interscale Transfer Operators
Pavel B. Bochevi S. Scott Collis Reese E. Jones2
Richard B. Lehoucql Michael L. Parks Guglielmo Scovazzi s
Stewart A. Silling4 Jeremy A. Templeton5 Gregory J. Wagners
iComputational Mathematics and Algorithms
3Computational Shock and Multiphysics
4Multiscale Dynamic Material Modeling
Sandia National Laboratories
P.O. Box 5800
Albuquerque, NM 87185-1320
2Mechanics of Materials
SThermal/Fluid Science and Engineering
Sandia National Laboratories
P.O. Box 969
Livermore, CA 94551
This report is a collection of documents written as part of the Laboratory Directed Research and
Development (LDRD) project A Mathematical Framework for Multiscale Science and Engineering:
The Variational Multiscale Method and Interscale Transfer Operators. We present developments
in two categories of multiscale mathematics and analysis. The first, continuum-to-continuum (CtC)
multiscale, includes problems that allow application of the same continuum model at all scales with
the primary barrier to simulation being computing resources. The second, atomistic-to-continuum
(AtC) multiscale, represents applications where detailed physics at the atomistic or molecular level
must be simulated to resolve the small scales, but the effect on and coupling to the continuum level
is frequently unclear.
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Wagner, Gregory John (Sandia National Laboratories, Livermore, CA); Collis, Samuel Scott; Templeton, Jeremy Alan (Sandia National Laboratories, Livermore, CA); Lehoucq, Richard B.; Parks, Michael L.; Jones, Reese E. (Sandia National Laboratories, Livermore, CA) et al. A mathematical framework for multiscale science and engineering : the variational multiscale method and interscale transfer operators., report, October 1, 2007; United States. (digital.library.unt.edu/ark:/67531/metadc899282/m1/3/: accessed January 18, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.