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Numerical Methods for High-Dimensional Kinetic Equations

  • Heyrim Cho
  • Daniele Venturi
  • George Em Karniadakis
Chapter
Part of the SEMA SIMAI Springer Series book series (SEMA SIMAI, volume 14)

Abstract

High-dimensionality is one of the major challenges in kinetic modeling and simulation of realistic physical systems. The most appropriate numerical scheme needs to balance accuracy and computational complexity, and it also needs to address issues such as multiple scales, lack of regularity, and long-term integration. In this chapter, we review state-of-the-art numerical techniques for high-dimensional kinetic equations, including low-rank tensor approximation, sparse grid collocation, and ANOVA decomposition.

Notes

Acknowledgements

We gratefully acknowledge support from DARPA grant N66001-15-2-4055, ARO grant W991NF-14-1-0425, and AFOSR grant FA9550-16-1-0092.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • Heyrim Cho
    • 1
  • Daniele Venturi
    • 2
  • George Em Karniadakis
    • 3
  1. 1.University of MarylandCollege ParkUSA
  2. 2.University of CaliforniaSanta CruzUSA
  3. 3.Brown UniversityProvidenceUSA

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