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23 - Time-Dependent Operators

from Part V - Applications, Developments, and Open Problems

Published online by Cambridge University Press:  10 October 2019

Houman Owhadi
Affiliation:
California Institute of Technology
Clint Scovel
Affiliation:
California Institute of Technology
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Summary

This chapter reviews the application of gamblets to the opening of the complexity bottleneck of implicit schemes for hyperbolic and parabolic ODEs/PDEs with rough coefficients. In this setting, the spatial component of the PDE is an elliptic operator on a Sobolev space, and since the natural truncationof the gamblet decomposition of the operator is rank-revealing, in that it is adapted to the eigensubspaces of the operator, these gamblet decompositionscan be naturally applied to the simulation of time-dependent operators. These gamblets are not only adapted to the coefficients of the underlying PDE but also to the numerical scheme used forits time discretization. For higher order PDEs these gamblets may be complex-valued.

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Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization
From a Game Theoretic Approach to Numerical Approximation and Algorithm Design
, pp. 410 - 420
Publisher: Cambridge University Press
Print publication year: 2019

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  • Time-Dependent Operators
  • Houman Owhadi, California Institute of Technology, Clint Scovel, California Institute of Technology
  • Book: Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization
  • Online publication: 10 October 2019
  • Chapter DOI: https://doi.org/10.1017/9781108594967.030
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  • Time-Dependent Operators
  • Houman Owhadi, California Institute of Technology, Clint Scovel, California Institute of Technology
  • Book: Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization
  • Online publication: 10 October 2019
  • Chapter DOI: https://doi.org/10.1017/9781108594967.030
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Time-Dependent Operators
  • Houman Owhadi, California Institute of Technology, Clint Scovel, California Institute of Technology
  • Book: Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization
  • Online publication: 10 October 2019
  • Chapter DOI: https://doi.org/10.1017/9781108594967.030
Available formats
×