expmARPACK
Krylov subspace exponential time domain solution of Maxwell’s equations in photonic crystal modeling. The exponential time integration, i.e., time integration which involves the matrix exponential, is an attractive tool for time domain modeling involving Maxwell’s equations. However, its application in practice often requires a substantial knowledge of numerical linear algebra algorithms, such as Krylov subspace methods. In this note we discuss exponential Krylov subspace time integration methods and provide a simple guide on how to use these methods in practice. While specifically aiming at nanophotonics applications, we intentionally keep the presentation as general as possible and consider full vector Maxwell’s equations with damping (i.e., with nonzero conductivity terms). Efficient techniques such as the Krylov shift-and-invert method and residual-based stopping criteria are discussed in detail. Numerical experiments are presented to demonstrate the efficiency of the discussed methods and their mesh independent convergence. Some of the algorithms described here are available as Octave/Matlab codes from url{http://www.math.utwente.nl/ botchevma/expm/}.
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References in zbMATH (referenced in 9 articles )
Showing results 1 to 9 of 9.
Sorted by year (- Botchev, M. A.: An accurate restarting for shift-and-invert Krylov subspaces computing matrix exponential actions of nonsymmetric matrices (2021)
- Botchev, Mike A.; Knizhnerman, Leonid; Tyrtyshnikov, Eugene E.: Residual and restarting in Krylov subspace evaluation of the (\varphi) function (2021)
- Hashimoto, Yuka; Nodera, Takashi: Inexact rational Krylov method for evolution equations (2021)
- Botchev, M. A.: A nested Schur complement solver with mesh-independent convergence for the time domain photonics modeling (2020)
- Botchev, M. A.; Knizhnerman, L. A.: ART: adaptive residual-time restarting for Krylov subspace matrix exponential evaluations (2020)
- Pieper, Konstantin; Sockwell, K. Chad; Gunzburger, Max: Exponential time differencing for mimetic multilayer Ocean models (2019)
- Botchev, M. A.; Hanse, A. M.; Uppu, R.: Exponential Krylov time integration for modeling multi-frequency optical response with monochromatic sources (2018)
- Grimm, Volker; Göckler, Tanja: Automatic smoothness detection of the resolvent Krylov subspace method for the approximation of (C_0)-semigroups (2017)
- Botchev, Mikhail A.: Krylov subspace exponential time domain solution of Maxwell’s equations in photonic crystal modeling (2016)