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 Kr...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 293; pp. 20 - 34
Main Author: Botchev, Mikhail A.
Format: Journal Article
Language:English
Published: Elsevier B.V 01.02.2016
Subjects:
Algorithms
Finite difference time domain (FDTD) method
Krylov subspace methods
Mathematical models
Matlab
Matrix exponential
Maxwell's equations
Nanostructure
Photonic crystals
Subspaces
Time domain
Time integration
65L05
65F60
Krylov subspace methods
65F30
Maxwell’s equations
Photonic crystals
Finite difference time domain (FDTD) method
65N22
35Q61
Matrix exponential
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Summary: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 www.math.utwente.nl/~botchevma/expm/.
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ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2015.04.022