Articles | Volume 13
https://doi.org/10.5194/ars-13-19-2015
https://doi.org/10.5194/ars-13-19-2015
03 Nov 2015
 | 03 Nov 2015

Efficient determination of the left-eigenvectors for the Method of Lines

S. F. Helfert

Cited articles

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Arnoldi, W.: The Principle of minimized iterations in the solution of the matrix eigenvalue problem, Quarterly Appl. Mathem., 9, 17–29, 1951.
Berenger, J.-P.: A perfectly matched layer for the absorption of electromagnetic waves, J. Computat. Phys., 114, 185–200, 1994.
Cucinotta, A., Pelosi, G., Selleri, S., Vincetti, L., and Zoboli, M.: Perfectly matched anisotropic layers for optical waveguide analysis through the finite element beam propagation method, Microw. Opt, Tech. Lett., 23, 67–69, 1999.
Gerdes, J.: Bidirectional eigenmode propagation analysis of optical waveguides based on method of lines, Electron. Lett., 30, 550–551, 1994.
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Short summary
To enforce the continuity of transverse electric and magnetic fields at boundaries, rectangular matrices containing the field distribution ('right eigenvectors') have to be inverted. This can be done with left eigenvectors. Here, it is shown how the latter ones can be determined with simple matrix products from previously determined right eigenvectors. For this purpose the relation between the transverse electric and magnetic fields known from Maxwell's equations is utilized.