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Spectral approximation of quadratic operator polynomials arising in photonic band structure calculations
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (UMIT)
2014 (English)In: Numerische Mathematik, ISSN 0029-599X, E-ISSN 0945-3245, Vol. 126, no 3, 413-440 p.Article in journal (Refereed) Published
Abstract [en]

Galerkin spectral approximation theory for non-self-adjoint quadratic operator polynomials with periodic coefficients is considered. The main applications are complex band structure calculations in metallic photonic crystals, periodic waveguides, and metamaterials. We show that the spectrum of the considered operator polynomials consists of isolated eigenvalues of finite multiplicity with a nonzero imaginary part. The spectral problem is equivalent to a non-compact block operator matrix and norm convergence is shown for a block operator matrix having the same generalized eigenvectors as the original operator. Convergence rates of finite element discretizations are considered and numerical experiments with the p -version and the h -version of the finite element method confirm the theoretical convergence rates.

Place, publisher, year, edition, pages
Springer, 2014. Vol. 126, no 3, 413-440 p.
Keyword [en]
65M60, 65F15, 47A56, 35P30
National Category
Computational Mathematics
Research subject
URN: urn:nbn:se:umu:diva-80997DOI: 10.1007/s00211-013-0568-yISI: 000330976600002OAI: diva2:652217
Available from: 2013-09-30 Created: 2013-09-30 Last updated: 2015-05-11Bibliographically approved

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Engström, Christian
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Department of Mathematics and Mathematical Statistics
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