Inverse Iteration for Nonlinear Eigenvalue Problems in Electromagnetic Scattering

A Spence; C G Poulton; A B Movchan

doi:10.1007/1-4020-2604-8_54

Inverse Iteration for Nonlinear Eigenvalue Problems in Electromagnetic Scattering

A Spence
, C G Poulton
, A B Movchan (Editor)

Department of Mathematical Sciences

Research output: Contribution to conference › Paper

Abstract

We present an extension of the well-known method of “inverse iteration” for the standard eigenvalue problem to the nonlinear problem of finding dispersion relations for electromagnetic waves moving through a doublyperiodic structure. Numerical results are presented to illustrate the performance of the technique. A further improvement is described that allows an e cient “path following” algorithm where a curve of solutions is computed in (ω, Kbloch) space. We present dispersion relations calculated via this new method and compare the efficiency of this algorithm with that of more traditional methods.

Original language	English
DOIs	https://doi.org/10.1007/1-4020-2604-8_54
Publication status	Published - Dec 2003
Event	IUTAM Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics - Dordrecht Duration: 1 Dec 2003 → …

Conference

Conference	IUTAM Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics
City	Dordrecht
Period	1/12/03 → …

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10.1007/1-4020-2604-8_54

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title = "Inverse Iteration for Nonlinear Eigenvalue Problems in Electromagnetic Scattering",

abstract = "We present an extension of the well-known method of “inverse iteration” for the standard eigenvalue problem to the nonlinear problem of finding dispersion relations for electromagnetic waves moving through a doublyperiodic structure. Numerical results are presented to illustrate the performance of the technique. A further improvement is described that allows an e cient “path following” algorithm where a curve of solutions is computed in (ω, Kbloch) space. We present dispersion relations calculated via this new method and compare the efficiency of this algorithm with that of more traditional methods. ",

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AU - Spence, A

AU - Poulton, C G

A2 - Movchan, A B

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N2 - We present an extension of the well-known method of “inverse iteration” for the standard eigenvalue problem to the nonlinear problem of finding dispersion relations for electromagnetic waves moving through a doublyperiodic structure. Numerical results are presented to illustrate the performance of the technique. A further improvement is described that allows an e cient “path following” algorithm where a curve of solutions is computed in (ω, Kbloch) space. We present dispersion relations calculated via this new method and compare the efficiency of this algorithm with that of more traditional methods.

AB - We present an extension of the well-known method of “inverse iteration” for the standard eigenvalue problem to the nonlinear problem of finding dispersion relations for electromagnetic waves moving through a doublyperiodic structure. Numerical results are presented to illustrate the performance of the technique. A further improvement is described that allows an e cient “path following” algorithm where a curve of solutions is computed in (ω, Kbloch) space. We present dispersion relations calculated via this new method and compare the efficiency of this algorithm with that of more traditional methods.

U2 - 10.1007/1-4020-2604-8_54

DO - 10.1007/1-4020-2604-8_54

M3 - Paper

T2 - IUTAM Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics

Y2 - 1 December 2003

ER -

Inverse Iteration for Nonlinear Eigenvalue Problems in Electromagnetic Scattering

Abstract

Conference

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