Inverse iteration for nonlinear eigenvalue problems in electromagnetic scattering

Publication Type:
Conference Proceeding
Solid Mechanics and its Applications vol 113: IUTAM Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics, 2003, 113 pp. 585 - 594
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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 (?, 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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