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A Nonlinear Multigrid Eigenproblem Solver for the Complex Helmholtz Equation

Please always quote using this URN: urn:nbn:de:0297-zib-3240
  • The paper is motivated by the need for a fast robust adaptive multigrid method to solve complex Helmholtz eigenvalue problems arising from the design of optical chips. A nonlinear multigrid method is developed, which can be regarded as an extension of a previous adaptive Rayleigh quotient minimization method for selfadjoint Helmholtz eigenproblems. Since the complex Helmholtz operator is just a compact nonselfadjoint perturbation of a selfadjoint operator, linear algebra techniques like Schur decomposition can be extended from the finite dimensional case. The efficiency of the derived adaptive nonlinear multigrid method is illustrated by computations for a technologically relevant integrated optics component containing Multi Quantum Well Layers.

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Metadaten
Author:Peter Deuflhard, Tilmann Friese, Frank Schmidt
Document Type:ZIB-Report
Date of first Publication:1997/11/17
Series (Serial Number):ZIB-Report (SC-97-55)
ZIB-Reportnumber:SC-97-55
Published in:Appeared under the title: " A Multigrid Method for the Complex Helmholtz Eigenvalue Problem" in: Choi-Hong Lai et al. (eds.) Proc. 11th Int. Conf. on Domain Decomposition Methods. Bergen: DDM-org Press 1999. Pp. 18-26
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