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.
Author: | Peter Deuflhard, Tilmann Friese, Frank Schmidt |
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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 |