A complex Jacobi iterative method for the indefinite Helmholtz equation

An iterative procedure is described for the solution of the indefinite Helmholtz equation that is a two-step generalization of classic Jacobi iteration using complex iteration parameters. The method converges for well-posed problems at a rate dependent only upon the grid size, wavelength and the eff...

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Bibliographic Details
Published in:	Journal of computational physics Vol. 203; no. 1; pp. 358 - 370
Main Author:	Hadley, G. Ronald
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier Inc 10-02-2005 Elsevier
Subjects:	Computational techniques Exact sciences and technology Helmholtz Iterative methods Jacobi Mathematical methods in physics Physics 78A45 65N12 65F10 78-08 Jacobi Helmholtz Iterative methods 65N22 78A45 Helmholtz Helmholtz equations Waveguides Well posed problem Calculation Calculation methods
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Summary:	An iterative procedure is described for the solution of the indefinite Helmholtz equation that is a two-step generalization of classic Jacobi iteration using complex iteration parameters. The method converges for well-posed problems at a rate dependent only upon the grid size, wavelength and the effective absorption seen by the field. The use of a simple Jacobi preconditioner allows the solution of 3D problems of interest in waveguide optics in reasonable runtimes on a personal computer with memory usage that scales linearly with the number of grid points. Both the iterative method and the preconditioner are fully parallelizable.
Bibliography:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0021-9991 1090-2716
DOI:	10.1016/j.jcp.2004.09.015