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Title: Helmholtz beam propagation by the method of Lanczos reduction

Abstract

The solution of the Helmholtz wave equation requires the application of an exponentiated square root operator to an initial field. This operation is greatly facilitated by the introduction of a representation in which the aforementioned operator is diagonal. The Lanczos method allows the diagonalization to be performed in a low dimensional space, e.g., of the order of 4-6, if one is interested in advancing the field over a limited propagation step of length {Delta}z. Although some boundary conditions may be ill-posed for the unapproximated Helmholtz equation, in the sense that certain plane wave components cannot propagate in the forward direction, the Lanczos method damps all of these components exponentially, thus guaranteeing the correctness of the solution. 8 refs.

Authors:
Publication Date:
Research Org.:
Lawrence Livermore National Lab., CA (United States)
Sponsoring Org.:
USDOE, Washington, DC (United States)
OSTI Identifier:
10107192
Report Number(s):
UCRL-JC-108128; CONF-9109230-10
ON: DE92003974
DOE Contract Number:  
W-7405-ENG-48
Resource Type:
Conference
Resource Relation:
Conference: OE/Fibers `91: Society of Photovoltaic Instrumentation Engineers (SPIE) meeting,Boston, MA (United States),3-6 Sep 1991; Other Information: PBD: 6 Aug 1991
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; WAVE EQUATIONS; NUMERICAL SOLUTION; WAVEGUIDES; WAVE PROPAGATION; MATHEMATICAL OPERATORS; DAMPING; ITERATIVE METHODS; REFRACTIVITY; MATRICES; 661000; 990200; GENERAL PHYSICS; MATHEMATICS AND COMPUTERS

Citation Formats

Fleck, Jr, J A. Helmholtz beam propagation by the method of Lanczos reduction. United States: N. p., 1991. Web.
Fleck, Jr, J A. Helmholtz beam propagation by the method of Lanczos reduction. United States.
Fleck, Jr, J A. 1991. "Helmholtz beam propagation by the method of Lanczos reduction". United States.
@article{osti_10107192,
title = {Helmholtz beam propagation by the method of Lanczos reduction},
author = {Fleck, Jr, J A},
abstractNote = {The solution of the Helmholtz wave equation requires the application of an exponentiated square root operator to an initial field. This operation is greatly facilitated by the introduction of a representation in which the aforementioned operator is diagonal. The Lanczos method allows the diagonalization to be performed in a low dimensional space, e.g., of the order of 4-6, if one is interested in advancing the field over a limited propagation step of length {Delta}z. Although some boundary conditions may be ill-posed for the unapproximated Helmholtz equation, in the sense that certain plane wave components cannot propagate in the forward direction, the Lanczos method damps all of these components exponentially, thus guaranteeing the correctness of the solution. 8 refs.},
doi = {},
url = {https://www.osti.gov/biblio/10107192}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Tue Aug 06 00:00:00 EDT 1991},
month = {Tue Aug 06 00:00:00 EDT 1991}
}

Conference:
Other availability
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