Helmholtz beam propagation by the method of Lanczos reduction
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.
- Research Organization:
- Lawrence Livermore National Lab., CA (United States)
- Sponsoring Organization:
- USDOE; USDOE, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 5889523
- Report Number(s):
- UCRL-JC-108128; CONF-9109230-10; ON: DE92003974
- Resource Relation:
- Conference: SPIE meeting, Boston, MA (United States), 3-6 Sep 1991
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
WAVE EQUATIONS
NUMERICAL SOLUTION
WAVEGUIDES
WAVE PROPAGATION
DAMPING
ITERATIVE METHODS
MATHEMATICAL OPERATORS
MATRICES
REFRACTIVITY
DIFFERENTIAL EQUATIONS
EQUATIONS
OPTICAL PROPERTIES
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICAL PROPERTIES
661000* - General Physics- (1992-)
990200 - Mathematics & Computers