Harmonic functions satisfying a radiation boundary condition

Green H.S., Bracken A.J. and Bass L. (1991) Harmonic functions satisfying a radiation boundary condition. Computers and Mathematics with Applications, 22 2: 23-38. doi:10.1016/0898-1221(91)90039-7


Author Green H.S.
Bracken A.J.
Bass L.
Title Harmonic functions satisfying a radiation boundary condition
Journal name Computers and Mathematics with Applications   Check publisher's open access policy
ISSN 0898-1221
Publication date 1991-01-01
Sub-type Article (original research)
DOI 10.1016/0898-1221(91)90039-7
Volume 22
Issue 2
Start page 23
End page 38
Total pages 16
Subject 2604 Applied Mathematics
2605 Computational Mathematics
2611 Modelling and Simulation
Abstract A conformal method is developed for generating solutions of Laplace's equation which satisfy the radiation boundary condition at a smooth convoluted surface, such as the membrane of a cell which is steadily absorbing a diffusing substance. It is shown that almost all solutions which are analytic in the neighborhood of the surface have one or more branch points somewhere outside the surface, and are therefore not admissible in general; this feature presents a difficulty for both analytical and numerical methods of solution. In two-dimensional problems the difficulty can be overcome by the superposition of solutions in two sheets of the complex plane, and a complete set of admissible solutions is obtained in this way. The method is illustrated by its application to corrugated planes and cylinders, where exact solutions, free of singularities, are obtained in terms of elliptic functions. It is shown that methods of obtaining radiation surfaces from analytical solutions may encounter analogous difficulties. An extension of the conformal method to three-dimensional problems is given and illustrated.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collection: Scopus Import
 
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Created: Tue, 12 Jul 2016, 13:38:06 EST by System User