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Source field superposition analysis of two‐dimensional potential problems
Author(s) -
Fenner R. T.
Publication year - 1991
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620320510
Subject(s) - superposition principle , domain (mathematical analysis) , laplace's equation , mathematics , laplace transform , mathematical analysis , fictitious domain method , boundary (topology) , field (mathematics) , finite element method , perimeter , boundary value problem , geometry , boundary element method , physics , pure mathematics , thermodynamics
The source field superposition method for problems governed by Laplace's equation involves representing the potential field in a given solution domain as a superposition of fields generated by a number of sources. These sources are located outside the solution domain, and in the case of two‐dimensional singly‐connected finite domain problems can be uniformly distributed around the perimeter of a circle enclosing the physical domain. Some test problems are used to make detailed comparisons with the boundary element method. The results show that remarkable accuracy can be achieved, often to five or six significant figures, with very little computational effort relative to other numerical methods. In contrast to the boundary element method, however, geometric corners require no special treatment, and high aspect ratio of the solution domain is not a significant limitation.