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A direct numerical method for the solution of field problems
Author(s) -
Tottenham H.
Publication year - 1970
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.1620020111
Subject(s) - mathematics , algebraic equation , set (abstract data type) , numerical analysis , solution set , field (mathematics) , algebraic number , numerical integration , mathematical analysis , computer science , pure mathematics , nonlinear system , physics , quantum mechanics , programming language
A numerical method for the analysis of field problems is described. The algorithm is based upon the generalized Betti‐Maxwell theorem. Using a set of known solutions to problems with similar boundary conditions produces a set of ‘integral’ equations for the required solution. Using any convenient numerical integration formula reduces the problem to the solution of a set of simultaneous algebraic equations. The accuracy of the solution depends upon the accuracy of the integration formula as applied to the problem under consideration and is independent of the known auxiliary solutions. The method is described in detail as applied to harmonic problems.