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A complex variable boundary element method: Development
Author(s) -
Hromadka T. V.,
Guymon G. L.
Publication year - 1984
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.1620200104
Subject(s) - mathematics , boundary element method , mathematical analysis , cauchy's integral formula , integral equation , line integral , variable (mathematics) , cauchy distribution , quadrature (astronomy) , laplace's equation , boundary value problem , boundary (topology) , laplace transform , singular boundary method , cauchy problem , finite element method , initial value problem , physics , optics , thermodynamics
A generalized boundary integral equation method for the solution of the Laplace equation is developed based on the Cauchy integral theorem for analytical complex variable functions. Although the approach is complicated by the utilization of complex variable theory, the resulting model involves direct integration along straight‐line boundary segments (elements) rather than using quadrature formulae that are required in current real variable boundary element formulations. Previously published boundary integral equation methods based on the Cauchy integral theorem are shown to be a subset of the generalized model theory developed in this paper.