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Optimal transformations of the integration variables in computation of singular integrals in BEM
Author(s) -
Sladek V.,
Sladek J.,
Tanaka M.
Publication year - 2000
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/(sici)1097-0207(20000310)47:7<1263::aid-nme811>3.0.co;2-i
Subject(s) - computation , mathematics , order of integration (calculus) , singular integral , calculus (dental) , mathematical optimization , computer science , algebra over a field , mathematical analysis , integral equation , algorithm , pure mathematics , medicine , dentistry
The paper deals with numerical integrations of singular integrals in BEMs. It is shown that from the point of view of numerical integrations, the only serious problem which can arise is due to weakly singular and nearly singular integrals. We pay attention to the study of numerical integrations of nearly singular integrals by using transformations of the integration variables. Theoretical considerations and numerical experiments are performed for the integrals occurring in 2‐D BEM formulations. The use of optimal transformation is confronted with the optimization of a polynomial transformation. Copyright © 2000 John Wiley & Sons, Ltd.