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A self‐adaptive co‐ordinate transformation for efficient numerical evaluation of general boundary element integrals

A self‐adaptive co‐ordinate transformation for efficient numerical evaluation of general boundary... Almost all general purpose boundary element computer packages include a curved geometry modelling capability. Thus, numerical quadrature schemes play an important role in the efficiency of programming the technique. The present work discusses this problem in detail and introduces efficient means of computing singular or nearly singular integrals currently found in two‐dimensional, axisymmetric and three‐dimensional applications. Emphasis is given to a new third degree polynomial transformation which was found greatly to improve the accuracy of Gaussian quadrature scheme's within the near‐singularity range. The procedure can easily be implemented into existing BE codes and presents the important feature of being self‐adaptive, i.e. it produces a variable lumping of the Gauss stations toward the singularity, depending on the minimum distance from the source point to the element. The self‐adaptiveness of the scheme also makes it inactive when not useful (large source distances) which makes it very safe for general usage. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal for Numerical Methods in Engineering Wiley

A self‐adaptive co‐ordinate transformation for efficient numerical evaluation of general boundary element integrals

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References (12)

Publisher
Wiley
Copyright
Copyright © 1987 Wiley Subscription Services, Inc., A Wiley Company
ISSN
0029-5981
eISSN
1097-0207
DOI
10.1002/nme.1620240509
Publisher site
See Article on Publisher Site

Abstract

Almost all general purpose boundary element computer packages include a curved geometry modelling capability. Thus, numerical quadrature schemes play an important role in the efficiency of programming the technique. The present work discusses this problem in detail and introduces efficient means of computing singular or nearly singular integrals currently found in two‐dimensional, axisymmetric and three‐dimensional applications. Emphasis is given to a new third degree polynomial transformation which was found greatly to improve the accuracy of Gaussian quadrature scheme's within the near‐singularity range. The procedure can easily be implemented into existing BE codes and presents the important feature of being self‐adaptive, i.e. it produces a variable lumping of the Gauss stations toward the singularity, depending on the minimum distance from the source point to the element. The self‐adaptiveness of the scheme also makes it inactive when not useful (large source distances) which makes it very safe for general usage.

Journal

International Journal for Numerical Methods in EngineeringWiley

Published: May 1, 1987

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