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

✍ Scribed by J. C. F. Telles

• Publisher: John Wiley and Sons
• Year: 1987
• Tongue: English
• Weight: 820 KB
• Volume: 24
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620240509

✦ Synopsis

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 programniing the technique. The present work discusses this problcm in detail and introduces efficient means of computing singular or ncarly singular integrals currently found in two-dimcnsional, axisymmctric and three-dimensional applications. Emphasis i s given to a new third degree polynomial transformation which was found greatly to improve the accuracy of Gaussian quadrature schemes within the near-singularity range. The procedure can easily be implemented into existing BE codcs 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 i t very safe for general usage.