Premium
A self‐adaptive co‐ordinate transformation for efficient numerical evaluation of general boundary element integrals
Author(s) -
Telles J. C. F.
Publication year - 1987
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.1620240509
Subject(s) - gaussian quadrature , singularity , quadrature (astronomy) , boundary element method , singular boundary method , mathematics , adaptive quadrature , transformation (genetics) , boundary value problem , rotational symmetry , boundary (topology) , mathematical analysis , computer science , finite element method , geometry , nyström method , control theory (sociology) , engineering , structural engineering , control (management) , artificial intelligence , electrical engineering , biochemistry , chemistry , gene
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.