Taylor expansions for singular kernels in the boundary element method

✍ Scribed by M. H. Aliabadi; W. S. Hall; T. G. Phemister

• Publisher: John Wiley and Sons
• Year: 1985
• Tongue: English
• Weight: 752 KB
• Volume: 21
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620211208

✦ Synopsis

The problem treated is the integration of singular functions which arise in three-dimensional isoparametric formulations of boundary integral equations. A Taylor expansion in the local parametric co-ordinates is developed for the singular integrand, so allowing singular terms to be integrated in closed form, even for curved surface elements. The remainder integral obtained by subtracting out the worst singularities is integrated by repeated Gaussian quadrature.

Two groups of tests are presented. First, the accuracy of the integrations has been checked for plane parallelograms (for which exact solutions have been developed) and for curved elements on a sphere. Secondly, results from complete boundary element calculations based on point collocation have been compared with known analytical solutions to two problems; zonal surface harmonics on a sphere and the capacitance of an ellipsoid. The agreement obtained with few degrees-of-freedom suggests that errors which have previously been attributed to point collocation might have arisen in the numerical integration.