Weighted Gaussian quadratures for singular and near -singular integrands

✍ Scribed by Peter P. Silvester

• Publisher: John Wiley and Sons
• Year: 1989
• Tongue: English
• Weight: 636 KB
• Volume: 2
• Category: Article
• ISSN: 0894-3370
• DOI: 10.1002/jnm.1660020304

✦ Synopsis

Numerical quadratures encountered in solving integral equations and in finite element analysis often involve singular integrands, or integrands with very rapid local variation whose numerical stability resembles that of singularities. It is shown that specialized quadrature formulae of Gauss-Christoffel type can be generated for such integrands, using a recursive procedure based on the properties of the underlying orthogonal polynomials. Quadrature formulae of moderately high degree can be computed rapidly enough to allow them to be constructed as needed. An algorithm for generating quadrature formulae is given in detail. Singular or near-singular functions encountered in finite element analysis typically require three-point or four-point quadratures; such formulae are readily obtained, to seven-figure accuracy, in computing times short enough to regard the formulae as disposable and not worth preserving in tables.