An Algorithm for Integration of Certain Singular Functions over a Triangle

Carino, R.L., Robinson, I., & DeDoncker, E. (1992). An Algorithm for Integration of Certain Singular Functions over a Triangle. In T.O. Espelid and A. Genz (Eds.), Numerical Integration: Recent Developments, Software, and Applications. Springer. 295-304. DOI:10.1007/978-94-011-2646-5_23.

We describe an automatic cubature routine which, in addition to being suitable for regular functions, is specifically designed for functions which are singular at a vertex or along an edge of the triangle of integration. The algorithm uses a non-adaptive subdivisional strategy based on the harmonic sequence of mesh ratios and incorporates the Levin utransformation for extrapolation. Numerical results are presented which indicate favorable comparison with other published algorithms when the integrand function has the prescribed properties.