Adaptive Cubature over a Collection of Triangles Using the D-transformation

Carino, R.L., Robinson, I., & Doncker, E. d. (1994). Adaptive Cubature over a Collection of Triangles Using the D-transformation. Journal of Computational and Applied Mathematics . Elsevier Science B.V. . 50(1), 171-183.

We describe an automatic routine to integrate a function over a collection of triangles where on each triangle the function is well behaved, or has singularities of certain types at one or more vertices or edges. The underlying algorithm is globally adaptive and incorporates the d-transformation for extrapolation. Results from performance profile testing indicate that the routine is superior to other published routines when the singularities are located along edges of the triangles.