ALGORITHM 720 - AN ALGORITHM FOR ADAPTIVE CUBATURE OVER A COLLECTION OF 3-DIMENSIONAL SIMPLICES

An adaptive algorithm for computing an approximation to the integral o f each element in a vector of functions over a 3-dimensional region co vered by simplices is presented. The algorithm is encoded in FORTRAN 7 7. Locally, a cubature formula of degree 8 with 43 points is used to a pproximate an integral. The local error estimate is based on the same evaluation points. The error estimation procedure tries to decide whet her the approximation for each function has asymptotic behavior, and d ifferent actions are taken depending on that decision. The simplex wit h the largest error is subdivided into 8 simplices. The local procedur e is then applied to each new region. This procedure is repeated until convergence,