TWODQD an adaptive routine for two-dimensional integration

摘要

This is an adaptive subroutine that computes an approximation to the integral of a function f(x, y) over a two dimensional region made up of triangles. Lyness–Jespersen rules form the basis for a local quadrature module that is used to estimate the integral and the error over each triangle. The triangle with the largest error is subdivided and the local quadrature module is applied to each sub-triangle to obtain new estimates of the integral and the error. This process is repeated until either (1) an error tolerance is satisfied, (2) the number of triangles exceeds an input parameter MAXTRI, (3) the number of integrand evaluations exceeds an input parameter MEVALS, or (4) the subroutine senses that round-off error is beginning to contaminate the result.