Computing multigroup radiation integrals using polylogarithm-based methods

A new method is derived that is effective in calculating multigroup radiation integrals, i.e., the multigroup Planck spectrum and its derivatives with respect to temperature. This new, polylogarithm-based, method is actually a set of methods that can be made arbitrarily accurate. The accuracy and speed of the new methods are compared with three methods based on: a rational polynomial fit, interpolation in tabular data, and a simple numerical integration scheme. The polylogarithm-based methods are unsurpassed in accuracy, and their execution speed is competitive with the fastest methods tested. In addition, the multigroup integrals that are calculated using the new methods have some desirable properties: proper normalization, positivity, and continuity: that do not all exist in any one of the other methods. copyright 1987 Academic Press, Inc