Generalized Fermi-Dirac functions and derivatives: properties and evaluation. Z. Gong, L. Zejda, W. Dappen, J.M. Aparicio.

PROGRAM SUMMARY
Title of program: GFD_D3
Catalogue identifier: ADNX
Ref. in CPC: 136(2001)294
Distribution format: tar gzip file
Operating system: Solaris 5.6, Linux (Red Hat 5.2), IRIX 64
Number of lines in distributed program, including test data, etc: 1274
Keywords: Fermi-Dirac functions, Equation of state, Electron gas, Numeric method, Astrophysics plasma, Stellar evolution, General purpose.
Programming language used: Fortran
Computer: Sun E4500/E5500 , Compaq DEC Alpha , SGI Origin 2000 , HP Convex Exemplar , Cray SV1-1A/16-8 , AMD K6 PC , IBM SP2 .

Nature of problem:
Provide numerical method to evaluate generalized Fermi-Dirac functions and their derivatives with respect to eta and beta up to third order. The results are important for a highly accurate calculation of thermodynamic quantities of an electron gas with partial degeneracy and relatively high temperatures with very high order of accuracy.

Method of solution:
Following the scheme proposed by Aparicio [1], the generalized Fermi-Dirac integration is split into four optimized regions. Gauss-Legendre quadrature is used in the first three pieces, and Gauss-Laguerre quadrature in the last part when the e^-x term in the integrand dominates. Different break points are individually chosen for each eta derivative.

Typical running time:
Less than 1 ms for each data point on a DEC Alpha station with a 533 MHz CPU in double precision.