An overview of PURGATORIO, a new implementation of the INFERNO 1 equation of state model, is presented. The new algorithm emphasizes a novel decimation scheme for automatically resolving the structure of the continuum density of states, circumventing limitations of the pseudo-R matrix algorithm previously utilized.

The unresolved transition array (UTA) model of atomic spectra describes the lines in a configuration-to-configuration transition array with a single feature that conserves the total strength as well as the energy first and second strength-weighted moments. A new model is proposed that uses a relatively small detailed line calculation together with the extant variance formula to generate a series of Gaussians to describe the transition array. This partially resolved transition array (PRTA) model conserves the known array properties, yields improved higher moments, and systematically accounts for initial level populations. Numerical examples show that the PRTA model provides excellent fidelity to line-by-line methods using only a small fraction of the computational effort for the full calculations.

The Hartree–Fock equations for atoms are solved with the p version of the finite element method, which differs from the traditional finite element method in using high order, hierarchic polynomials as basis functions. Recursion formulas are developed for the analytical evaluation of integrals, which are crucial in reducing the computation time and maintaining the accuracy of the solution. A hierarchic computational approach is used where the solution at a certain level is used to start the calculation at the next level. Results are presented for closed and open shell atoms taken from various columns of the periodic table that show excellent agreement with accurate numerical calculations.

Several equation of state models for hot, dense matter are compared with experimental data for the shock Hugoniots of beryllium, aluminum, iron, copper, and molybdenum up to extreme pressures. The best models are in good agreement with experiment and with one another, suggesting that our understanding of dense, partially ionized matter is good.  2001 Published by Elsevier Science B.V.