Open AccessAn iterative technique for solving equations of statistical equilibrium
Author(s) -
Lucy L.B.
Publication year - 2001
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1046/j.1365-8711.2001.04506.x
Subject(s) - physics , relaxation (psychology) , iterative method , scaling , simple (philosophy) , mathematics , atom (system on chip) , statistical physics , linear equation , computational physics , algorithm , mathematical analysis , geometry , psychology , social psychology , philosophy , epistemology , computer science , embedded system
Superlevel partitioning is combined with a simple relaxation procedure to construct an iterative technique for solving equations of statistical equilibrium. In treating an N ‐level model atom, the technique avoids the N 3 scaling in computer time for direct solutions with standard linear equation routines and also does not fail at large N due to the accumulation of round‐off errors. As a consequence, the technique allows detailed model atoms with N≳10 3 , such as those required for iron peak elements, to be incorporated into diagnostic codes for analysing astronomical spectra. Tests are reported for a 394‐level Fe ii ion and a 1266‐level Ni i – iv atom.