Calculating large systems with plane waves: Is it a N3 or N2 scaling problem?

N. Troullier, James R. Chelikowsky, Y. Saad

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


It is commonly asserted that in performing large scale plane wave calculations with N plane waves, and indirect diagonalization, the N3 orthogonalization step quickly becomes the limiting factor. Using a pre-condition Lanczos subspace diagonalization algorithm we find that while the orthogonalization will eventually become the dominate cpu restriction, this is not the limiting factor. Typically the limitation resides not with the cpu, but with the memory limitations of the current computer systems. The memory needed to store the wave functions scales as Natom2. This scaling "limitation" is reached before the cpu time becomes the dominate factor. We illustrate this scaling with a Na vacancy calculation using up to 2000 atoms.

Original languageEnglish (US)
Pages (from-to)225-230
Number of pages6
JournalSolid State Communications
Issue number3
StatePublished - Jan 1995


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