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Comparison of Solvers

At this point, it would be beneficial to compare the serial performance of the four eigensolvers we have available. The table below gives the calculation time and number of times the TDDFT operator is applied to converge the lowest 20 eigenvalues of our H$_2$ test system, containing $\sim$10,000 plane-waves.

Solver Time (s) # of operations
ARPACK 171 756
EA19 195 848
Conjugate Gradients 291 1290
Block Davidson 114 520

This trend in the performance is as expected from Tretiak's paper [10]. The state-by-state CG solver is not without its benefits, however, as it has very modest memory usage.

Dominik Jochym 2010-07-20