  Iterative multiscale methods for electronic structure calculations offer
several advantages for large-scale problems. Here we examine a nonlinear full
approximation scheme (FAS) multigrid method for solving fixed potential and
self-consistent eigenvalue problems. In principle, the expensive
orthogonalization and Ritz projection operations can be moved to coarse levels,
thus substantially reducing the overall computational expense. Results of the
nonlinear multiscale approach are presented for simple fixed potential problems
and for self-consistent pseudopotential calculations on large molecules. It is
shown that, while excellent efficiencies can be obtained for problems with
small numbers of states or well-defined eigenvalue cluster structure, the
algorithm in its original form stalls for large-molecule problems with tens of
occupied levels. Work is in progress to attempt to alleviate those
difficulties.
