This presentation will discuss ongoing work related to the solution of a
set of eigenvalue problems in electronic structure calculations. The
presentation will first discuss unconstrained minimization schemes for
the solution of such problems. These schemes employ a preconditioned
conjugate gradient approach that avoids an explicit reorthogonalization
of the trial eigenvectors, in contrast to typical iterative eigenvalue
solvers. The resulting reduction in communication becomes an attractive
feature when solving large problems on massively parallel computers. We
show results for a set of benchmark systems with an implementation of
the unconstrained minimization in first-principles materials and
chemistry codes that perform electronic structure calculations based on
a density functional theory (DFT) approximation to the solution of the
many-body Schrödinger equation. The remaining part of the presentation
will discuss the use of substructuring for the solution of eigenvalue
problems in electronic structure calculations. Substructuring has been
used in elasticity problems (finite element analysis), and we see an
opportunity to examine its feasibility when the matrices related to
electronic systems can be potentially partitioned.