"Numerical methods in electronic structure calculations"

Yousef Saad,
University of Minnesota


The Density  Functional Theory  (DFT) formalism provides  an efficient
tool for solving various problems  in quantum mechanics.  In this talk
we examine the main linear algebra techniques used in this area, which
revolve around  the solution of  eigenvalue problems arising  from the
Schrodinger  equation.   We  will  also examine  open  problems  whose
effective  solution can lead  to major  breakthroughs. A  new emerging
area  in  materials science  is  the  Time-Dependent Density  Function
Theory  (TDDFT).   This  essentially  consists of  a  linear  response
approach,  and gives  rise to  extremely challenging  numerical linear
algebra problems.  We will give an overview of the techniques in TDDFT
and show how a frequency-space based method can be speeded up by using
a   combination    of   effective   algorithms    (e.g.,   block   CG,
preconditioning)  and code optimization  (e.g., load  balancing, cache
reuse,...)


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