title: Multilevel preconditioning techniques with applications.

abstract: In  this talk  we will give  an overview of  some multilevel
ILU-type techniques for solving linear systems and will also present a
few  related  applications.  Among  the multilevel  methods,  we  will
present the Albraic  Recursive Multilevel Solver (ARMS) and  see how a
class   of    `coarsening'   schemes   can   be    adapted   to   this
framework. ILU-type  preconditioners have difficulties  for some types
of  indefinite problems.  We  will show  how they  can be  adapted for
problems  arising from Helmholtz  equations. We  will then  present an
application in dynamic  mean field theory (DMFT) where  the problem is
to compute  the diagonal  of the inverse  of a matrix.   Finally, some
recent work  on developing sparse  iterative solvers for GPUs  will be
briefly discussed.