"Preconditioning techniques for highly indefinite systems"

Y. Saad, University of Minnesota 

Many practical  situations require  the solution of  highly indefinite
linear systems of equations. Among  these are systems which arise from
the Helmholtz equation or the very irregularly structured systems that
are obtained from circuit simulation for example.

This  talk  will discuss  preconditioning  techniques which  emphasize
robustness.   One  such  technique  is based  on  combining  two-sided
permutations with a multilevel approach.  The nonsymmetric permutation
technique  exploits a  greedy strategy  to  put large  entries of  the
matrix in the diagonal of  the upper leading submatrix.  This leads to
an  effective  incomplete  factorization  preconditioner  for  general
nonsymmetric,  irregularly  structured,  sparse linear  systems.   The
algorithm is implemented in a  multilevel fashion and borrows from the
Algebraic Recursive  Multilevel Solver (ARMS)  framework.  Preliminary
parallel implementations  using a Domain  Decomposition framework will
also  be  discussed.  Preliminary  illustrations  with  the  Helmholtz
equations and the Maxwell equation will be reported