The current progress and maturation of parallel computing paradigms,
is enabling the solution of extremely
large linear and nonlinear equations. It has
become clear in recent years that direct solution methods for
such problems bear an unacceptable cost disadvantage
relative to iterative methods. This in turn is spurring new
research activities on iterative techniques that are reliable
and effective.
In this talk we present a number of techniques for solving distributed
sparse linear systems of equations. The general approach
used is a domain-decomposition type method in which a
processor is assigned a certain number of rows of the linear
system to be solved. Strategies that are discussed include
non-standard graph partitioners, and a forced load-balance
technique for the local iterations. We will also present an
Algebraic Recursive Multilevel Solver (ARMS) the goal of which
is to retain the 'general-purpose'
nature of ILU-type preconditioners while presenting
the scalability of multigrid-type methods. Finally, we will
show how these techniques are put to work to solve a challenging problem
in liquid-solid flows.