Conclusions

The results presented in this paper show that using state of the art algorithms and software for large sparse linear systems, it is possible to achieve very good scaling on Linux clusters. In particular, on 256 processors of a Pentium 3 Linux cluster at NCSA, we were able to solve a linear system with 64 million unknowns in under 23 seconds. Our scaled speedup results show that the $400^3$ problem on 256 processors took only 1.3 times longer than the $64^3$ problem on one processor in the symmetric case, and 1.25 times longer for the non-symmetric case.

In the future we will extend the current studies to include Itanium 2 based Linux clusters. We plan to use matrices from an application code for supernova simulations. We are exploring the possibility of using the hypre solvers as preconditioners through PETSc. This will include the algebraic multigrid and sparse approximate inverse preconditioners in Hypre.