The goal of this research is to develop parallel system solvers for symmetric indefinite and non-symmetric systems such as those occurring in computational fluid dynamics, develop parallel techniques for solving time-dependent problems, and construct a rapid prototyping environment for developing and experimenting with algorithms in sparse matrix computations on shared and distributed memory multiprocessors. In particular, the are examined: (1) parallel solution schemes for solving Stokes-like linear arising in CFD and other augmented Lagrangian problems such interior point methods of linear programming, (2) incomplete Newton methods with Krylov or row projection solvers for the inner iteration, (3) solution of time-dependent problems using high-order methods in time, (4) defining and developing sparse matrix primitives analogous to the highly effective BLAS-3's for dense computations, and (5) implementing sparse factorization and solution schemes. The goal is portable efficiency and scalability, by parallelism on multiple levels. This in turn allows the work be used across a wide spectrum of existing and future architectures, instead of simply a particular machine.
