We discuss issues related to domain decomposition and multilevel preconditioning techniques which are often employed for solving large sparse linear systems in parallel computations. We implement a parallel preconditioner for solving general sparse linear systems based on a two level block ILU factorization strategy. We give some new data structures and strategies to construct a local coefficient matrix and a local Schur complement matrix on each processor. The preconditioner constructed is fast and robust for solving certain large sparse matrices. Numerical experiments show that our domain based two level block ILU preconditioners are more robust and more efficient than some published ILU preconditioners based on Schur complement techniques for parallel sparse matrix solutions.
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