A Parallel Direct/Iterative Solver Based on a Schur Complement Approach

In this paper, we present HIPS (hierarchical iterative parallel solver) a parallel sparse linear solver that combines effectively direct and iterative methods through a Schur complement approach. The corner stone of our method is to use a special decomposition and ordering of the matrix that allows to construct a reduced system and a robust preconditioner at low memory cost. The parallelization scheme we describe is original for this type of solver and provide a natural way to find a good trade-off between memory and convergence. Eventually, we give some results obtained by our solver on large referenced test cases.