On the Memory Usage of a Parallel Multifrontal Solver

We are interested in the memory usage of sparse direct solvers. We particularl- y focus on the parallel multifrontal scheme. In the multifrontal approach two kinds of memory can be distinguished: a static one which corresponds to the result of the factorization process (ie, the factors), and a dynamic or active one, usually handled by a stack mechanism, which corresponds to the working space of the factorization process. For some problems the stack size may be as large as and even greater than the final factors. The size of the stack depends on the assembly tree and on how the computation is distributed. We present an extensive study of the impact of state-of-the-art sparse matrix reordering techniques on the assembly tree and on the memory occupation of the solver in both sequential and parallel executions. The main observation of this study is that the stack of parallel multifrontal solvers does not scale well if a dynamic scheduling strategy based only on the balance of the workload is used