Towards a Parallel Out-of-core Multifrontal Solver: Preliminary Study.

(eng) The memory usage of sparse direct solvers can be the bottleneck to solve large-scale problems involving sparse systems of linear equations of the form A x = b. This report describes a prototype implementation of an out-of-core extension to a parallel multifrontal solver (MUMPS), where disk is used to store data that cannot fit in memory. We show that, by storing the factors to disk, larger problems can be solved on limited-memory machines with reasonable performance. We illustrate the impact of low-level IO mechanisms on the behaviour of our parallel out-of-core factorization. Then we use simulations to analyze the gains that can be expected when also storing the so called active memory on disk. We discuss both the minimum memory requirements and the minimum volume of I/O in a limited memory environment. Finally we summarize the main points that we identified to be critical when designing parallel sparse direct solvers in an out-of-core environment