On the I/O Volume in Out-of-Core Multifrontal Methods with a Flexible Allocation Scheme

Sparse direct solvers, and in particular multifrontal methods, are widely used in various simulation problems. Because of their large memory requirements, the use of out-of-core solvers is compulsory for large-scale problems, where disks are used to extend the core memory. This study is at the junction of two previous independent works: it extends the problem of the minimization of the Volume of I/O [4] in the multifrontal method to the more general flexible parent allocation algorithm [8], We explain how to compute the I/O volume with respect to this scheme and propose an efficient greedy heuristic which significantly reduces the I/O volume on real-life problems in this new context.