Some Memory Issues in the Multifrontal Method. |
|
|
|
|
|
|
| Multifrontal methods are sparse direct algorithms to solve large irregular systems of linear equations. They are based on an assembly tree (which itself depends on the reordering of the unknowns applied) and are robust and efficient compared to iterative methods. However they have large memory requirements. We are concerned with the memory usage of sparse direct solvers. We particularly focus on the influence of state-of-the-art sparse matrix reordering techniques on the active memory usage of a multifrontal solver, {\mumps}, and present variants of the algorithm by Liu to modify the assembly tree traversal for an optimal memory usage in the sequential case. After that, we study the scalability of the memory for parallel executions and show that the memory scalability is limited if a dynamic scheduling strategy mainly based on the balance of the workload is used. We then discuss some current related work to improve both the parallel and sequential memory usage. One approach consists in designing new scheduling strategies based on memory informations where we particularly focus on dynamic aspects such as worker selection and task management. Finally, in the case where paging occurs (limited physical memory), we show the behaviour of the memory paging in {\mumps} and present new paging strategies adapted to {\mumps}. Those are based on a low-level system module from LaRIA. |
|
|
algweb@cerfacs.fr Last Update: Apr 17, 2003 |