On the Out-Of-Core Factorization of Large Sparse Matrices

Emmanuel Agullo 1
1 GRAAL - Algorithms and Scheduling for Distributed Heterogeneous Platforms
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : Factorizing a sparse matrix is a robust way to solve large sparse systems of linear equations. However such an approach is known to be costly both in terms of computation and storage. When the storage required to process a matrix is greater than the amount of memory available on the platform, so-called out-of-core approaches have to be employed: disks extend the main memory to provide enough storage capacity. In this thesis, we investigate both theoretical and practical aspects of such out-of-core factorizations. The MUMPS and SuperLU software packages are used to illustrate our discussions on real-life matrices. First, we propose and study various out-of-core models that aim at limiting the overhead due to data transfers between memory and disks on uniprocessor machines. To do so, we revisit the algorithms to schedule the operations of the factorization and propose new memory management schemes to fit out-of-core constraints. Then we focus on a particular factorization method, the multifrontal method, that we push as far as possible in a parallel out-of-core context with a pragmatic approach. We show that out-of-core techniques allow to solve large sparse linear systems efficiently. When only the factors are stored on disks, a particular attention must be paid to temporary data, which remain in core memory. To achieve a high scalability of core memory usage, we rethink the whole schedule of the out-of-core parallel factorization.
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Emmanuel Agullo. On the Out-Of-Core Factorization of Large Sparse Matrices. Modeling and Simulation. Ecole normale supérieure de lyon - ENS LYON, 2008. English. ⟨tel-00563463⟩

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