A New Approach to Parallel Sparse Cholesky Factorization on Distributed Memory Parallel Computers
نویسندگان
چکیده
Nowadays, programming distributed memory parallel computers (DMPCs) evokes the \no pain, no gain" idea. That is, for a given problem to be solved in parallel, the message passing programming model involves distributing the data and the computations among the processors. While this can be easily feasible for well structured problems, it can become fairly hard on unstructured ones, like sparse matrix computations. In this paper, we consider a relatively new approach to implementing the Cholesky factorization on a DMPC running a shared virtual memory (SVM). The abstraction of a shared memory on top of a distributed memory allows us to introduce a large-grain factorization algorithm, synchronized with events. Several scheduling strategies are compared, and experiments conducted so far show that this approach can provide the power of DMPCs and the ease of programming with shared variables. Une nouvelle approche pour la factorisation de Cholesky de matrices creuses sur les machines parall eles a m emoire distribu ee R esum e : L'exploitation eecace de machines parall eles a m emoire distri-bu ee n ecessite des eeorts importants de la part des utilisateurs. En eeet, la mise en uvre d'applications parall eles dans le mod ele de programmation par envoi de messages requiert une distribution des donn ees ainsi que des calculs sur les dii erents processeurs. Cette t^ ache peut se r ev eler complexe sur des pro-bl emes irr eguliers tels que les calcul sur matrices creuses. Dans cet article, nous consid erons une nouvelle approche de la factorisation de Cholesky de matrices creuses sur les machines a m emoire distribu ee dot ees d'une m emoire virtuelle partag ee. L'abstraction d'une m emoire partag ee au dessus d'une m emoire physique distribu ee nous permet d'introduire un algorithme de factorisation a grain large synchronis e par ev enements. Plusieurs strat egies d'ordonnancement sont compar ees. Les r esultats actuels montrent que nous pouvons aboutir a une utili-sation eecace des machines parall eles a m emoire distribu ee, tout en conservant l'avantage d'une programmation ais ee gr^ ace a la communication par variables partag ees.
منابع مشابه
A New Approach to Parallel Sparse Cholesky Factorization on Distributed Memory Parallel Computers Mounir Hahad, Jocelyne Erhel, Thierry Priol
Nowadays, programming distributed memory parallel computers (DMPCs) evokes the \no pain, no gain" idea. That is, for a given problem to be solved in parallel, the message passing programming model involves distributing the data and the computations among the processors. While this can be easily feasible for well structured problems, it can become fairly hard on unstructured ones, like sparse ma...
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