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Exploiting Generic Tiled Algorithms Toward Scalable H-Matrices Factorizations on Top of Runtime Systems

Abstract : Hierarchical matrices (H-matrices) have become important in applications where accuracy can be reduced to decrease to a logarithmic order both the execution time and memory consumption. It happens for instance when solving Boundary Element Methods (BEM) problems. However the natural hierarchical structure of the H-Matrices makes it more difficult to efficiently parallelize with modern programming paradigm such as task-based implementations. We discuss in this presentation how we can combine, Chameleon, a tiled dense linear algebra software relying on sequential task-based algorithms and runtime systems such as StarPU, and Hmat-oss, a library focused on providing a set of sequential algorithms for H-algebra operations. We will discuss the limitations in terms of H-matrices structure and memory compression that are imposed by the use of a tiled algorithm, and we will show the performance that can be brought by such a generic solution with respect to more advanced implementation fully exploiting the hierarchical data structure.
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https://hal.inria.fr/hal-03149953
Contributor : Mathieu Faverge Connect in order to contact the contributor
Submitted on : Tuesday, February 23, 2021 - 2:08:27 PM
Last modification on : Friday, January 21, 2022 - 3:11:48 AM

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  • HAL Id : hal-03149953, version 1

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Rocío Carratalá-Sáez, Mathieu Faverge, Grégoire Pichon, Enrique Salvador Quintana-Ortí, Guillaume Sylvand. Exploiting Generic Tiled Algorithms Toward Scalable H-Matrices Factorizations on Top of Runtime Systems. SIAM PP20 - SIAM Conference on Parallel Processing for Scientific Computing, Feb 2020, Seattle, United States. ⟨hal-03149953⟩

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