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Tiled Algorithms for Efficient Task-Parallel H-Matrix Solvers

Abstract : In this paper, we describe and evaluate an extension of the Chameleon library to operate with hierarchical matrices (H-Matrices) and hierarchical arithmetic (H-Arithmetic), producing efficient solvers for linear systems arising in Boundary Element Methods (BEM). Our approach builds upon an open-source H-Matrices library from Airbus, named Hmat-oss, that collects sequential numerical kernels for both hierarchical and low-rank structures; the tiled algorithms and task-parallel decompositions available in Chameleon for the solution of linear systems; and the StarPU runtime system to orchestrate an efficient task-parallel (multi-threaded) execution on a multicore architecture. Using an application producing matrices with features close to real industrial applications, we present shared-memory results that demonstrate a fair level of performance, close to (and sometimes better than) the one offered by a pure H-Matrix approach, as proposed by Airbus Hmat proprietary (and non open-source) library. Hence, this combination Chameleon + Hmat-oss proposes the most efficient fully open-source software stack to solve dense compressible linear systems on shared memory architectures (distributed memory is under development).
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https://hal.inria.fr/hal-02489269
Contributor : Gregoire Pichon <>
Submitted on : Monday, February 24, 2020 - 12:43:52 PM
Last modification on : Monday, March 9, 2020 - 3:10:51 PM
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  • HAL Id : hal-02489269, version 1

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Rocío Carratalá-Sáez, Mathieu Faverge, Grégoire Pichon, Guillaume Sylvand, Enrique Quintana-Ortí. Tiled Algorithms for Efficient Task-Parallel H-Matrix Solvers. [Research Report] RR-9327, Inria. 2020. ⟨hal-02489269⟩

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