Tiled Algorithms For Efficient Task-Parallel H-Matrix Solvers
2020 IEEE 34TH INTERNATIONAL PARALLEL AND DISTRIBUTED PROCESSING SYMPOSIUM WORKSHOPS (IPDPSW 2020)(2020)
摘要
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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关键词
Hierarchical matrices, LU factorization, linear systems, task-parallelism, multicore processors
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