Tiled Algorithms for Efficient Task-Parallel ℌ-Matrix Solvers

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).