International Conference on Scientific Computation and Differential Equations

# Invited Talk

### A task-based H-matrix solver for acoustic and electromagnetic problems on multicore architectures

B. Lize, G. Sylvand, E. Agullo and S. Thibault

Abstract
$\mathcal{H}$-Matrix [1, 2] is a hierarchical, data-sparse approximate representation of matrices that allows the fast approximate computation of matrix products, $LU$ and $LDL^T$ decompositions, inversion and more. This representation is suitable for the direct solution of large dense linear systems arising from the Boundary Element Method in $O(N \log_2^\alpha(N))$ operations. However, the recursive and irregular nature of these algorithms makes an efficient parallel implementation more challenging, especially when relying on a "Bulk Synchronous Parallel" paradigm [3]. We consider an alternative parallelization for multicore architectures using a task-based approach on top of a runtime system [4]. We show that our method leads to a highly efficient, fully pipelined computation on large real-world industrial test cases in acoustics and electromagnetism.

Bibliography
[1] W. Hackbusch, \textitA Sparse Matrix Arithmetic Based on H-Matrices. Part I: Introduction to H-Matrices, Computing, Volume 62, Issue 2, 1999, Pages 89-108.
[2] Lars Grasedyck and Wolfgang Hackbusch, \textitConstruction and Arithmetics of H-Matrices, Computing, Volume 70, Issue 4, 2003, Pages 296-334.
[3] R. Kriemann, \textitParallel H-Matrix Arithmetics on Shared Memory Systems, Computing, Volume 74, Issue 3, 2005, Pages 273-297.
[4] Cédric Augonnet, \textitScheduling Tasks over Multicore machines enhanced with Accelerators: a Runtime System's Perspective, PhD Thesis, Univeristé Bordeaux 1, 2011

Organized by