A hierarchical fast direct solver for distributed memory machines with manycore nodes

Cédric Augonnet (1) , David Goudin (1) , Matthieu Kuhn (1) , Xavier Lacoste (2) , Raymond Namyst (3, 4) , Pierre Ramet (3, 5)

1 CESTA - Centre d'études scientifiques et techniques d'Aquitaine
2 Total E&P
3 UB - Université de Bordeaux
4 STORM - STatic Optimizations, Runtime Methods
5 HiePACS - High-End Parallel Algorithms for Challenging Numerical Simulations

Compression techniques have revolutionized the Boundary Element Method used to solve the Maxwell equations in frequency domain. In spite of the several orders of magnitude gained in terms of computational cost, and resource consumption, their implementation in a direct solver remains challenging, especially on distributed memory machines. We present the design of an efficient and scalable hierarchical fast direct solver capable of factorizing H-matrices on large scale machines with manycore nodes. This task-based solver relies on a flexible execution model which features an extension of the sequential task flow (STF) paradigm, enabling seamless expression of complex dependencies between hierarchical data over distributed memory machines. We demonstrate its efficiency and its scalability by solving large scale problems over hundred of manycore nodes, and for example factorize a H-matrix with 4.4 million unknowns compressed at 99% in less than 40 minutes with about 70% of parallel efficiency over 24,320 cores.

Domaines: Calcul parallèle, distribué et partagé [cs.DC]; Algorithme et structure de données [cs.DS]

Cédric Augonnet, David Goudin, Matthieu Kuhn, Xavier Lacoste, Raymond Namyst, et al.. A hierarchical fast direct solver for distributed memory machines with manycore nodes. [Research Report] CEA/DAM; Total E&P; Université de Bordeaux. 2019. ⟨cea-02304706⟩