Sparse supernodal solver with low-rank compression for solving the frequency-domain Maxwell equations discretized by a high order HDG method

Grégoire Pichon (1) , Eric Darve (2, 3) , Mathieu Faverge (1) , Stéphane Lanteri (4) , Pierre Ramet (1) , Jean Roman (1)

1 HiePACS - High-End Parallel Algorithms for Challenging Numerical Simulations
2 ICME - Institute for Computational and Mathematical Engineering [Stanford]
3 Department of Mechanical Engineering [Stanford]
4 NACHOS - Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media

In this talk, we present the use of PaStiX sparse direct solver in a Schwarz method for solving the frequencydomain Maxwell equations discretized by a high order HDG method. More precisely, the sparse solver is used to solve a system on sub-domains while iterative refinement is performed to get the global solution. Recently, low-rank compression have been added to PaStiX in order to reduce the time-to-solution or the memory footprint of the solver. The resulting low-rank solver can be used either as a direct solver at a lower accuracy or as a good preconditionner for iterative methods. We will investigate the use of low-rank compression for the frequency-domain Maxwell equations on large systems to experiment the compressibility of this equation.

Mots clés: block low-rank compression; PaStiX direct solver; Sparse linear solver

Domaines: Calcul parallèle, distribué et partagé [cs.DC]

Grégoire Pichon, Eric Darve, Mathieu Faverge, Stéphane Lanteri, Pierre Ramet, et al.. Sparse supernodal solver with low-rank compression for solving the frequency-domain Maxwell equations discretized by a high order HDG method. Journées jeunes chercheur-e-s - Résolution de problèmes d’ondes harmoniques de grande taille, Nov 2017, PARIS, France. pp.1-55, 2017. ⟨hal-01660653⟩