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Section: New Results

High performance numerical computing

High order HDG schemes and domain decomposition solvers for frequency-domain electromagnetics

Participants : Emmanuel Agullo [HIEPACS project-team, Inria Bordeaux - Sud-Ouest] , Théophile Chaumont-Frelet, Luc Giraud [HIEPACS project-team, Inria Bordeaux - Sud-Ouest] , Stéphane Lanteri.

This work is undertaken in the context of PRACE 6IP project and aims at the development of scalable frequency-domain electromagnetic wave propagation solvers, in the framework of the DIOGENeS software suite. This solver is based on a high order HDG scheme formulated on an unstructured tetrahedral grid for the discretization of the system of three-dimensional Maxwell equations in dispersive media, leading to the formulation of large sparse undefinite linear system for the hybrid variable unknowns. This system is solved with domain decomposition strategies that can be either a purely algebraic algorithm working at the matrix operator level (i.e. a black-box solver), or a tailored algorithm designed at the continuous PDE level (i.e. a PDE-based solver). In the former case, we collaborate with the HIEPACS project-team at Inria Bordeaux - Sud-Ouest in view of adapting and exploiting the MaPHyS (Massively Parallel Hybrid Solver - https://gitlab.inria.fr/solverstack/maphys) algebraic hybrid iterative-direct domain decomposition solver. More precisely, this collaboration is concerned with two topics: one one hand,= the improvement of the iterative convergence of MaPHyS for the HDG hybrid variable linear system.