Parallel preconditioners for high order discretizations arising from full system modeling for brain microwave imaging

Marcella Bonazzoli (1) , Victorita Dolean (1, 2) , Francesca Rapetti (1) , Pierre-Henri Tournier (3, 4)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 Department of Mathematics and Statistics [Univ Strathclyde]
3 LJLL - Laboratoire Jacques-Louis Lions
4 Inria de Paris

This paper combines the use of high order finite element methods with parallel preconditioners of domain decomposition type for solving electromagnetic problems arising from brain microwave imaging. The numerical algorithms involved in such complex imaging systems are computationally expensive since they require solving the direct problem of Maxwell's equations several times. Moreover, wave propagation problems in the high frequency regime are challenging because a sufficiently high number of unknowns is required to accurately represent the solution. In order to use these algorithms in practice for brain stroke diagnosis, running time should be reasonable. The method presented in this paper, coupling high order finite elements and parallel preconditioners, makes it possible to reduce the overall computational cost and simulation time while maintaining accuracy.

Mots clés: Schwarz preconditioners; high order finite elements; edge elements; time-harmonic Maxwell's equations; microwave imaging

Domaines: Analyse numérique [math.NA]

Marcella Bonazzoli, Victorita Dolean, Francesca Rapetti, Pierre-Henri Tournier. Parallel preconditioners for high order discretizations arising from full system modeling for brain microwave imaging. 2016. ⟨hal-01328197v1⟩