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, 3) , Pierre-Henri Tournier (4, 5)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 Department of Mathematics and Statistics [Univ Strathclyde]
3 CASTOR - Control, Analysis and Simulations for TOkamak Research
4 ALPINES - Algorithms and parallel tools for integrated numerical simulations
5 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

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: High order finite elements; Edge elements; Microwave imaging; Schwarz preconditioners; Time-harmonic Maxwell's equations

Domaines: Analyse numérique [math.NA]; Imagerie médicale; Imagerie

Marcella Bonazzoli, Victorita Dolean, Francesca Rapetti, Pierre-Henri Tournier. Parallel preconditioners for high order discretizations arising from full system modeling for brain microwave imaging. International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, 2018, 31 (2), ⟨10.1002/jnm.2229⟩. ⟨hal-01328197v2⟩