Publications

PhD dissertation

Efficient high order and domain decomposition methods for the time-harmonic Maxwell's equations (Manuscript)
I defended my PhD thesis in September 2017 at Laboratoire J.A. Dieudonné (UCA, Nice, France). My advisors were Victorita Dolean and Francesca Rapetti.
I worked on both the precise discretization and the efficient solution of the time-harmonic Maxwell's equations, whose variational formulation is sign-indefinite when the frequency is large. Our strategy couples high order edge finite elements with parallel Schwarz domain decomposition preconditioners. In the framework of the ANR project MEDIMAX, we have applied these methods to a large scale problem arising from the modeling of a microwave imaging system, for the detection and monitoring of brain strokes. For the solution of such large scale problems, we took advantage of the Curie supercomputer (TGCC-CEA).

I was a finalist of the 2020 ERCIM Cor Baayen Young Researcher Award.

Preprints

M. Bonazzoli, H. Haddar, T. A. Vu.
On the convergence analysis of one-shot inversion methods
Accepted for publication in SIAM Journal on Applied Mathematics. Preprint available here.

Articles, proceedings and research reports

M. Bonazzoli, X. Claeys.
Multidomain FEM-BEM coupling for acoustic scattering
Journal of Integral Equations and Applications. 36(2):129-167, 2024. Preprint available here.

A. Boisneault, M. Bonazzoli, X. Claeys, P. Marchand.
Substructuring based FEM-BEM coupling for Helmholtz problems
16th International Conference on Mathematical and Numerical Aspects of Wave Propagation, 2024. Preprint available here.

M.A. Boukraa, L. Audibert, M. Bonazzoli, H. Haddar, D. Vautrin.
Imaging a dam-rock interface with inversion of a full elastic-acoustic model
11th International Conference on Inverse Problems in Engineering: Theory and Practice, 2024. Preprint available here.

M.A. Boukraa, L. Audibert, M. Bonazzoli, H. Haddar, D. Vautrin.
High-Resolution Seismic Imaging for Dam-Rock Interface using Full-Waveform Inversion
16th International Conference on Mathematical and Numerical Aspects of Wave Propagation, 2024. Preprint available here.

M.A. Boukraa, L. Audibert, M. Bonazzoli, H. Haddar, D. Vautrin.
Imagerie d'interface barrage-fondation par inversion de forme d'onde complète
E3S Web Conf., 504, 04002, 2024. Preprint available here.

M. Bonazzoli, X. Claeys, F. Nataf, P.-H. Tournier.
How does the partition of unity influence SORAS preconditioner?
In Domain Decomposition Methods in Science and Engineering XXVII, Lecture Notes in Computational Science and Engineering, 149:61-68, 2024. Preprint available here.

M. Bonazzoli, H. Haddar, T. A. Vu.
Convergence analysis of multi-step one-shot methods for linear inverse problems
Research Report RR-9477, Inria Saclay and ENSTA Paris, 2022. Report available here.

M. Bonazzoli, X. Claeys, F. Nataf, P.-H. Tournier.
Analysis of the SORAS domain decomposition preconditioner for non-self-adjoint or indefinite problems
Journal of Scientific Computing, 89, 19, 2021. Preprint available here.

M. Bonazzoli, V. Dolean, I. G. Graham, E. A. Spence, P.-H. Tournier.
Domain decomposition preconditioning for the high-frequency time-harmonic Maxwell equations with absorption
Mathematics of Computation, 88:2559-2604, 2019. Preprint available here.

P.-H. Tournier, I. Aliferis, M. Bonazzoli, M. De Buhan, M. Darbas, V. Dolean, F. Hecht, P. Jolivet, I. El Kanfoud, C. Migliaccio, F. Nataf, C. Pichot, S. Semenov.
Microwave tomographic imaging of cerebrovascular accidents by using High-Performance Computing
Parallel Computing, 85:88-97, 2019. Preprint available here.

I. Ben Gharbia, M. Bonazzoli, X. Claeys, P. Marchand, P.-H. Tournier.
Fast solution of boundary integral equations for elasticity around a crack network: a comparative study
In ESAIM: ProcS, CEMRACS 2016 - Numerical challenges in parallel scientific computing, 63:135-151, 2018. Preprint available here.

M. Bonazzoli, V. Dolean, I. G. Graham, E. A. Spence, P.-H. Tournier.
A two-level domain-decomposition preconditioner for the time-harmonic Maxwell's equations
In Domain Decomposition Methods in Science and Engineering XXIV, Lecture Notes in Computational Science and Engineering, 125:149-157, 2018. Preprint available here (Errata Corrige). See more details in the forthcoming paper.

M. Bonazzoli, V. Dolean, I. G. Graham, E. A. Spence, P.-H. Tournier.
Two-level preconditioners for the Helmholtz equation
In Domain Decomposition Methods in Science and Engineering XXIV, Lecture Notes in Computational Science and Engineering, 125:139-147, 2018. Preprint available here.

M. Bonazzoli, V. Dolean, F. Hecht, F. Rapetti.
An example of explicit implementation strategy and preconditioning for the high order edge finite elements applied to the time-harmonic Maxwell's equations
Computers and Mathematics with Applications, 75(5):1498-1514, 2018. Preprint available here.

M. Bonazzoli, V. Dolean, F. Rapetti, P.-H. 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, 31(2):22-29, 2018. Preprint available here.

M. Bonazzoli, F. Rapetti, C. Venturini.
Dispersion analysis of triangle-based Whitney element methods for electromagnetic wave propagation
Applied Mathematics and Computation, 319:274-286, 2018.

M. Bonazzoli, F. Rapetti, P.-H. Tournier, C. Venturini.
High order edge elements for electromagnetic waves: remarks on numerical dispersion
In Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016, Lecture Notes in Computational Science and Engineering, 119:215-227, 2017.

P.-H. Tournier, M. Bonazzoli, V. Dolean, F. Rapetti, F. Hecht, F. Nataf, I. Aliferis, I. El Kanfoud, C. Migliaccio, M. de Buhan, M. Darbas, S. Semenov, C. Pichot.
Numerical modelling and high speed parallel computing: new perspectives for brain strokes detection and monitoring
IEEE Antennas and Propagation Magazine, Special issue on Electromagnetic Inverse Problems for Sensing and Imaging, 59(5):98-110, 2017. Preprint available here.

M. Bonazzoli, V. Dolean, R. Pasquetti, and F. Rapetti.
Schwarz preconditioning for high order edge element discretizations of the time-harmonic Maxwell's equations
In Domain Decomposition Methods in Science and Engineering XXIII, Lecture Notes in Computational Science and Engineering, 116:117-124, 2017. Preprint available here.

M. Bonazzoli, F. Rapetti.
High-order finite elements in numerical electromagnetism: degrees of freedom and generators in duality
Numerical Algorithms, 74(1):111-136, 2017. Preprint available here.

M. Bonazzoli, E. Gaburro, V. Dolean, F. Rapetti.
High order edge finite element approximations for the time-harmonic Maxwell's equations
Proceedings of 2014 IEEE Conference on Antenna Measurements and Applications (CAMA)