My research interests encompass computational methods and both modeling and programming aspects for large-scale wave propagation problems. I am interested in a wide range of applications (in acoustics, seismic imaging, electromagnetism, oceanography, …), especially those requiring HPC resources.

A complete list of publications is available on my on my HAL page or on my Google Scholar page.

The publications are listed by topic below. Some publications appear under more than one topic.

 

Accelerated Iterative Solvers for Time-Harmonic Problems

Discontinuous Galerkin Finite Element Methods

  • S. Pescuma, G. Gabard, T. Chaumont-Frelet, A. M. (2026). A HDG method with transmission variables for time-harmonic wave propagation problems with constant coefficients. Submitted for publication. [preprint]
  • A. E. Rappaport, T. Chaumont-Frelet, A. M. (2026). A hybridizable discontinuous Galerkin method with transmission variables for time-harmonic electromagnetic problems. In SIAM Journal on Scientific Computing. [link] [preprint]
  • S. Pescuma, G. Gabard, T. Chaumont-Frelet, A. M. (2025). A hybridizable Discontinuous Galerkin method with transmission variables for time-harmonic acoustic problems in heterogeneous media. In Journal of Computational Physics. [link] [preprint]
  • A. M., T. Chaumont-Frelet (2023). A hybridizable discontinuous Galerkin method with characteristic variables for Helmholtz problems. In Journal of Computational Physics. [link] [preprint]

Domain Decomposition Methods

  • M. Bonazzoli, P. Ciarlet, A. M. , A. E. Rappaport (2026). Analysis of a two-level domain decomposition preconditioner for the time-harmonic Maxwell equations in anisotropic media. In preparation. [preprint]
  • A. Royer, C. Geuzaine, E. Béchet, A. M. (2021). A non-overlapping domain decomposition method with perfectly matched layer transmission conditions for the Helmholtz equation. In Computer Methods in Applied Mechanics and Engineering. [preprint]
  • R. Dai, A. M., J.-F. Remacle, C. Geuzaine (2021). Multidirectional sweeping preconditioners with non-overlapping checkerboard domain decomposition for Helmholtz problems. In Journal of Computational Physics [preprint]
  • A. M., A. Royer, X. Antoine, X. Geuzaine (2020). A non-overlapping domain decomposition method with high-order transmission conditions and cross-point treatment for Helmholtz problems. In Computer Methods in Applied Mechanics and Engineering. [preprint] [codes]

Problems Near Resonances — Deflation

  • V. Dolean, P. Marchand, A. M., T. Raynaud (2025). Convergence analysis of GMRES applied to Helmholtz problems near resonances. Submitted for publication. [preprint]
  • V. Dolean, P. Marchand, A. M., T. Raynaud (2025). Preconditioning of GMRES for Helmholtz problems with quasimodes. In Proceedings of the 29th International Conference on Domain Decomposition Methods (DD29). [preprint]

 

GPU Computing

Discontinuous Galerkin Solvers for Time-Harmonic Problems

  • A. M., R. Greffe, C. Geuzaine, A. Rappaport, A. Chabib (2026). Méthode d’éléments finis discontinus hybridisée pour la résolution itérative accélérée de problèmes d’ondes en fréquence. In Actes de conférences de 17ème Colloque National en Calcul des Structures (CSMA 2026). [proceeding] (in french)
  • A. Chabib, R. Greffe, C. Geuzaine, A. M. (2025). Portage GPU d’un solveur éléments finis discontinus hybridisé pour les problèmes d’ondes en fréquence. In Actes de conférences du 26e Congrès Français de Mécanique (CFM 2025). [proceeding] (in french)

Discontinuous Galerkin Solvers for Time-Dependent Problems

  • A. M., A. St-Cyr, T. Warburton (2016). GPU performance analysis of a nodal discontinuous Galerkin method for acoustic and elastic models. In Computers & Geophysics. [link] [preprint]
  • J. Chan, Z. Wang, A. M., J.-F. Remacle, T. Warburton. GPU-accelerated discontinuous Galerkin methods on hybrid meshes. In Journal of Computational Physics. [link] [preprint]
  • A. M., A. St-Cyr, W. A. Mulder, T. Warburton (2015). A nodal discontinuous Galerkin method for reverse-time migration on GPU clusters. In Geophysical Journal International. [link] [preprint]

 

Domain Truncation

Movie: Scattering of an acoustic wave by a submarine, in a domain surrounded with a PML. Alternative version with an absorbing boundary condition here.

Artificial absorbing boundary conditions and absorbing Layers are used to deal with wave-like problems defined on unbounded domains. In numerical simulations with finite difference or finite element methods, they surround the computational domain that is truncated. I have worked on the design of PMLs for generally-shaped truncated domains, and the selection of the parameters. I have recently worked on the implementation of high-order ABCs for 3D geometries with corners and edges.

Corner Treatment for High-Order Absorbing Boundary Conditions (ABC)

  • A. M., X. Geuzaine, X. Antoine (2020). Corner treatments for high-order absorbing boundary conditions in high-frequency acoustic scattering problems. In Journal of Computational Physics. [link] [preprint] [codes]
  • A. M., A. Atle, J. Chan, T. Warburton (2017). A GPU‐accelerated nodal discontinuous Galerkin method with high‐order absorbing boundary conditions and corner/edge compatibility. In International Journal of Numerical Methods in Engineering. [link] [preprint]

Perfectly Matched Layers (PML) for generally-shaped convex domains

  • H. Beriot, A. M. (2020). An automatic PML for acoustic finite element simulations with generally-shaped convex domains. In International Journal for Numerical Methods in Engineering. [link] [preprint]
  • A. M., J. Lambrechts, C. Geuzaine (2017). Perfectly Matched Layers for Convex Truncated Domains with Discontinuous Galerkin Time Domain Simulations. In Computers & Mathematics with Applications. [link] [preprint]

Parameter Selection for Absorbing Layers and PML

  • A. M., E. Delhez, C. Geuzaine (2014). Optimizing Perfectly Matched Layers in Discrete Contexts. In International Journal of Numerical Methods in Engineering. [link] [preprint]
  • A. M., E. Deleersnijder, E. Delhez (2010). On the parameters of absorbing layers for shallow water models. In Ocean Dynamics. [link] [preprint]

 

Electromagnetic Waves in General Media

  • M. Bonazzoli, P. Ciarlet, A. M. , A. E. Rappaport (2026). Analysis of a two-level domain decomposition preconditioner for the time-harmonic Maxwell equations in anisotropic media. In preparation. [preprint]
  • P. Ciarlet Jr, A. M. (2026). Analysis of time-harmonic electromagnetic problems with elliptic material coefficients. In Mathematical Methods in the Applied Sciences. [link] [preprint]
  • D. Chicaud, P. Ciarlet Jr, A. M. (2021). Analysis of variational formulations and low-regularity solutions for time-harmonic electromagnetic problems in complex anisotropic media. In SIAM Journal on Mathematical Analysis. [link] [preprint]

 

Application-Oriented Publications

Seismic Imaging
Numerical schemes based on nodal discontinuous Galerkin (DG) schemes exhibit interesting features for massively parallel computation, especially with accelerators such as GPUs. In collaboration with Tim Warburton’s team and Oil & Gas companies, I am working on DG schemes and efficient implementations for reverse-time migration with accelerators.

  • A. M., A. St-Cyr, W. A. Mulder, T. Warburton (2015). A nodal discontinuous Galerkin method for reverse-time migration on GPU clusters. In Geophysical Journal International. [link] [preprint]

Electromagnetic Compatibility
With the increasing use of electrical, electronic, electromagnetic systems, the study of their undesirable interactions and side effects is an important aspect to be considered. Numerical methods are intensively used for such studies. In a collaboration with the Laboratoire de Génie Electrique de Paris and the Université catholique de Louvain, we have developed a discontinuous finite element code with specific interface and boundary conditions.

  • M. Boubekeur, A. Kameni, L. Pichon, A. M., C. Geuzaine (2014). Analysis of transient scattering problems using a discontinuous Galerkin method: application to the shielding effectiveness of enclosures with heterogeneous walls. In International Journal of Numerical Modelling: Electronic Networks, Devices and Fields. [link] [preprint]
  • A. M., A. Kameni, J. Lambrechts, E. Delhez, L. Pichon. C. Geuzaine (2013). An optimum PML for scattering problems in the time domain. In The European Physical Journal – Applied Physics. [link] [preprint]
  • A. Kameni, A. M., M. Boubekeur, V. Preault, L. Pichon, C. Geuzaine (2013). Evaluation of shielding effectiveness of composite wall with a Time Domain Discontinuous Galerkin Method. In The European Physical Journal – Applied Physics. [link] [preprint]
Movie: Traveling storm.

Ocean Modeling
In regional oceanic numerical modeling, the treatment of artificial boundaries at open seas are often seen as a major source of uncertainty or even error. During my PhD, I worked on absorbing layers to deal with such boundaries in two different codes.

  • A. M., E. Deleersnijder, E. Delhez (2010). On the parameters of absorbing layers for shallow water models. In Ocean Dynamics. [link] [preprint]