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. Here is a brief survey of past and current research topics with relevant publications.

Domain decomposition methods (DDMs) for Helmholtz problems

• 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. Submitted for publication [preprint]
• R. Dai, A. M., J.-F. Remacle, C. Geuzaine (2021). Multidirectionnal sweeping preconditioners with non-overlapping checkerboard domain decomposition for Helmholtz problems. Accepted for publication in J. Comput. Phys. [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. Accepted in Comput. Methods Appl. Mech. Eng. [preprint] [codes]

Absorbing boundary conditions (ABCs) and perfectly matched layers (PMLs)

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

Absorbing Boundary Conditions (ABCs) and Perfectly Matched Layers (PMLs) 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.

• H. Beriot, A. M. (2020). An automatic PML for acoustic finite element simulations with generally-shaped convex domains. Submitted for publication. [preprint]
• 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. [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. [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. [preprint]
• A. M., E. Delhez, C. Geuzaine (2014). Optimizing Perfectly Matched Layers in Discrete Contexts. In International Journal of Numerical Methods in Engineering. [preprint]

Discontinuous Galerkin for seismic imaging with GPU clusters

Fig.: Strong scalability of a DG code for a RTM procedure (involving data transfers) with up to 32 GPUs. [Preprint]

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, T. Warburton (2016). GPU performance analysis of a nodal discontinuous Galerkin method for acoustic and elastic models. In Computers & Geophysics. [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. [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. [preprint]

Discontinuous Galerkin for electromagnetic compatibility

Fig.: Shielding effectiveness of a cavity with an aperture.

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. [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. [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. [preprint]

Open sea boundaries for oceanography

Movie: Traveling storm.

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. [preprint]