Martin Averseng's homepage

About me

I am a researcher in applied Mathematics. I study high frequency wave propagation problems and their numerical resolution by the finite and boundary element methods (FEM and BEM).

Here is a link to my CV.

Exposé aux journées portes ourvertes du centre Borelli, 3 Septembre 2026

Les notes que j'ai rédigées pour préparer mon exposé sont disponibles ici (merci de me signaler toute coquille !)

Papers

M. Averseng, N. Frantz, F. Hérau, N. Raymond Localization of the eigenfunctions of a Bloch-Torrey operator on the half-plane (preprint)

M. Averseng, N. Frantz, F. Hérau, N. Raymond Semiclassical tunneling for some 1D Schrödinger operators with complex-valued potentials (arXiv preprint)

M. Averseng, J. Galkowski, E. A. Spence Non-uniform finite-element meshes defined by ray dynamics for Helmholtz problems (arXiv preprint),

M. Averseng, X. Claeys, R. Hiptmair, Boundary Element Methods for the Laplace Hypersingular Integral Equation on Multiscreens: a two-level Substructuring Preconditioner (arXiv preprint),

M. Averseng, J. Galkowski, E. A. Spence Helmholtz FEM solutions are locally quasi-optimal modulo low frequencies,

M. Averseng, Jump-preserving polynomial interpolation in non-manifold polyhedra (arXiv preprint),

M. Averseng, X. Claeys, R. Hiptmair, Fractured meshes,

M. Averseng, Stability of a weighted L2 projection in a weighted Sobolev norm,

F. Alouges, M. Averseng, Quasi-local and frequency robust preconditioners for the Helmholtz first-kind integral equations on the disk,

F. Alouges, M. Averseng, New preconditioners for the Laplace and Helmholtz integral equations on open curves: analytical framework and numerical results,

M. Averseng, Pseudo-differential analysis of the Helmholtz layer potentials on open curves (arXiv preprint),

M. Averseng Fast discrete convolution in R2 with radial kernels using non-uniform fast Fourier transform with nonequispaced frequencies,

Software

Multi-screen-bem3D-ddm: A Matlab/C++ prototype for 3D BEM simulations on multi-screens, and domain decomposition preconditioning.

FracMeshLib: A Matlab toolbox to manipulate generalized meshes, including fractured meshes and polygonal multi-screens. Prototype for FEM simulations on these geometries.

SqPrecondDiskScreen: Square-root preconditioners on the unit disk in R3.

EBD: The "Efficient Bessel Decomposition" toolbox, to perform fast convolutions by (gradients of) radial kernels in dimension 2.

You can find here a gallery of numerical simulations.

Teaching

Python L2 Angers (2024-2025) : Une introduction à la programmation avec Python
Analyse complexe L3 ENS Paris-Saclay (2025-2026)
- Polycopié des exercices
- Annales
Analyse de la diffraction à haute fréquence (M2 AMS, 2025-2026)
I gave a 3-days course at the occasion of the annual Angers Masterclass organized by the Centre Henri-Lebesgue. The course is about the semiclassical analysis of the finite-element approximation of the Helmholtz equation at high-frequency. You can find the lecture notes here .