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). I am interested in fast methods, including acceleration and preconditioning. I have mostly focused on those problems in the context of singular geometries, namely scattering by (complex) screens (see pictures below). I also have a long-standing interest in pseudo-differential analysis, and, more recently, semiclassical analysis.

Here is a link to my CV.

Papers

M. Averseng, J. Galkowski, E. A. Spence, Non-uniform finite element meshes defined by ray dynamics for Helmholtz trapping problems (in preparation). Proceedings from WAVES 2024.,

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 (arXiv preprint),

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.