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, 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.