Martin Averseng

activity

20172026

most citedBoundary Element Methods for the Laplace Hypersingular Integral Equation on Multiscreens: a two-level Substructuring Preconditioner

1 citations · 1 across the 10 of their papers we have counts for

collaborators

11 papers

math.AP2026

Cartesian PML truncation for the Helmholtz equation is exponentially accurate at high frequency

Martin Averseng, Jeffrey Galkowski, Euan A. Spence

For a wide class of Helmholtz scattering problems (namely, those fitting in the black-box framework of Sjöstrand--Zworski) we prove that the error incurred by approximating the rad…

math-ph2025

Localization of the eigenfunctions of a Bloch-Torrey operator on the half-plane

Martin Averseng, Nicolas Frantz, Frédéric Hérau +1

We consider a non-self adjoint operator of the form $- h^{2} Δ + i (V (x) + α (x) y)$ on the upper half plane $y > 0$ with Dirichlet boundary conditions on ${y = 0}$ with $V \geq 0$ , $V$ …

math-ph2025

Semiclassical tunneling for some 1D Schrödinger operators with complex-valued potentials

Martin Averseng, Nicolas Frantz, Frédéric Hérau +1

We consider the non-selfadjoint, semiclassical Schrödinger operator $L (h) := - h^{2} \partial_{x}^{2} + e^{i α} V$ , where $α \in (- π, π)$ and $V : R \to R_{+}$ is even an…

math.NA2025

Non-uniform finite-element meshes defined by ray dynamics for Helmholtz problems

Martin Averseng, Jeffrey Galkowski, Euan A. Spence

The $h$ -version of the finite-element method ( $h$ -FEM) applied to the high-frequency Helmholtz equation has been a classic topic in numerical analysis since the 1990s. It is now ri…

math.NA2023★ 1 cited

Boundary Element Methods for the Laplace Hypersingular Integral Equation on Multiscreens: a two-level Substructuring Preconditioner

Martin Averseng, Xavier Claeys, Ralf Hiptmair

We present a preconditioning method for the linear systems arising from the boundary element discretization of the Laplace hypersingular equation on a $2$ -dimensional triangulated…

math.NA2023

Helmholtz FEM solutions are locally quasi-optimal modulo low frequencies

Martin Averseng, Euan A. Spence, Jeffrey Galkowski

For $h$ -FEM discretisations of the Helmholtz equation with wavenumber $k$ , we obtain $k$ -explicit analogues of the classic local FEM error bounds of [Nitsche, Schatz 1974], [Wahlbi…

math.NA2022

Fractured Meshes

Martin Averseng, Xavier Claeys, Ralf Hiptmair

This work introduces ``generalized meshes", a type of meshes suited for the discretization of partial differential equations in non-regular geometries. Generalized meshes extend re…

math.NA2022

Jump-preserving polynomial interpolation in non-manifold polyhedra

Martin Averseng

We construct a piecewise-polynomial interpolant $u \mapsto Π u$ for functions $u : Ω ∖ Γ \to R$ , where $Ω \subset R^{d}$ is a Lipschitz polyhedron and $Γ\subset Ω…

math.NA2019

Pseudo-differential analysis of the Helmholtz layer potentials on open curves

Martin Averseng

We introduce two new classes of pseudo-differential operators on open curves. They correspond via a change of variables to subclasses of the periodic pseudo-differential operators,…

math.NA2019

New preconditioners for Laplace and Helmholtz integral equations on open curves: Analytical framework and Numerical results

François Alouges, Martin Averseng

The Helmholtz wave scattering problem by screens in 2D can be recast into first-kind integral equations which lead to ill-conditioned linear systems after discretization. We introd…

math.NA2017

Fast discrete convolution in $R^{2}$ using Sparse Bessel Decomposition

Martin Averseng

We describe an efficient algorithm for computing the matrix vector products that appear in the numerical resolution of boundary integral equations in 2 space dimension. This work i…

Cartesian PML truncation for the Helmholtz equation is exponentially accurate at high frequency

Localization of the eigenfunctions of a Bloch-Torrey operator on the half-plane

Semiclassical tunneling for some 1D Schrödinger operators with complex-valued potentials

Non-uniform finite-element meshes defined by ray dynamics for Helmholtz problems

Boundary Element Methods for the Laplace Hypersingular Integral Equation on Multiscreens: a two-level Substructuring Preconditioner

Helmholtz FEM solutions are locally quasi-optimal modulo low frequencies

Fractured Meshes

Jump-preserving polynomial interpolation in non-manifold polyhedra

Pseudo-differential analysis of the Helmholtz layer potentials on open curves

New preconditioners for Laplace and Helmholtz integral equations on open curves: Analytical framework and Numerical results

Fast discrete convolution in R2 using Sparse Bessel Decomposition

Fast discrete convolution in $R^{2}$ using Sparse Bessel Decomposition