Martin Averseng

activity

20242026

collaborators

5 papers

math.NA2026

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-ph2026

Semiclassical tunneling for some 1D SchrÃ¶dinger operators with complex-valued potentials

Martin Averseng, Nicolas Frantz, FrÃ©dÃ©ric HÃ©rau +1

We consider the non-selfadjoint, semiclassical SchrÃ¶dinger operator $L (h) := - h^{2} \partial_{x}^{2} + e^{i I^\pm} V$ , where $I^\pm \in (- I ¨ , I ¨ )$ and $V : R \to R_{+}$ is ev…

math-ph2025

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

Martin Averseng, Nicolas Frantz, FrÃ©dÃ©ric HÃ©rau +1

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

math.NA2024

Jump-preserving polynomial interpolation in non-manifold polyhedra

Martin Averseng

We construct a piecewise-polynomial interpolant $u \mapsto I^u$ for functions $u : I^c ◯ ∖ I^ \to R$ , where $I^c ◯ \subset R^{d}$ is a Lipschitz polyhedron and $Î\sub…

math.NA2024

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…