activity
20242026
collaborators

5 papers

math.AP2026

Modal bases of coaxial electromagnetic step index fibers

Martin Halla

We consider the eigenvalue problem to find the modes of an electromagnetic coaxial step index fiber. More specific, we consider a closed (meaning PEC boundary conditions) cylindric…

math.AP2026

Length-explicit stability analysis of Helmholtz problems in leaky circular waveguides

Leszek Demkowicz, Martin Halla, Jens Markus Melenk

Motivated by the study and simulation of long, coiled optical fibers we consider in this article a simplified model that is prevalent in the engineering community. Mathematically,…

math.NA2025

Hybrid discontinuous Galerkin discretizations for the damped time-harmonic Galbrun's equation

Martin Halla, Christoph Lehrenfeld, Tim van Beeck

In this article, we study the damped time-harmonic Galbrun's equation which models solar and stellar oscillations. We introduce and analyze hybrid discontinuous Galerkin discretiza…

math.NA2025

On the instabilities of naive FEM discretizations for PDEs with sign-changing coefficients

Martin Halla, Florian Oberender

We consider a scalar diffusion equation with a sign-changing coefficient in its principle part. The well-posedness of such problems has already been studied extensively provided th…

math.NA2024

Radial perfectly matched layers and infinite elements for the anisotropic wave equation

Martin Halla, Maryna Kachanovska, Markus Wess

We consider the scalar anisotropic wave equation. Recently a convergence analysis for radial perfectly matched layers (PML) in the frequency domain was reported and in the present…