1 citations · 2 across the 6 of their papers we have counts for
7 papers
The Calderón operator for time-harmonic Maxwell's equations in closed waveguides
Martin Halla
We consider the time-harmonic Maxwell's equations in a closed, cylindrical waveguide with longitudinal invariant but heterogeneous permittivity and permeability. We consider minima…
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…
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,…
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…
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…
A new numerical method for scalar eigenvalue problems in heterogeneous, dispersive, sign-changing materials
Martin Halla, Thorsten Hohage, Florian Oberender
We consider time-harmonic scalar transmission problems between dielectric and dispersive materials with generalized Lorentz frequency laws. For certain frequency ranges such equati…
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…