arXiv subjects

Vincent Bosboom

Publications and source records attributed to Vincent Bosboom.

3 recordsLinked to original sources

arXiv2024

A metriplectic formulation of polarized radiative transfer

We present a metriplectic formulation of the radiative transfer equation with polarization and varying refractive index and show that this formulation automatically satisfies the first two laws of thermodynamics. In particular, the derived antisymmetric bracket enjoys the Jacobi identity. To obtain this formulation we suitably transform the equation and show that important physical quantities derived from the solution remain invariant under such a transformation.

math-ph↗

arXiv2023

Analysis and systematic discretization of a Fokker-Planck equation with Lorentz force

The propagation of charged particles through a scattering medium in the presence of a magnetic field can be described by a Fokker-Planck equation with Lorentz force. This model is studied both, from a theoretical and a numerical point of view. A particular trace estimate is derived for the relevant function spaces to clarify the meaning of boundary values. Existence of a weak solution is then proven by the Rothe method. In the second step of our investigations, a fully practical discretization scheme is proposed based on an implicit Euler method for the energy variable and a spherical-harmonics finite-element discretization with respect to the remaining variables. A complete error analysis of the resulting scheme is given and numerical test are presented to illustrate the theoretical results and the performance of the proposed method.

math.NA↗

arXiv2022

On the unique solvability of radiative transfer equations with polarization

We investigate the well-posedness of the radiative transfer equation with polarization and varying refractive index. The well-posedness analysis includes non-homogeneous boundary value problems on bounded spatial domains, which requires the analysis of suitable trace spaces. Additionally, we discuss positivity, Hermiticity, and norm-preservation of the matrix-valued solution. As auxiliary results, we derive new trace inequalities for products of matrices.

math.AP↗