34 citations · 112 across the 26 of their papers we have counts for
15 papers · 1 filter
Uniform convergence of diffusion synthetic acceleration for heterogeneous slab transport
Matthias Schlottbom
The diffusion synthetic accelerated (DSA) source iteration is a standard solver for the radiative transfer equation. Using Fourier analysis, a convergence rate \(ρ_\infty(c)\le0.22…
Analysis and systematic discretization of a Fokker-Planck equation with Lorentz force
Vincent Bosboom, Herbert Egger, Matthias Schlottbom
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…
An extension of the approximate component mode synthesis method to the heterogeneous Helmholtz equation
Elena Giammatteo, Alexander Heinlein, Matthias Schlottbom
In this work we propose and analyze an extension of the approximate component mode synthesis (ACMS) method to the heterogeneous Helmholtz equation. The ACMS method has originally b…
Data driven gradient flows
Jan-F. Pietschmann, Matthias Schlottbom
We present a framework enabling variational data assimilation for gradient flows in general metric spaces, based on the minimizing movement (or Jordan-Kinderlehrer-Otto) approximat…
A phase-space discontinuous Galerkin approximation for the radiative transfer equation in slab geometry
Riccardo Bardin, Fleurianne Bertrand, Olena Palii +1
We derive and analyze a symmetric interior penalty discontinuous Galerkin scheme for the approximation of the second-order form of the radiative transfer equation in slab geometry.…
On robustly convergent and efficient iterative methods for anisotropic radiative transfer
Jürgen Dölz, Olena Palii, Matthias Schlottbom
This paper considers the iterative solution of linear systems arising from discretization of the anisotropic radiative transfer equation with discontinuous elements on the sphere.…
Analysis of a mixed discontinuous Galerkin method for the time-harmonic Maxwell equations with minimal smoothness requirements
Kaifang Liu, Dietmar Gallistl, Matthias Schlottbom +1
An error analysis of a mixed discontinuous Galerkin (DG) method with Brezzi numerical flux for the time-harmonic Maxwell equations with minimal smoothness requirements is presented…
A model reduction approach for inverse problems with operator valued data
Jürgen Dölz, Herbert Egger, Matthias Schlottbom
We study the efficient numerical solution of linear inverse problems with operator valued data which arise, e.g., in seismic exploration, inverse scattering, or tomographic imaging…
On a convergent DSA preconditioned source iteration for a DGFEM method for radiative transfer
Olena Palii, Matthias Schlottbom
We consider the numerical approximation of the radiative transfer equation using discontinuous angular and continuous spatial approximations for the even parts of the solution. The…
A perfectly matched layer approach for radiative transfer in highly scattering regimes
Herbert Egger, Matthias Schlottbom
We consider the numerical approximation of boundary conditions in radiative transfer problems by a perfectly matched layer approach. The main idea is to extend the computational do…
A class of Galerkin schemes for time-dependent radiative transfer
Herbert Egger, Matthias Schlottbom
The numerical solution of time-dependent radiative transfer problems is challenging, both, due to the high dimension as well as the anisotropic structure of the underlying integro-…
Diffuse Interface Methods for Inverse Problems: Case Study for an Elliptic Cauchy Problem
Martin Burger, Ole Loseth Elvetun, Matthias Schlottbom
Many inverse problems have to deal with complex, evolving and often not exactly known geometries, e.g. as domains of forward problems modeled by partial differential equations. Thi…
Error analysis of a diffuse interface method for elliptic problems with Dirichlet boundary conditions
Matthias Schlottbom
We use a diffuse interface method for solving Poisson's equation with a Dirichlet condition on an embedded curved interface. The resulting diffuse interface problem is identified a…
Analysis of the Diffuse Domain Method for second order elliptic boundary value problems
Martin Burger, Ole Løseth Elvetun, Matthias Schlottbom
The diffuse domain method for partial differential equations on complicated geometries recently received strong attention in particular from practitioners, but many fundamental iss…
Numerical identification of a nonlinear diffusion law via regularization in Hilbert scales
Herbert Egger, Jan-Frederik Pietschmann, Matthias Schlottbom
We consider the reconstruction of a diffusion coefficient in a quasilinear elliptic problem from a single measurement of overspecified Neumann and Dirichlet data. The uniqueness fo…