34 citations · 112 across the 26 of their papers we have counts for
31 papers
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…
A trace theorem for spherical kinetic Sobolev spaces on -convex domains
Herbert Egger, Matthias Schlottbom
Trace theorems are an indispensable tool for the analysis of kinetic equations. They have been established in wide generality by Cessenat and co-workers for radiative transfer and…
Kreiss stability analysis of Hagstrom-Warburton nonreflecting boundary conditions for the first-order time-dependent Maxwell equations
Kaifang Liu, Matthias Schlottbom, J. J. W. van der Vegt +1
We analyze the stability of the Hagstrom-Warburton nonreflecting boundary conditions (HW-NRBCs) for the first-order time-dependent Maxwell equations. The HW-NRBCs enjoy very small…
A kinetic chemotaxis model and its diffusion limit in slab geometry
Herbert Egger, Kathrin Hellmuth, Nora Philippi +1
Chemotaxis describes the intricate interplay of cellular motion in response to a chemical signal. We here consider the case of slab geometry which models chemotactic motion between…
Unsupervised Machine Learning to Classify the Confinement of Waves in Periodic Superstructures
Marek Kozoň, Rutger Schrijver, Matthias Schlottbom +2
We employ unsupervised machine learning to enhance the accuracy of our recently presented scaling method for wave confinement analysis [1]. We employ the standard k-means++ algorit…
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…
A metriplectic formulation of polarized radiative transfer
Vincent Bosboom, Michael Kraus, Matthias Schlottbom
We present a metriplectic formulation of the radiative transfer equation with polarization and varying refractive index and show that this formulation automatically satisfies the f…
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…
Scaling theory of wave confinement in classical and quantum periodic systems
Marek Kozoň, Ad Lagendijk, Matthias Schlottbom +2
Functional defects in periodic media confine waves - acoustic, electromagnetic, electronic, spin, etc. - in various dimensions, depending on the structure of the defect. While defe…
On the unique solvability of radiative transfer equations with polarization
Vincent Bosboom, Matthias Schlottbom, Felix Schwenninger
We investigate the well-posedness of the radiative transfer equation with polarization and varying refractive index. The well-posedness analysis includes non-homogeneous boundary v…
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…
Parameter identification in a structured population model
Alexander Lorz, Jan-Frederik Pietschmann, Matthias Schlottbom
We study parameter identification problems in a structured population model without mutations. Given measurements of the total population size or critical points of the population,…
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…
On the uniqueness of nonlinear diffusion coefficients in the presence of lower order terms
Herbert Egger, Jan-Frederik Pietschmann, Matthias Schlottbom
We consider the identification of nonlinear diffusion coefficients of the form or in quasi-linear parabolic and elliptic equations. Uniqueness for this inverse prob…
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-…
Notes on a PDE System for Biological Network Formation
Jan Haskovec, Peter Markowich, Benoit Perthame +1
We present new analytical and numerical results for the elliptic-parabolic system of partial differential equations proposed by Hu and Cai, which models the formation of biological…
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…