42 citations · 54 across the 7 of their papers we have counts for
7 papers
Distributed model order reduction of a model for microtubule-based cell polarization using HAPOD
Tobias Leibner, Maja Matis, Mario Ohlberger +1
In this contribution we investigate in mathematical modeling and efficient simulation of biological cells with a particular emphasis on effective modeling of structural properties…
A new entropy-variable-based discretization method for minimum entropy moment approximations of linear kinetic equations
Tobias Leibner, Mario Ohlberger
In this contribution we derive and analyze a new numerical method for kinetic equations based on a variable transformation of the moment approximation. Classical minimum-entropy mo…
First-order continuous- and discontinuous-Galerkin moment models for a linear kinetic equation: realizability-preserving splitting scheme and numerical analysis
Florian Schneider, Tobias Leibner
We derive a second-order realizability-preserving scheme for moment models for linear kinetic equations. We apply this scheme to the first-order continuous and discontinuous models…
First-order continuous- and discontinuous-Galerkin moment models for a linear kinetic equation: model derivation and realizability theory
Florian Schneider, Tobias Leibner
We provide two new classes of moment models for linear kinetic equations in slab and three-dimensional geometry. They are based on classical finite elements and low-order discontin…
Hierarchical Approximate Proper Orthogonal Decomposition
Christian Himpe, Tobias Leibner, Stephan Rave
Proper Orthogonal Decomposition (POD) is a widely used technique for the construction of low-dimensional approximation spaces from high-dimensional input data. For large-scale appl…
Extending DUNE: The dune-xt modules
Tobias Leibner, René Milk, Felix Schindler
We present our effort to extend and complement the core modules of the Distributed and Unified Numerics Environment DUNE (http://dune-project.org) by a well tested and structured c…
Problem adapted Hierarchical Model Reduction for the Fokker-Planck equation
Julia Brunken, Tobias Leibner, Mario Ohlberger +1
In this paper we introduce a new hierarchical model reduction framework for the Fokker-Planck equation. We reduce the dimension of the equation by a truncated basis expansion in th…