63 citations · 347 across the 39 of their papers we have counts for
5 papers · 2 filters
A structure-preserving surrogate model for the closure of the moment system of the Boltzmann equation using convex deep neural networks
Steffen Schotthöfer, Tianbai Xiao, Martin Frank +1
Direct simulation of physical processes on a kinetic level is prohibitively expensive in aerospace applications due to the extremely high dimension of the solution spaces. In this…
On the convergence of the regularized entropy-based moment method for kinetic equations
Graham W. Alldredge, Martin Frank, Jan Giesselmann
The entropy-based moment method is a well-known discretization for the velocity variable in kinetic equations which has many desirable theoretical properties but is difficult to im…
A Realizable Filtered Intrusive Polynomial Moment Method
Graham Alldredge, Martin Frank, Jonas Kusch +1
Intrusive uncertainty quantification methods for hyperbolic problems exhibit spurious oscillations at shocks, which leads to a significant reduction of the overall approximation qu…
Dynamical low-rank approximation for Burgers' equation with uncertainty
Jonas Kusch, Gianluca Ceruti, Lukas Einkemmer +1
Quantifying uncertainties in hyperbolic equations is a source of several challenges. First, the solution forms shocks leading to oscillatory behaviour in the numerical approximatio…
A parallel-in-time collocation method using diagonalization: theory and implementation for linear problems
Gayatri Caklovic, Robert Speck, Martin Frank
We present and analyze a parallel implementation of a parallel-in-time collocation method based on -circulant preconditioned Richardson iterations. While many papers explore thi…