189 citations · 595 across the 24 of their papers we have counts for
14 papers · 1 filter
A Discontinuous Galerkin Consistent Splitting Method for the Incompressible Navier-Stokes Equations
Dominik Still, Natalia Nebulishvili, Richard Schussnig +2
This work presents the discontinuous Galerkin discretization of the consistent splitting scheme proposed by Liu [J. Liu, J. Comp. Phys., 228(19), 2009]. The method enforces the div…
A dual grid geometric electromagnetic particle in cell method
Katharina Kormann, Eric Sonnendrücker
Geometric particle-in-cell discretizations have been derived based on a discretization of the fields that is conforming with the de Rham structure of the Maxwell's equation and a s…
Perfect Conductor Boundary Conditions for Geometric Particle-in-Cell Simulations of the Vlasov-Maxwell System in Curvilinear Coordinates
Benedikt Perse, Katharina Kormann, Eric Sonnendrücker
Structure-preserving methods can be derived for the Vlasov-Maxwell system from a discretisation of the Poisson bracket with compatible finite-elements for the fields and a particle…
Variational Framework for Structure-Preserving Electromagnetic Particle-In-Cell Methods
Martin Campos Pinto, Katharina Kormann, Eric Sonnendrücker
In this article we apply a discrete action principle for the Vlasov--Maxwell equations in a structure-preserving particle-field discretization framework. In this framework the fini…
Geometric Particle-in-Cell Simulations of the Vlasov--Maxwell System in Curvilinear Coordinates
Benedikt Perse, Katharina Kormann, Eric Sonnendrücker
Numerical schemes that preserve the structure of the kinetic equations can provide stable simulation results over a long time. An electromagnetic particle-in-cell solver for the Vl…
Energy-conserving time propagation for a geometric particle-in-cell Vlasov--Maxwell solver
Katharina Kormann, Eric Sonnendrücker
This paper discusses energy-conserving time-discretizations for finite element particle-in-cell discretizations of the Vlasov--Maxwell system. A geometric spatially discrete system…
A Hermite-like basis for faster matrix-free evaluation of interior penalty discontinuous Galerkin operators
Martin Kronbichler, Katharina Kormann, Niklas Fehn +2
This work proposes a basis for improved throughput of matrix-free evaluation of discontinuous Galerkin symmetric interior penalty discretizations on hexahedral elements. The basis…
Stable interpolation with isotropic and anisotropic Gaussians using Hermite generating function
Katharina Kormann, Caroline Lasser, Anna Yurova
Gaussian kernels can be an efficient and accurate tool for multivariate interpolation. In practice, high accuracies are often achieved in the flat limit where the interpolation mat…
Efficient Explicit Time Stepping of High Order Discontinuous Galerkin Schemes for Waves
Svenja Schoeder, Katharina Kormann, Wolfgang Wall +1
This work presents algorithms for the efficient implementation of discontinuous Galerkin methods with explicit time stepping for acoustic wave propagation on unstructured meshes of…
Stable evaluation of Gaussian radial basis functions using Hermite polynomials
Anna Yurova, Katharina Kormann
Gaussian radial basis functions can be an accurate basis for multivariate interpolation. In practise, high accuracies are often achieved in the flat limit where the interpolation m…
Error Control for Exponential Integration of the Master Equation
Katharina Kormann, Shev MacNamara
Error estimates for the numerical solution of the master equation are presented. Estimates are based on adjoint methods. We find that a good estimate can often be computed without…
GEMPIC: Geometric ElectroMagnetic Particle-In-Cell Methods
Michael Kraus, Katharina Kormann, Philip J. Morrison +1
We present a novel framework for Finite Element Particle-in-Cell methods based on the discretization of the underlying Hamiltonian structure of the Vlasov-Maxwell system. We derive…
A semi-Lagrangian Vlasov solver in tensor train format
Katharina Kormann
In this article, we derive a semi-Lagrangian scheme for the solution of the Vlasov equation represented as a low-parametric tensor. Grid-based methods for the Vlasov equation have…
Stable difference methods for block-oriented adaptive grids
Anna Nissen, Katharina Kormann, Magnus Grandin +1
In this paper, we present a block-oriented scheme for adaptive mesh refinement based on summation-by-parts (SBP) finite difference methods and simultaneous-approximation-term (SAT)…