90 citations · 1k across the 88 of their papers we have counts for
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Overcoming order reduction in diffusion-reaction splitting. Part 1: Dirichlet boundary conditions
Lukas Einkemmer, Alexander Ostermann
For diffusion-reaction equations employing a splitting procedure is attractive as it reduces the computational demand and facilitates a parallel implementation. Moreover, it opens…
A modern resistive magnetohydrodynamics solver using C++ and the Boost library
Lukas Einkemmer
In this paper we describe the implementation of our C++ resistive magnetohydrodynamics solver. The framework developed facilitates the separation of the code implementing the speci…
A splitting approach for the Kadomtsev--Petviashvili equation
Lukas Einkemmer, Alexander Ostermann
We consider a splitting approach for the Kadomtsev--Petviashvili equation with periodic boundary conditions and show that the necessary interpolation procedure can be efficiently i…
On the error propagation of semi-Lagrange and Fourier methods for advection problems
Lukas Einkemmer, Alexander Ostermann
In this paper we study the error propagation of numerical schemes for the advection equation in the case where high precision is desired. The numerical methods considered are based…
A strategy to suppress recurrence in grid-based Vlasov solvers
Lukas Einkemmer, Alexander Ostermann
In this paper we propose a strategy to suppress the recurrence effect present in grid-based Vlasov solvers. This method is formulated by introducing a cutoff frequency in Fourier s…
A Hamiltonian splitting for the Vlasov-Maxwell system
Nicolas Crouseilles, Lukas Einkemmer, Erwan Faou
A new splitting is proposed for solving the Vlasov-Maxwell system. This splitting is based on a decomposition of the Hamiltonian of the Vlasov-Maxwell system and allows for the con…