no code implementations • 3 Feb 2021 • Martin Campos Pinto, Jakob Ameres, Katharina Kormann, Eric Sonnendrücker
In this framework, which extends the recent Finite Element based Geometric Electromagnetic PIC (GEMPIC) method to a variety of field solvers, the discretization of the electromagnetic potentials and fields is represented by a de Rham sequence of compatible spaces, and the particle-field coupling procedure is described by approximation operators that commute with the differential operators in the sequence.
Computational Physics
no code implementations • 22 Jan 2021 • 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.
Numerical Analysis Numerical Analysis Mathematical Physics Mathematical Physics 35Q70 (Primary), 65P10, 35Q61 (Secondary)
1 code implementation • 19 Feb 2020 • Peter Munch, Katharina Kormann, Martin Kronbichler
This work presents the efficient, matrix-free finite-element library hyper. deal for solving partial differential equations in two to six dimensions with high-order discontinuous Galerkin methods.
Mathematical Software Numerical Analysis Numerical Analysis G.4
1 code implementation • 9 May 2018 • Svenja Schoeder, Katharina Kormann, Wolfgang Wall, Martin Kronbichler
A crucial step towards efficiency is to evaluate operators in a matrix-free way with sum-factorization kernels.
Numerical Analysis 65M60, 65Y20, 68Q25, 68W40
3 code implementations • 9 Nov 2017 • Martin Kronbichler, Katharina Kormann
Our performance analysis shows that the results are often within 10\% of the available memory bandwidth for the proposed implementation, with the exception of the Cartesian mesh case where the cost of gather operations and MPI communication are more substantial.
Mathematical Software Numerical Analysis Numerical Analysis
1 code implementation • 7 Sep 2017 • Anna Yurova, Katharina Kormann
Stable evaluation algorithms have been proposed by Fornberg, Larsson & Flyer based on a Chebyshev expansion of the Gaussian basis and by Fasshauer & McCourt based on a Mercer expansion with Hermite polynomials.
Numerical Analysis
