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Discrete Dirac Mechanics and Geometric Numerical Integration Methods for Plasma Physics

Total Cost €


EC-Contrib. €






Project "DDM-GNI" data sheet

The following table provides information about the project.


Organization address
postcode: 80539
website: n.a.

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Germany [DE]
 Project website
 Total cost 181˙002 €
 EC max contribution 181˙002 € (100%)
 Programme 1. H2020-EU.1.3.2. (Nurturing excellence by means of cross-border and cross-sector mobility)
 Code Call H2020-MSCA-IF-2015
 Funding Scheme MSCA-IF-GF
 Starting year 2016
 Duration (year-month-day) from 2016-04-01   to  2018-03-31


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
2    WASEDA UNIVERSITY JP (TOKYO) partner 0.00


 Project objective

In recent years it has been realised that the preservation of certain structures and properties of mathematical equations is of utmost importance when bringing them in a form understandable by computers. Ignoring such properties often leads to incorrect results in the corresponding simulations. In plasma and fusion physics this is especially true as the mathematical equations are highly complex and direct comparison with the experiments is very difficult. Still, the application of structure-preserving numerical algorithms to plasma physics has not gained much attention and todays computer codes do not use such methods. Consequently, these codes are not able to reproduce important physical effects observed in the experiments, hindering progress in research. This project is devoted to the development of a flexible and general framework for the derivation of geometric numerical integrators, referred to as discrete Dirac mechanics, which will be applicable to many problems from plasma physics, but also to equations from other research fields such as optimal control, meteorology, oceanography, geo dynamics, fluid dynamics, elasticity, solar physics, astrophysics and cosmology. This framework will be used to derive novel numerical methods for important systems used in plasma and fusion physics modelling. After successful prototype implementation, verification and validation of the new methods, these will be implemented in an open source library and transferred to leading application codes in order to improve their predictive capabilities and physical correctness. By combining the expertise of all participants, it will be possible to establish an innovative line of research which will lead to numerous applications and strengthen the European leadership in scientific computing. The know-how acquired through the proposed actions will complement my theoretical, technical as well as transferrable skills and put me in a position to establish an independent research group.


year authors and title journal last update
List of publications.
2018 Hirvijoki, Eero; Kraus, Michael; Burby, Joshua W.
Metriplectic particle-in-cell integrators for the Landau collision operator
published pages: , ISSN: , DOI:
Submitted to Physics of Plasmas 2019-06-13
2018 C. L. Ellison, J. M. Finn, J. W. Burby, M. Kraus, H. Qin, W. M. Tang
Degenerate variational integrators for magnetic field line flow and guiding center trajectories
published pages: 52502, ISSN: 1070-664X, DOI: 10.1063/1.5022277
Physics of Plasmas 25/5 2019-06-13
2017 Kraus, Michael
Projected Variational Integrators for Degenerate Lagrangian Systems
published pages: , ISSN: , DOI:
Submitted to Numerische Mathematik 2019-06-13
2017 Michael Kraus, Eero Hirvijoki
Metriplectic integrators for the Landau collision operator
published pages: 102311, ISSN: 1070-664X, DOI: 10.1063/1.4998610
Physics of Plasmas 24/10 2019-06-13
2017 Michael Kraus, Katharina Kormann, Philip J. Morrison, Eric Sonnendrücker
GEMPIC: geometric electromagnetic particle-in-cell methods
published pages: 905830401, ISSN: 0022-3778, DOI: 10.1017/S002237781700040X
Journal of Plasma Physics 83/04 2019-06-13

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