LEOPART: A particle library for FENICS

Jakob M. Maljaars*, Chris N. Richardson, Nathan Sime

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

8 Citations (Scopus)
23 Downloads (Pure)


This paper introduces LEOPART, an add-on for the open-source finite element software library FENICS to seamlessly integrate Lagrangian particle functionality with (Eulerian) mesh-based finite element (FE) approaches. LEOPART- which is so much as to say: ‘Lagrangian–Eulerian on Particles’ - contains tools for efficient, accurate and scalable advection of Lagrangian particles on simplicial meshes. In addition, LEOPART comes with several projection operators for exchanging information between the scattered particles and the mesh and vice versa. These projection operators are based on a variational framework, which allows extension to high-order accuracy. In particular, by implementing a dedicated PDE-constrained particle–mesh projection operator, LEOPART provides all the tools for diffusion-free advection, while simultaneously achieving optimal convergence and ensuring conservation of the projected particle quantities on the underlying mesh. A range of numerical examples that are prototypical to passive and active tracer methods highlight the properties and the parallel performance of the different tools in LEOPART. Lastly, future developments are identified. The source code for LEOPART is actively maintained and available under an open-source license at https://bitbucket.org/jakob_maljaars/leopart.

Original languageEnglish
Pages (from-to)289-315
Number of pages27
JournalComputers and Mathematics with Applications
Publication statusPublished - 2021


  • Finite elements
  • Open-source software
  • Particle tracking
  • Particle-in-cell
  • PDE-constrained optimization


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