#finite #element #fem #pde


A library for advanced finite element computations in Rust

19 releases

Uses new Rust 2021

0.0.19 Jan 27, 2022
0.0.18 Dec 17, 2021
0.0.13 Nov 17, 2021
0.0.5 Oct 29, 2021
0.0.0 Apr 6, 2021

#112 in Science

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606 downloads per month
Used in fenris-solid


14K SLoC

Fenris logo

A Rust library for building advanced applications with the Finite Element Method (FEM).

Although developed with a special emphasis on solid mechanics in computer graphics, Fenris is a highly generic and versatile library applicable to many other domains.


As of October 2021, Fenris is heavily developed alongside several of our ongoing academic projects, with the overarching goal of supporting our research efforts.

Our goal is to rework, document and polish the library for external users during 2022. In its current state, Fenris is not recommended for general usage. We currently offer no API stability whatsoever, the documentation is severely lacking, and only parts of the library has been extensively tested. Moreover, some parts of the library will likely be removed altogether in future versions.


With Fenris, we aim to provide an open-source, composable, flexible and performant library for advanced finite element computations in Rust.

Fenris is intended primarily as an alternative to C++ FEM libraries. With Fenris, users can take advantage of the significant productivity boost afforded by working with Rust, a modern programming language with a best-in-class dependency management system and a revolutionary model for memory-safe, high-performance system programming.

This statement is motivated by our own experiences writing FEM code in Rust: gone are the hours upon hours of wrestling with CMake to integrate an external library. Furthermore, the expressive type system and borrow checker model employed by Rust encourages good designs that are free of the myriads of footguns associated with (even modern) C++. And perhaps even more important, the excellent generic trait system found in Rust - which importantly is type-checked at compile time - allows us to write highly generic code with explicit invariants encoded in the type system that are automatically and correctly represented in the generated documentation.

In short, we have found that Rust allows us to spend more time on solving interesting and complex problems (the fun part), and less time on dealing with auxiliary issues largely caused by language deficiencies (the annoying part).

Summary of technical goals

  • Provide a number of low-order and high-order standard Lagrange elements of a variety of geometric shapes in 2D and 3D (at the very least triangles, quadrilaterals, tetrahedra and hexahedra).
  • High-performance shared-memory parallelism for assembly.
  • A composable architecture: Higher-level functionality is built by the composition of lower-level functionality. Users choose the level at which they need to work at.
  • Facilitates generic programming: write code once and have it work across a number of different elements, dimensions and operators.
  • Convenient I/O, currently in the form of export to VTK/VTU for visualization in ParaView.


  • Fenris is not intended to compete with the likes of FEniCS or similar libraries that let users provide high-level weak formulations of PDEs. In contrast, Fenris targets users who need lower-level functionality, and is perhaps more comparable to the likes of deal.II.
  • Fenris by itself provides no functionality for solving (non-)linear systems, only the functionality for assembling (as scalars/vectors/matrices) and applying discrete operators.
  • We have no plans for supporting distributed computing or GPU acceleration at this time.


An older incarnation of Fenris was used for the code associated with the following academic papers:

  • Longva, A., Löschner, F., Kugelstadt, T., Fernández-Fernández, J. A., & Bender, J. (2020). Higher-order finite elements for embedded simulation. ACM Transactions on Graphics (TOG), 39(6), 1-14.
  • Löschner, F., Longva, A., Jeske, S., Kugelstadt, T., & Bender, J. (2020).
    Higher‐Order Time Integration for Deformable Solids. In Computer Graphics Forum (Vol. 39, No. 8, pp. 157-169).


Apart from minor bug fixes or changes, we do not accept source code contributions at this time. We would however be happy for daring users who want to try out our library to report issues on our issue tracker.

We have a number of unrealized plans that will require significant reworking of parts of the library. Once the library is in a more stable state we will be grateful for contributions from the community.


Fenris is distributed under the terms of both the MIT license and the Apache License (Version 2.0). See LICENSE-APACHE and LICENSE-MIT for details. Opening a pull requests is assumed to signal agreement with these licensing terms.


~182K SLoC