Ferrite.jl is a Julia package providing the basic building blocks to develop finite element simulations of partial differential equations. The package provides extensive examples to start from and is designed as a compromise between simplicity and generality, trying to map finite element concepts 1:1 with the code in a low-level . Ferrite is actively used in teaching finite element to students at several universities across different countries (e.g. Ruhr-University Bochum and Chalmers University of Technology). Further infrastructure is provided in the form of different mesh parsers and a Julia based visualizer called FerriteViz.jl.
Below we provide a four of potential project ideas in Ferrite.jl. However, interested students should feel free to explore ideas they are interested in. Please contact any of the mentors listed below, or join the #ferrite-fem channel on the Julia slack to discuss. Projects in finite element visualization are also possible with FerriteViz.jl.
Difficulty: Easy-Medium (depending on your specific background)
Project size: 150-300 hours
Problem: Ferrite.jl is designed with the possibility to define partial differential equations on subdomains. This makes it well-suited for interface-coupled multi-physics problems, as for example fluid-structure interaction problems. However, we currently do not have an example showing this capability in our documentation. We also do not provide all necessary utilities for interface-coupled problems.
Minimum goal: The minimal goal of this project is to create a functional and documented linear fluid-structure interaction example coupling linear elasticity with a stokes flow in a simple setup. The code should come with proper test coverage.
Extended goal: With this minimally functional example it is possible to extend the project into different directions, e.g. optimized solvers or nonlinear fluid-structure interaction.
Recommended skills:
Basic knowledge the finite element method
Basic knowledge about solids or fluids
The ability (or eagerness to learn) to write fast code
Mentors: Dennis Ogiermann and Fredrik Ekre
Difficulty: Medium
Project size: 250-350 hours
Problem: Ferrite.jl has an outstanding performance in single-threaded finite element simulations due to elaborate elimination of redundant workloads. However, we recently identified that the way the single-threaded assembly works makes parallel assembly memory bound, rendering the implementation for "cheap" assembly loops not scalable on a wide range of systems. This problem will also translate to high-order schemes, where the single-threaded strategy as is prevents certain common optimization strategies (e.g. sum factorization).
Minimum goal: As a first step towards better parallel assembly performance it is the investion of different assembly strategies. Local and global matrix-free schemes are a possibility to explore here. The code has to be properly benchmarked and tested to identify different performance problems.
Extended goal: With this minimally functional example it is possible to extend the project into different directions, e.g. optimized matrix-free solvers or GPU assembly.
Recommended skills:
Basic knowledge the finite element method
Basic knowledge about benchmarking
The ability (or eagerness to learn) to write fast code
Mentors: Maximilian Köhler and Dennis Ogiermann