Initiated about 25 years ago by Manfred Kaltenbacher the project has been developed at various research institutions and companies under various names (CFS++, NACS). Through open-sourcing the code under the permissive MIT license in 2020, the finite element software openCFS is now publicly available.
The software is designed to solve coupled-field problems in engineering and research applications using the finite element method.
The talk will give an overview of the main features of CFS, from the various implemented PDEs and couplings to the user-friendly XML-based input format, and on to pre- and post-processing routines. Furthermore, some recently implemented features, such as harmonic balancing, topology optimisation (in acoustics), and acoustic boundary layers, will be presented. Finally, we will share our experience with open-sourcing an academic project.

In this talk we review our experience with porting the MFEM finite element library (https://mfem.org) to GPU-based exascale architectures. This development included both software and algorithmic changes, as well as co-design with hardware vendors and large-scale multi-physics applications as part of the US Exascale Computing Project (ECP). Modern architectures favor algorithms, such as high-order finite elements, that expose fine-grain parallelism and maximize the ratio of floating-point operations to energy intensive data movement. These methods are particularly well-suited for exascale architectures with GPU accelerators, where their efficiency and scalability rely on the adoption of partially assembled algorithms that reduce memory data motion. The matrix-free nature of partial assembly algorithms enables higher efficiency, but also motivates new research in areas such as meshing, discretizations and solvers. We will present some of the recent work on GPU-oriented algorithms and software in MFEM, and also report on developments in related projects, including high-order ALE compressible hydrodynamics in LLNL's BLAST code; GPU benchmarks from the Center for Efficient Exascale Discretizations in the ECP; and the Cascadia project for acoustic–gravity waves in tsunami modeling.

Continua with microstructure — gas bubbles in a liquid, or the rod-shaped molecules of a nematic liquid crystal — can be described below the macroscopic scale by a kinetic theory that extends the usual phase space with the generalized angular momenta of the ordered degrees of freedom. Such a unified kinetic theory for ordered fluids has recently been developed (Carrillo, Farrell, Medaglia & Zerbinati, A Kinetic Theory Approach to Ordered Fluids, arXiv:2508.10744), together with its conservation laws, H-theorem, and conditions for the emergence of collective order.

Solving the resulting kinetic equation is hard precisely because its distribution function lives on a high-dimensional phase space: position, translational velocity, orientation, and conjugate angular momentum, evolving in time. A deterministic grid discretisation incurs the curse of dimensionality, cost growing exponentially in the number of phase-space coordinates, and a nonlocal, quadratic collision integral on top. Direct Simulation Monte Carlo (DSMC) sidesteps both: it represents the distribution by computational particles, so statistical error decays like the inverse square root of the particle count independently of dimension, and it evolves collisions stochastically rather than integrating the full kernel.

We present an open-source Python implementation of a particle-based DSMC solvers on top of PETSc's DMSwarm and petsc4py, inheriting distributed-memory parallelism, particle migration across MPI ranks, and mesh management. A shared core Strang-split transport and collision, particle initialisation, and diagnostics supports interchangeable collision kernels (Nanbu, BGK, Bird's No-Time-Counter for a hard-needle cross-section), a cloud-in-cell mean-field Vlasov force, and an Andersen thermostat for canonical-ensemble runs. This is enough to resolve the coupled translational–orientational kinetics of calamitic particles and to recover the Onsager isotropic–nematic phase transition, while the same abstractions also solve the space-inhomogeneous Boltzmann equation. We discuss the software design that makes kinetic solvers composable and a suite of reproducible physics benchmarks.