More about the FEniCS project.

Register for the event: https://forms.monday.com/forms/7586258f2db5d4458f580960cf4685c4?r=euc1

Note: In person registration will close as the room reaches capacity.

The workshop lasts from September 8th at 12:30 until 17:30. Then begins again on the 9th from 9:00 until 13:00.

Programme

Tuesday, September 8

12:30 – 12:50: Registration and coffee

12:50 – 13:00: Opening remarks

13:00 – 15:00: FEniCS at Simula in the past and present

15:00 – 15:30: Break

15:30 – 17:30: FEniCS in academia part I

Wednesday, September 9

09:00 – 10:40: FEniCS in academia part II

10:40 – 11:00: Break

11:00 – 12:00: FEniCS in industry

12:00 – 13:00: Lunch, Simula, canteen 1st floor

Contact

Jørgen Dokken (dokken@simula.no)

Cécile Daversin-Catty (cecile@simula.no)

Ada Johanne Ellingsrud (ada@simula.no)

Eirik Valseth (eirikva@simula.no)

Abstracts

Joakim Sundes, Simula Research Laboratory 

From Diffpack to FEniCS: Scientific Software at Simula Research Laboratory

When Simula was established in 2001, the main tool for the Scientific Computing group was Diffpack, which had been developed through the 90s by Hans Petter Langtangen and Are Magnus Bruaset. Diffpack was at that time a well established tool, which everyone in the group knew well and used on a daily basis, making for a very productive research community. However, more modern ideas were emerging, and at that time Diffpack had been commercialized and was no longer open source. These factors created a strong motivation for developing something new, and ultimately drove Simula to become a key, foundational contributor to the FEniCS project. In this presentation we will look back at 25 years of scientific computing at Simula, highlighting the transition from the object-oriented C++ foundations of Diffpack to the automated code generation of FEniCS. Particular focus will be put on some of the groundbreaking ideas and key events that shaped the software development and continue to drive  modern, open-source computational science today.

Simon Funke,  (formerly) Simula Research Laboratory

How dolfin-adjoint made differentiating PDEs in FEniCS boring 

Derivatives of PDE simulations power optimisation, inverse problems, and data assimilation — but deriving adjoints by hand was often a research project in itself.

This talk shows how dolfin-adjoint can reduce their derivation to a one-liner by exploiting FEniCS's symbolic structure, and reflects on its impact.

Cécile Daversin-Catty, Simula Research Laboratory

Navigating Mixed Dimensions: the journey of the FEniCS mixed-dimensional framework

Mixed-dimensional partial differential equations (PDEs) are equations coupling fields defined over distinct domains that may differ in topological dimension. Such PDEs naturally arise in a wide range of fields including geology, bio-medicine, and fracture mechanics. The assembly of such systems is non-standard and non-trivial, and requires the design of both generic high level software abstractions and lower level algorithms. 

Historically, several external FEniCS-based libraries – such as fenics-ii and multiphenics – were dedicated to addressing these challenges, paving the way for a native mixed-dimensional framework implemented as a core feature of (legacy) FEniCS. This framework has since been ported to FEniCSx, taking advantage of the underlying upgrades in the library features and design. This talk discusses the evolution of the mixed-dimensional framework across the FEniCS ecosystem, illustrated by concrete applications in engineering and biomedicine.

Kent-Andre Mardal, Simula Research Laboratory 

TBA

TBA

Henrik Finsberg, Simula Research Laboratory

Computational cardiology at Simula: The past, the present and the future

For over a decade, Simula Research Laboratory has leveraged the FEniCS platform to push the boundaries of computational cardiology. This talk begins with a brief introduction to the foundational principles of cardiac modeling, outlining the core mathematical and physiological challenges of simulating the heart. We will then review our journey from early models to our current ecosystem of specialized libraries and modern FEniCSx workflows. Finally, we look ahead to the future, discussing how the next generation of finite element software will address emerging challenges in patient-specific modeling and clinical translation.

Thomas Surowiec, Simula Research Laboratory

TBA

TBA

Johan Hoffmann, KTH Royal Institute of Technology

FEniCS: Here, there and everywhere

This talk is a personal reflection on FEniCS from the origins to where we are today, with a specific focus on its relationship with Simula, which has been central to this story from the start. Over its 25 year history the FEniCS project has spanned a number of computing eras, from code generation, high performance computing, to cloud computing, and now AI. The project has also been a melting pot of mathematics, computer science, and applications, as well as academia and industry, which has contributed to its dynamic development. I will also discuss how FEniCS has impacted my own activities in research, education and industry, and how this, in turn, has shaped my engagement with the project over the years. In particular, I will share some recent results on turbulence which connect to questions posed already in my doctoral thesis, which also included the first version on DOLFIN developed together with Anders Logg. Finally, I will give my perspective on the future of FEniCS and our field. 

Padmini Rangamani, University of California San Diego 

Leveraging FEniCS for new discoveries in cellular physiology

All living cells use compartmentalized biochemical reactions to regulate their function.

Computational modeling has been used for many years now to not just explain experimental

observations but also to generate experimentally testable predictions. Spatiotemporal

modeling of cell signaling requires considerations of realistic cellular geometries and the ability to solve mixed-dimensional reaction-diffusion equations in such realistic geometries. In this brief talk, I will highlight how FEniCS is a powerful tool for simulating spatiotemporal dynamics of cellular signaling. I will demonstrate how such simulations have led to new predictions that were tested experimentally.

Chris Richardson, University of Cambridge

GPU journey: challenges for FEniCSx on future HPC systems

Future HPC systems are likely to be dominated by GPU devices, which offer greater computational efficiency than CPUs. Using GPUs is not always easy, and getting the best performance out of them is difficult. I will describe some of the work we have done on GPU in the last couple of years, and how this can translate to high performance codes which can run on HPC systems with many nodes, as well as some of the work which needs to be done to move things forward in the future.

Francesco Ballarin, Università Cattolica del Sacro Cuore

Projection-Based Reduced Order Modelling of Coupled Poromechanics Problems in FEniCSx

This presentation discusses projection-based reduced order modelling strategies for coupled poromechanics problems, with emphasis on their finite element implementation in FEniCSx. The methodology follows an offline-online paradigm. In the offline stage, high-fidelity finite element solvers are built in FEniCSx for monolithic and decoupled iterative formulations of coupled systems, including linear thermo-poroelasticity and Biot's consolidation model.

A first approach, introduced in [1], employs a fixed-stress splitting strategy for thermo-poroelasticity, where flow, heat, and mechanics subproblems are solved sequentially at each time step until convergence to the monolithic high-fidelity solution. A second approach, introduced in [2], extends this idea to a global-in-time iterative decoupled algorithm for the three-field Biot model, using BDF time discretization and sequential solution of diffusion and generalized Stokes-type subproblems over the full temporal interval.

Snapshot solutions generated from FEniCSx (as a high-fidelity solver) are compressed using proper orthogonal decomposition to construct reduced basis spaces for the physical variables. The online stage then applies a Galerkin projection onto these spaces, yielding reduced systems that preserve the structure of the original decoupled algorithms while substantially lowering the computational cost.

References:

[1] Francesco Ballarin, Sanghyun Lee, and Son-Young Yi. Projection-based reduced order modeling of an iterative scheme for linear thermo-poroelasticity. Results in Applied Mathematics, 21:100430, 2024. doi:10.1016/j.rinam.2023.100430.

[2] Huipeng Gu, Francesco Ballarin, Mingchao Cai, and Jingzhi Li. POD-based reduced order modeling of global-in-time iterative decoupled algorithms for Biot's consolidation model. SIAM Journal on Scientific Computing, in press, 2026. arXiv:2508.04082.

Remi Delaporte-Mathurin, MIT

FESTIM: a framework for hydrogen isotope transport on top of FEniCS

Hydrogen and its isotopes play a critical role across multiple fields: fusion energy applications require understanding tritium breeding and transport in blanket materials, aerospace engineering demands modelling of hydrogen embrittlement in structural components, and materials science relies on accurate predictions of hydrogen behaviour in components. Yet the complexity of multi-physics phenomena (diffusion, trapping, desorption, and thermal effects) has made this modelling challenging. For a long time, researchers had no open-source option; the landscape was dominated by closed-source/commercial tools with significant limitations (eg. restricted to single materials, limited to 1D geometries). In this presentation, I will discuss how FESTIM was built on top of FEniCS to address this critical gap and democratise access to sophisticated hydrogen transport modelling.

FEniCS provided the ideal foundation: its high-level Python API enabled rapid development without sacrificing performance, its powerful finite element abstractions handled complex geometries and multi-dimensional problems seamlessly, and its active community ensured long-term sustainability. By leveraging FEniCS, we could focus on domain-specific physics rather than low-level implementation details.

I will showcase FESTIM's capabilities through real applications, from benchmark problems in materials science to coupled tritium breeding blanket simulations, and discuss how the framework has evolved to support both academic research and industrial use cases. I will also reflect on the mutual benefits of this relationship: how FEniCS enabled FESTIM's success, and how FESTIM's requirements have informed improvements to FEniCS itself.

Robert Kirby, Baylor University

TBA

TBA

Hyunsun Alicia Kim, University of California San Diego 

Topology Optimization with FEniCS

Topology optimization provides a powerful framework for designing structures governed by complex physical behavior. In this talk, we will discuss how FEniCS has been used in our group to conduct research and develop topology optimization problems to new classes of engineering designs, including heat transfer, fluid mechanics, and solid mechanics. We will highlight examples involving nonlinear and transient responses, different objective and constraint functions, and coupled physical models, as well as recent work using multifidelity approaches to improve computational efficiency. FEniCS has been particularly valuable for rapidly developing finite element models for optimization thanks to its near-mathematical syntax of variational forms and support for automated derivative calculations. These capabilities are important for nonlinear problems, and more broadly for gradient-based optimization, where accurate and efficient sensitivities are particularly essential. The talk will conclude with perspectives on the role of automatic differentiation and enabling scalable topology optimization workflows towards the future engineering of complex systems.

David Ham, Imperial College London

The Unified Form Language: evolution and future

UFL, whose development was led by Martin Alnæs starting over 15 years ago, is the symbolic language for vector calculus at the heart of FEniCS, Firedrake and now other automated simulation systems. By representing weak forms symbolically, UFL enables automated reasoning: software that can combine symbolic mathematical manipulation with numerical computation. The original application of this was to automate the solution of PDEs, including generating the Jacobian. However, users were able to leverage this to automate new mathematical tasks, including the derivation and solution of adjoint equations, and the discovery of multiple solutions of nonlinear PDEs. The Unified Form Language itself has also been significantly extended: to support complex arithmetic, reasoning about temporal discretisations, dual spaces, and coupled  computations over subdomains. In recent years a foreign function interface has been added which enables two-way composition between UFL and other differentiable programming tools, including popular machine learning frameworks. At the same time, significant work has been occurring under the hood to modernise the software engineering underpinning the language and increase its composability and extensibility.

Susanne Claus, ONERA

From libCutFEM to CutFEMx: Cut Finite Element Methods in the FEniCS Ecosystem

Cut finite element methods allow standard finite element formulations to be posed on geometries and interfaces that cut through a background mesh. My work on this topic has been closely linked to the FEniCS project, starting with a research stay at Simula in 2013, which played an important role in the development of libCutFEM, a cut finite element library for legacy FEniCS co-authored with André Massing.

In this talk, I will present ongoing work towards a modular CutFEM ecosystem for FEniCSx. At its centre is CutFEMx (github.com/sclaus2/CutFEMx), which acts as the interface between DOLFINx and several specialized components: a library for automatic differentiation of level-set geometries with respect to spatial coordinates and geometric parameters, such as thicknesses or radii; CutCells for cut-cell decompositions and quadrature rules; and runintgen, a runtime code-generation backend for the assembly of variational forms on cut entities.

I will also discuss how this structure supports differentiable CutFEM workflows by combining automatic differentiation in UFL with automatic differentiation of parametrized level-set geometries. This will be illustrated with an application to parametric shape optimization of graded lattice structures, where the geometry is described implicitly and optimized through its defining parameters.

Jack S. Hale, University of Luxembourg

TBA

TBA

Jeremy Bleyer, Ecole nationale des ponts et chaussées

FEniCSx as a versatile tool for solid mechanics

FEniCSx has become a widely adopted prototyping tool for computational solid mechanics, with comprehensive numerical tours demonstrating its capabilities across linear elasticity, structural dynamics, homogenization, contact, and complex structural elements including beams, plates, and shells. However, a fundamental limitation has been the difficulty of expressing general constitutive models in the variational forms required by its domain-specific language.

Recent developments have overcome this barrier through integration with external libraries, including material behavior generators, machine learning frameworks with automatic differentiation capabilities, and optimization solvers. This extensibility allows researchers to implement complex nonlinear material models without being constrained by native UFL operators, establishing FEniCSx as a mature ecosystem that bridges classical finite element methods with modern computational approaches for rapid material model development and exploration.

Antonio Baiano Svizzero, Undabit

 FEniCSx in Industrial Vibroacoustic Simulation: Challenges, Solutions, and Real-World Applications

Vibroacoustic simulation is a critical tool in modern engineering, yet the industry remains heavily dominated by expensive commercial software with limited transparency and flexibility. While these tools offer polished workflows and broad adoption, they often fall short when it comes to customization, extensibility, and handling of complex or non-standard configurations. In this talk, I will present how Undabit has built a production-ready vibroacoustic simulation workflow on top of FEniCSx, directly competing with established commercial solutions. I will discuss the specific capabilities we have developed to bridge the gap (including Perfectly Matched Layers for unbounded domains and non-conforming mesh coupling) and show how these enable us to tackle real-world industrial problems with accuracy and efficiency. The talk will conclude with a showcase of industrial applications demonstrating FEniCSx in action.

Neeraj Cherukunnath, Rolls Royce

Towards Exa-scale Multi-physics Simulations of Aero-Engines

The companies in the aviation industry such as Rolls-Royce are currently focussing on how to achieve net-zero carbon emission targets by delivering maximum reduction in emissions from the aero-engines through various means like usage of sustainable aviation fuels, hydrogen, electrification, innovative new propulsion technologies, and other efficiency improvements. Numerical simulation and modelling, enabled by high performance computing, have transformed the way aero-engines are designed and engineered. A fully coupled Electro-Magneto-Thermo-Mechanical Finite Element Simulation capability in high performance computing environment will lead faster and better understanding of complex multi-physics behaviour of the future aero-engine technology. This talk will provide an overall summary of the recent collaborative projects with FEniCS development team in University of Cambridge. Rolls-Royce has started developing a multi-physics simulation framework in high performance computing environment using FEniCS code. The main computing platform that is being used for these projects is ARCHER2, the UK’s national supercomputer.

Martin Řehoř

TBA 

TBA