FreeFEM++ Framework Webinar

The FreeFEM++ framework webinar took place online on June 25, 2026. The session presented FreeFEM++ as a high-level domain-specific language for finite-element multiphysics simulations, with emphasis on solver interfaces, PETSc integration, Exa-MA mini-apps, and roadmap items across WP1, WP3, WP5, and WP7.

1. Recording and Materials

Date: Thursday, June 25, 2026

Time: 14:09 CEST

Format: Online webinar

Recording: Zoom recording

Passcode: x^%Lz$2u

1.1. Slide Deck

Deck Presenter PDF

FreeFEM: a high-level DSL for multi-physics simulations

Pierre-Henri Tournier

2. Meeting Report

Presentation: FreeFEM: a high-level DSL for multi-physics simulations

Presenter: Pierre-Henri Tournier

Context: NumPEx / Exa-MA framework meeting

Main objective: identify FreeFEM capabilities, links with Exa-MA work packages, existing and future mini-apps, and concrete follow-up actions.

2.1. Participants Identified

  • Pierre-Henri Tournier

  • Christophe Prud’homme

  • Pierre Jolivet

  • Frederic Hecht

  • Isabelle Ramiere

  • Utpal Kiran

2.2. General Overview of FreeFEM

Pierre-Henri Tournier presented FreeFEM as a mature open-source high-level domain-specific language for finite element simulations.

FreeFEM is designed to stay close to the mathematical variational formulation while still giving access to efficient numerical backends. The main message was that FreeFEM allows rapid prototyping, teaching, and application development without losing access to high-performance solver infrastructure.

Key points:

  • FreeFEM is open source, distributed under LGPL 3.

  • It is written in C++ and supports distributed-memory parallelism with MPI.

  • It runs on Unix/Linux, Windows, macOS, smartphones, and supercomputers.

  • It provides a DSL close to finite element mathematics.

  • It has online documentation, a community forum, monthly developer/user meetings, FreeFEM days, and a YouTube channel.

  • The core development team includes Frederic Hecht, Pierre Jolivet, and Pierre-Henri Tournier.

  • Simon Legrand contributes to build system and CI/CD.

  • Pierre Marchand contributes to BEM-related developments.

  • Gerald Sadaka contributes to FreeVol / finite-volume aspects.

  • New developments are also supported by the ERC Synergy PSINumScat project, with research engineers and a postdoc.

2.3. Main Software Capabilities

The presentation highlighted the following FreeFEM capabilities:

  • PDEs in 2D and 3D, on curves, and on surfaces.

  • Simplicial meshes: segments in 1D, triangles in 2D, surface triangles in 3D, and tetrahedra in 3D.

  • In-house 2D unstructured mesh generation with bamg.

  • 2D anisotropic mesh adaptation.

  • 3D interfaces with TetGen, MMG, and ParMmg.

  • Finite element spaces: arbitrary order continuous Lagrange elements, Raviart-Thomas elements, Nedelec edge elements up to order 3, DG up to degree 4, and extension through C++ plugins.

  • Linear solvers: LU, Cholesky, Crout, CG, GMRES, UMFPACK, SuperLU, MUMPS, PETSc, and HPDDM through the parallel interface.

  • Nonlinear, time-dependent, optimization, and eigenvalue capabilities via PETSc/SLEPc: SNES, TS, TAO, EPS, and NEP.

  • Optimization libraries: IPOPT, NLopt, and PETSc TAO.

  • FEM-BEM coupling.

  • Time-dependent geometries and meshes.

  • C++ plugin mechanism for extending the language.

  • More than 600 examples.

2.4. PETSc, HPDDM, and Parallel Computing

The PETSc interface is a major strength of the FreeFEM ecosystem, largely thanks to Pierre Jolivet’s work.

The presentation showed how FreeFEM can move from a high-level variational form to matrix/vector access and PETSc-based parallel solution. The PETSc interface allows FreeFEM scripts to be used for prototyping and testing advanced methods while relying on scalable external solvers.

Important points:

  • FreeFEM can assemble variational forms and expose the corresponding linear algebra objects.

  • PETSc enables scalable parallel linear algebra and solver workflows.

  • FreeFEM can be used as a rapid prototyping layer for new domain decomposition methods.

  • Final high-performance implementations can then be pushed into PETSc/HPDDM when mature.

  • This workflow is particularly relevant for Exa-MA WP3.

2.5. Links with Exa-MA WP1: Discretization, Meshes, Adaptation

The WP1 discussion focused on meshes, finite element spaces, mesh adaptation, and high-order or wave-oriented mesh generation.

2.5.1. Current Capabilities

FreeFEM currently supports only simplicial meshes. For mesh generation and adaptation, it provides or interfaces with:

  • bamg for 2D unstructured mesh generation;

  • in-house 2D anisotropic adaptation tools;

  • TetGen, MMG, and ParMmg for 3D workflows;

  • Mshmet for metric computation.

2.5.2. D7.1 Benchmark

A D7.1 benchmark was presented for 3D heterogeneous linear elasticity in a hollow cylinder, with P1 and P3 discretizations.

The benchmark showed weak scaling results with increasing problem sizes. A key bottleneck was identified: initial mesh generation and partitioning are not scalable enough because the workflow currently relies on a global initial mesh.

This is an important Exa-MA point because it separates scalable solver/assembly behavior from non-scalable preprocessing steps.

2.5.3. Current WP1 Mini-App

The current identified WP1 mini-app is app-freefem-parmmg.

Its purpose is to test ParMmg performance for distributed anisotropic mesh adaptation on the Fichera corner.

2.5.4. WP1 Roadmap

The roadmap includes:

  • automatic generation of quasi-optimal non-uniform meshes for wave propagation;

  • identification of trapping, visible, and invisible regions using ray dynamics;

  • possible use of ray tracing on GPUs;

  • refinement of a posteriori estimators through ray-dynamics information;

  • implementation of curved elements, since only linear geometric elements are currently available.

2.6. Links with Exa-MA WP3: Solvers and Domain Decomposition

The WP3 link is particularly strong because FreeFEM developers are also involved in WP3 activities, especially through PETSc, HPDDM, and domain decomposition methods.

2.6.1. Role of FreeFEM for WP3

FreeFEM is useful for:

  • rapid setup of test cases for different physics;

  • prototyping of new domain decomposition algorithms;

  • testing PETSc/HPDDM and ffddm methods;

  • generating reproducible solver benchmarks;

  • exposing mathematical formulations and solver options in compact scripts.

2.6.2. D7.1 Maxwell Benchmark

A D7.1 benchmark was presented for time-harmonic second-order Maxwell equations in the unit cube, discretized with lowest-order Nedelec edge elements and solved with a nested two-grid optimized overlapping Schwarz preconditioner.

This benchmark is relevant for H(curl) discretizations, high-frequency wave problems, domain decomposition methods, scalability studies, and PETSc/HPDDM-based solver development.

2.6.3. Spectral Coarse Spaces for Waves

The presentation also showed results on spectral coarse spaces for waves, including a cobra cavity test case partitioned into 2916 subdomains.

The key point is that GenEO-like spectral coarse spaces can strongly reduce iteration counts for wave problems, but the coarse problem may become expensive at scale. This motivates further work on more efficient coarse spaces.

2.6.4. WP3 Roadmap

The WP3 roadmap includes:

  • rewrite of parallel data structures for distributed meshes and finite element spaces;

  • goal of moving from sequential to parallel scripts with minimal changes, for example by changing the mesh type from mesh to Dmesh;

  • ongoing work by P.-L. Bacq on these parallel data structures;

  • domain decomposition for coupled problems, including saddle-point systems from fluid-structure interaction;

  • mixed precision for GenEO, with adaptive strategies based on local condition number estimates;

  • PhD work of Tom Caruso on mixed precision;

  • improved GenEO-type domain decomposition preconditioners for H(curl) problems;

  • two-level domain decomposition for BEM discretizations of Helmholtz wave problems;

  • low-rank approximation for BEM, including hybrid cross approximation techniques through the Theia library, Htool-DDM, and FreeFEM.

2.7. Links with Exa-MA WP5: Optimization

FreeFEM has mature optimization capabilities and is interfaced with IPOPT, NLopt, and PETSc TAO.

It also includes shape and topology optimization toolboxes, especially for elastic structures, fluid mechanics, and PDE-constrained optimization.

A recent optimization book by Frederic Hecht, Gontran Lance, and Emmanuel Trelat provides FreeFEM scripts for PDE-constrained optimization.

2.7.1. Current WP5 Mini-App

The current identified WP5 mini-app is app-freefem-shape-opt-fem.

Purpose:

  • shape optimization;

  • volume-preserving constraint;

  • finite element discretization.

This app should be documented and made usable as an Exa-MA mini-app.

2.8. Links with Exa-MA WP7: Software, CI/CD, Packaging, Tooling

WP7-related points include software modernization and tooling.

2.8.1. CI/CD

FreeFEM’s CI/CD pipeline is being overhauled using GitHub Actions, with work by Simon Legrand.

2.8.2. CMake and Build System

FreeFEM is moving toward a modernized CMake build system for:

  • multi-platform compilation;

  • testing;

  • packaging.

This is important for Exa-MA reproducibility and deployment on supercomputers.

2.8.3. Debugger

A longer-term roadmap item is a FreeFEM debugger allowing users to pause the execution of a FreeFEM script, inspect FreeFEM variables, and improve the debugging experience for complex scripts.

2.9. Discussion Points

2.9.1. GPU Support

A question was raised about GPU support.

The conclusion is that there is currently no general FreeFEM GPU porting effort. The current FreeFEM workflow remains mostly CPU-oriented.

However, there are possible GPU-related directions:

  • ray tracing / ray dynamics on GPUs for wave-oriented mesh generation;

  • use of external backends such as PETSc/HPDDM where relevant;

  • possible future hybrid CPU/GPU mini-apps, but no clear action was decided.

2.9.2. StarPU

StarPU was mentioned as a possible direction, but no concrete FreeFEM/StarPU work plan was decided.

This should remain an open technical question unless a clear mini-app or runtime use case is identified.

2.9.3. HHO / HDG

The status of HHO / HDG support was raised.

The conclusion was not fully clear. It should be clarified whether:

  • HHO / HDG are already supported directly in FreeFEM;

  • they can be implemented through existing DG or plugin mechanisms;

  • a dedicated extension would be required;

  • there is a simple existing script that could be turned into a mini-app.

2.9.4. Variational Inequalities and Contact Mechanics

Isabelle Ramiere asked whether the GenEO / saddle-point preconditioning results could extend to variational inequalities, for example contact mechanics.

The answer was not definitive. The discussion suggested that:

  • the extension is not immediate;

  • additional mathematical work would be required;

  • contact mechanics could be a relevant follow-up topic;

  • this could become a PhD-level or postdoc-level research direction if aligned with Exa-MA priorities.

2.9.5. Radiative Transfer / Ray Tracing Mini-App

Christophe Prud’homme proposed considering a radiative transfer / ray tracing mini-app.

The idea would be to test computations involving many rays emitted in many directions, ray/surface interactions, topography or geometric complexity, scalability, and potentially hybrid CPU/GPU execution.

The proposed use case is not yet specified enough. It should be assessed with the FreeFEM team to determine whether it is a good Exa-MA mini-app and what exactly it would benchmark.

2.9.6. Definition and Packaging of FreeFEM Mini-Apps

A key discussion point was how to package FreeFEM mini-apps for Exa-MA.

The expectation is that an apps-freefem repository should contain, for each app:

  • FreeFEM scripts;

  • input data;

  • run instructions;

  • expected outputs;

  • figures or plots when relevant;

  • reference results;

  • performance/scalability metrics;

  • information on software dependencies;

  • deployment instructions for supercomputers.

Pierre Jolivet raised the question of what should be measured:

  • only selected timings, for example assembly or solver steps;

  • or the full FreeFEM workflow, including preprocessing, mesh partitioning, assembly, solver, and output.

This should be decided explicitly for each app.

2.9.7. Spack and Supercomputer Deployment

FreeFEM is available in Spack, but the current Spack formula does not appear to provide the PETSc-enabled configuration required for the intended Exa-MA supercomputer workflows.

Current practice on supercomputers is to rely on custom builds.

Issues to clarify:

  • how to update or use the FreeFEM Spack package with PETSc support;

  • whether separate builds are needed for real and complex PETSc scalar types;

  • how to handle the FreeFEM/PETSc plugin configuration;

  • what the recommended Spack practice is for this case.

Christophe Prud’homme proposed asking the Spack Slack channel about best practices for PETSc real/complex variants and FreeFEM packaging.

2.9.8. Mixed Precision Mini-App

Mixed precision was discussed as a promising Exa-MA mini-app direction.

The goal should not be only to switch some computations to single precision. The more interesting goal is to provide a certified or at least justified mixed-precision strategy.

Possible ingredients:

  • local factorization in single precision;

  • use of local condition number estimates;

  • adaptive choice of precision;

  • validation that the preconditioner is not damaged by reduced precision;

  • theoretical and numerical guarantees;

  • connection with HPDDM/PETSc and GenEO;

  • link with Tom Caruso’s PhD.

A possible mini-app name was mentioned: apps-freefem-mixed-precision.

2.10. Mini-Apps and Benchmarks

App / benchmark Status Exa-MA link Scientific / technical objective Stress point Contacts Next step

app-freefem-parmmg

Current / existing

WP1

Test ParMmg performance for distributed anisotropic mesh adaptation on the Fichera corner

Distributed mesh adaptation, scalability, preprocessing

Pierre-Henri Tournier; WP1 contacts; possibly A. Chabib

Document repository, scripts, data, expected outputs, and metrics

app-freefem-shape-opt-fem

Current / existing

WP5

Shape optimization with volume preservation using FEM

Optimization workflow, FreeFEM optimization toolboxes, IPOPT/NLopt/TAO links

Pierre-Henri Tournier; Frederic Hecht; WP5 contacts

Turn existing scripts into a reproducible Exa-MA app

3D heterogeneous elasticity hollow cylinder benchmark

Current benchmark / candidate app

WP1 / WP3

Weak scaling for P1/P3 discretizations on heterogeneous linear elasticity

Mesh generation, partitioning, assembly, solver, P1/P3 comparison

Pierre-Henri Tournier; Pierre Jolivet

Decide whether to promote from D7.1 benchmark to official app

Nearly incompressible elasticity with GenEO saddle-point preconditioner

Current result / candidate app

WP3

Robust GenEO domain decomposition for saddle-point problems

Heterogeneity, near incompressibility, saddle-point solvers, scalability

Pierre-Henri Tournier; Pierre Jolivet; Frederic Hecht

Clarify reproducibility package and expected benchmark metrics

Maxwell H(curl) D7.1 benchmark

Current benchmark / candidate app

WP3

Time-harmonic Maxwell equations with Nedelec elements and optimized Schwarz preconditioner

H(curl), wave problems, solver scalability, PETSc/HPDDM

Pierre Jolivet; Pierre-Henri Tournier

Decide whether to include as apps-freefem-maxwell or similar

Cobra cavity / spectral coarse spaces for waves

Current result / future app

WP3

Test GenEO-like spectral coarse spaces for high-frequency wave propagation

Wave propagation, coarse space size, scalability, iteration count reduction

Pierre-Henri Tournier; Pierre Jolivet; F. Nataf / E. Parolin links

Assess whether this is mature enough for an app

Mixed precision GenEO / HPDDM mini-app

Future / proposed

WP3

Evaluate adaptive mixed precision based on local condition numbers

Local factorizations, preconditioner robustness, theoretical guarantees

Pierre Jolivet; Pierre-Henri Tournier; Tom Caruso

Define minimal demonstrator and certification criteria

Radiative transfer / ray tracing mini-app

Future / exploratory

WP1 / WP3 / WP7

Test ray/surface interaction workflows with many rays and geometric complexity

Scalability, geometry, possible hybrid CPU/GPU execution

Christophe Prud’homme; Pierre-Henri Tournier; application owner TBD

Define physics, geometry, metrics, and whether FreeFEM is the right framework

Wave-oriented mesh adaptation using ray dynamics

Future / roadmap

WP1

Generate quasi-optimal non-uniform meshes for wave propagation using trapping/visible/invisible regions

Ray dynamics, a posteriori indicators, mesh adaptation

A. Chabib; Pierre-Henri Tournier

Clarify relation with app-freefem-parmmg and whether it becomes a separate app

Curved elements / high-order geometry app

Future / roadmap

WP1

Validate curved elements once implemented

Geometry approximation, high-order meshes, wave accuracy

Pierre-Henri Tournier; A. Chabib

Wait for implementation status; define validation case

Domain decomposition for coupled FSI saddle-point systems

Future / roadmap

WP3

Investigate DD strategies for coupled fluid-structure interaction

Coupled multiphysics, saddle-point systems, solver robustness

L. Spies; Pierre-Henri Tournier; Pierre Jolivet

Clarify app candidate and benchmark problem

GenEO for H(curl) problems

Future / roadmap

WP3

Improve GenEO-type DD preconditioners for H(curl) problems

Heterogeneities, topology, expensive coarse problem

Pierre-Henri Tournier; Pierre Jolivet

Identify benchmark and performance target

Two-level DD for BEM Helmholtz problems

Future / roadmap

WP3

Extend extended harmonic GenEO to BEM discretizations of wave problems

BEM, Helmholtz, two-level DD

E. Parolin; P. Marchand; Pierre-Henri Tournier

Decide whether it should become an Exa-MA app

Low-rank BEM / HCA app

Future / roadmap

WP3

Interface Theia in Htool-DDM and FreeFEM for hybrid cross approximation

Low-rank compression, BEM operators, memory/performance

I. Chollet; P. Marchand; Pierre-Henri Tournier

Clarify maturity and Exa-MA relevance

HHO / HDG example

Open / unclear

WP1 / WP3

Clarify whether HHO/HDG support can produce an app

Discretization support, implementation status

Pierre-Henri Tournier; Frederic Hecht; Pierre Jolivet

Clarify current support and possible example

StarPU-related FreeFEM app

Open / unclear

WP7 / runtime

Explore whether StarPU has a meaningful role in a FreeFEM workflow

Task runtime, hybrid execution

Christophe Prud’homme; Pierre-Henri Tournier

Keep open until a concrete use case is identified

2.11. Tasks and Action Items

# Task Owner(s) Target / comment

1

Finalize the official list of FreeFEM apps to track in the Exa-MA apps table

Christophe Prud’homme; Pierre-Henri Tournier

Include current apps and candidate/future apps.

2

Create or complete the apps-freefem repository structure

Pierre-Henri Tournier; WP7 support

Repository should include scripts, data, README, run instructions, expected outputs, plots, and performance metrics.

3

Document app-freefem-parmmg

Pierre-Henri Tournier

Include Fichera corner setup, ParMmg workflow, metrics, and scalability results.

4

Document app-freefem-shape-opt-fem

Pierre-Henri Tournier; Frederic Hecht

Reuse existing FreeFEM shape optimization scripts and make them reproducible for Exa-MA.

5

Decide whether the D7.1 3D elasticity benchmark becomes an official FreeFEM app

Pierre-Henri Tournier; Christophe Prud’homme

Important because it exposes the mesh generation/partitioning bottleneck.

6

Decide whether the D7.1 Maxwell H(curl) benchmark becomes an official FreeFEM app

Pierre Jolivet; Pierre-Henri Tournier

Candidate for WP3 solver and domain-decomposition benchmarking.

7

Define what each FreeFEM app should measure

Pierre Jolivet; Pierre-Henri Tournier; Christophe Prud’homme

Clarify kernel timings versus complete workflow timings.

8

Add standard benchmark metadata for each FreeFEM app

WP7; Pierre-Henri Tournier

Problem size, number of ranks, dofs, discretization, solver options, timings, output files.

9

Clarify GPU status and possible GPU-related routes

Pierre-Henri Tournier; Pierre Jolivet; Christophe Prud’homme

Current status: no general GPU effort. Possible routes: PETSc/HPDDM backends or ray tracing/ray dynamics.

10

Clarify whether StarPU is relevant for FreeFEM

Christophe Prud’homme; Pierre-Henri Tournier

No concrete direction decided yet. Needs a real use case.

11

Clarify HHO / HDG support in FreeFEM

Pierre-Henri Tournier; Frederic Hecht; Pierre Jolivet

Determine whether examples exist and whether they can become mini-apps.

12

Assess the radiative transfer / ray tracing mini-app idea

Christophe Prud’homme; Pierre-Henri Tournier

Define physics, geometry, expected outputs, scalability objective, and implementation route.

13

Clarify the Spack deployment strategy for FreeFEM on supercomputers

Pierre Jolivet; Pierre-Henri Tournier

Current Spack formula does not appear to support the needed PETSc-enabled workflow.

14

Ask the Spack community about PETSc real/complex variants

Christophe Prud’homme

Especially whether separate FreeFEM/PETSc builds are needed and how to package them.

15

Clarify FreeFEM builds with PETSc real and complex scalar types

Pierre Jolivet; Frederic Hecht; Pierre-Henri Tournier

Important for wave/Maxwell examples and PETSc plugin configuration.

16

Define the mixed-precision FreeFEM mini-app

Pierre Jolivet; Pierre-Henri Tournier; Tom Caruso

Candidate name: apps-freefem-mixed-precision.

17

Specify the certification/validation criteria for mixed precision

Pierre Jolivet; Tom Caruso

Need to show that reduced precision does not damage the preconditioner.

18

Identify which solver components can use single precision

Pierre Jolivet; Tom Caruso; Pierre-Henri Tournier

Likely focus: local factorizations and local condition-number-based strategies.

19

Follow up on GenEO / saddle-point preconditioners for variational inequalities and contact

Isabelle Ramiere; Pierre-Henri Tournier; Pierre Jolivet; Frederic Hecht

Potential mathematical research direction; not immediate.

20

Clarify the roadmap for parallel data structures and Dmesh

P.-L. Bacq; Pierre-Henri Tournier

Important for simplifying the transition from sequential to parallel FreeFEM scripts.

21

Clarify the roadmap for curved elements

Pierre-Henri Tournier; A. Chabib

Could become a WP1 validation app once implementation is mature.

22

Clarify the wave mesh adaptation / ray dynamics roadmap

A. Chabib; Pierre-Henri Tournier

Link with quasi-optimal non-uniform meshes and a posteriori estimators.

23

Assess whether BEM / Helmholtz / HCA developments should become Exa-MA apps

Pierre-Henri Tournier; P. Marchand; E. Parolin; I. Chollet

Future WP3 apps if maturity and reproducibility are sufficient.

24

Track FreeFEM CI/CD, CMake, packaging, and debugger work under WP7

Simon Legrand; Pierre-Henri Tournier

Relevant for reproducibility, deployment, and user-facing robustness.

25

Produce a concise summary of this meeting for the shared Google Doc

Pierre-Henri Tournier; Christophe Prud’homme

Include app table and task list.