ICIAM 2023 Tokyo  at Waseda University, Tokyo, Japan, August 20-25, 2023

10th International Congress on Industrial and Applied Mathematics

Mini Symposium

FreeFEM software package for finite element modeling of PDEs

Session Time & Room : 2E (Aug.22, 17:40-19:20) @E504

Abstract : FreeFEM is a software package for finite element computation and has been developing at the Laboratory of Jacques-Louis Lions, Sorbonne University for 25 years. The main feature of FreeFEM is having a domain specific language based on C++ grammar, which is designed to describe variational formulation of the partial differential equations and discretized matrices by using numerical quadrature on triangle and tetrahedral elements. Now it is drastically enhanced to perform large scale three dimensional computation using domain decomposition methods by linking with tetrahedral mesh generators and parallel linear solvers. FreeFEM allows us to tackle a new mathematical modeling and solution by expressing nonlinear weak formulation with surface and domain integration and by direct manipulation of finite element matrices.This mini-symposium focuses on recent advancement of FreeFEM and application in mathematical modeling.

Organizer(s) : Atsushi Suzuki, Takeshi Takaishi

Classification : 65-04, 65Fxx, 65Kxx, 65N30

Minisymposium Program :

01221 (1/1) : 2E @E504 [Chair: Atsushi Suzuki]

[02183] Phase field crack growth simulation using IPOPT package

Takeshi Takaishi (Musashino University)

Abstract : As the energy gradient flow equation of the Bourdin model, we introduced the time evolution model of irreversible crack growth by the phase field method. Its weak solution can be written in terms of variational inequalities, since it includes the irreversible crack state. Simulation results for this model with the IPOPT package in FreeFEM shows the energy dissipation process of crack growth precisely.

[02252] Direct factorization of indefinite matrix for constrained problem in finite element modeling

Atsushi Suzuki (RIKEN Center for Computational Science)

Abstract : Finite element computation of some physical problem with constraint uses a variational problem with Lagrange multipliers as dual variables. Physical constraints are supposed as incompressibility of the fluid, boundary conditions on internal interfaces, and so on. A linear system obtained by a discretization becomes indefinite and then the multifrontal method for parallelization of direct methods may suffer pseudo singularity of subproblems. Careful pivoting with keeping pair of primal and dual unknowns makes the factorization stable.

[02281] An easy-to-use framework for the density-based topology optimization of multiphysics systems written in FreeFEM-PETSc-ParMmg

Hao Li (Kyoto University)

Minghao Yu (China Academy of Engineering Physics)

Pierre Jolivet (LIP6, Sorbonne Universite)

Joe Alexandersen (University of Southern Denmark)

Atsushi Suzuki (Osaka University)

Shinji Nishiwaki (Kyoto University)

Abstract : Large-scale 3D topology optimization has been a big trend in the previous decade. However, it features a high computational cost, which may not always be available to general users. We constructed an easy-to-use and fully distributed framework written in FreeFEM-PETSc-ParMmg. We present various 2D and 3D benchmarks including a structural problem, a transient thermal cloaking design, and a thermal-fluidic problem.

[02204] Recent advances with FreeFEM in parallel and its interface to PETSc

Pierre Jolivet (CNRS)

Abstract : In this talk, I will present some new features of FreeFEM and its interface to PETSc and SLEPc. Coupled together, these libraries offer a flexible infrastructure to deal with coupled and/or high-dimensional systems, using MPI for distributed-memory parallelism. I will showcase some examples from fluid dynamics, radiative transfer, and boundary integral equations.