FELiScE

FELiScE (Finite Elements for Life Sciences and Engineering) is a parallel finite element library written in C++. The library provides an unified software environment for the development of state-of-the-art finite element solvers for the spatial discretization of partial differential equations (PDE) in 1D, 2D and 3D spatial dimensions. Several finite element interpolations are available. The current version handles mainly globally continuous approximations. Interfacial discontinuities can be incorporated via the Nitsche-XFEM unfitted mesh framework. Local arrays and linear algebra operations are implemented with the boost-uBLAS C++ template class library. The global (parallel) data structure and the (linear and non-linear) solvers are based on the PETSc package. The source code repository is maintained in gitlab.inria.fr.  The current stable solvers, motivated by the simulation of the cardiovascular and respiratory systems, are:

  • Fluid mechanics (incompressible flow): stabilized finite element methods  (SUPG/PSPG, CIP), Nitsche-XFEM, fictitious domain (with penalty or Lagrange multipliers), monolithic and fractional-step time-marching.
  • Solid mechanics: hyper-elastic solids, Reissner–Mindlin beam and shell models (MITC elements 2D and 3d), contact mechanics.
  • Electrophysiology: bi-domain and mono-domain models with different ionic dynamics.
  • Fluid-structure interaction: partitioned solution procedures (strongly coupled, semi-implicit and loosely coupled schemes), interfacing between fluid and solid solvers based on the PVM and ZeroMQ libraries.
  • Data assimilation: Luenberger observers and stabilized finite element methods for unique continuation problems.

The main users of FELiScE are the members (and former members) of COMMEDIA and members of the M3DISIM and SIMBIOTX project-teams.

Current developers:

  • M. Agbalessi (PhD COMMEDIA)
  • D. Corti (PhD COMMEDIA)
  • M.A. Fernández (DR COMMEDIA, scientific coordinator)
  • F. Lespagnol (PhD COMMEDIA and Politecnico di Milano)
  • M. Nechita (researcher TPI Roumanie)
  • O. Ruz (PhD COMMEDIA and M3DISIM)

Current users:

  • M. Champion (PhD COMMEDIA)
  • S. Costa (PhD COMMEDIA)
  • G. Delay (assistant professor Sorbonne Université)
  • J. Diaz (research engineer M3DISIM)
  • F. Gerosa (post-doc Stanford University)
  • F. Vergnet (assistant professor COMMEDIA)
  • N. Golse (PhD SIMBIOTX)
  • D. Lombardi (researcher COMMEDIA)
  • W. Liu (intern SIMBIOTX)
  • L. Papamanolis (intern SIMBIOTX)
  • L. Sala (post-doc SIMBIOTX)
  • I. Vignon-Clementel (DR SIMBIOTX)

Simulation gallery:

Micro-capsule in flow simulations: Incompressible Navier-Stokes equations (Eulerian) coupled with a thin-shell model (Lagrangian). The simulations are based on a Nitsche-XFEM unfitted mesh method.
        
Heart valve FSI simulations: Incompressible Navier-Stokes equations (ALE) and non-linear shell model. Fictitious domain method and a loosely coupled scheme. Left: Aortic valve. Right: EPYGON artificial valve.
        
FSI simulation of the mitral valve: Incompressible Navier-Stokes equations (ALE) and non-linear beam model. Fictitious domain method (with interfacial grad-div penalty) and a loosely coupled scheme. Left: Mitral regurgitation. Right: Ring correction.
         
Left Ventricle Hemodynamics: Incompressible Navier-Stokes equations (ALE) and reduced immersed surface modeling of valve dynamics. Left: Velocity. Right: Pressure.
          
Immersed FSI with contact: Incompressible Navier-Stokes equations (Eulerian) coupled with an immersed non-linear curved beam (Lagrangian). Left: Fictitious domain method (with interfacial grad-div penalty) and a loosely coupled scheme. Right: Nitsche-XFEM unfitted mesh method with a semi-implicit coupling scheme.
          
Incompressible Navier-Stokes equations (Eulerian) coupled with two immersed membranes (Lagrangian). The simulations are based on a Nitsche-XFEM unfitted mesh method.
          
Incompressible Navier-Stokes equations (Eulerian) coupled with two immersed membranes (Lagrangian). The simulations are based on a Nitsche-XFEM unfitted mesh method.
          
Incompressible Navier-Stokes equations in ALE formulation coupled with a non-linear shell (Reissner-Mindlin) model. Simulation performed with a Robin-Neumann explicit coupling scheme.
Incompressible Navier-Stokes equations in ALE formulation coupled with a linear shell (Reissner-Mindlin) model. Simulation performed with a Robin-Neumann explicit coupling scheme. Incompressible Navier-Stokes equations in ALE formulation coupled with non-linear elastodynamics (Saint-Venant-Kirchhoff material). Simulation performed with a generalized Robin-Neumann explicit coupling scheme.
          
Incompressible Navier-Stokes equations in ALE formulation coupled with non-linear elastodynamics (Saint-Venant-Kirchhoff material). Simulation performed with a generalized Robin-Neumann explicit coupling scheme.

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