LifeV - A Parallel Finite Element Library


LifeV (to be read Life Five) is an open source library for the numerical solution of partial differential equations with the finite element method. The choice of the finite element method is motivated by its rigorous mathematical background, with a sound control of the accuracy, coupled with excellent flexibility in managing complex geometries.

LifeV is written in C++ and is entirely coded with an Object Oriented approach and advanced programming features. The project started in 1999 from the collaboration of the Department of Mathematics at EPFL, Lausanne, Switzerland, of the Department of Mathematics at Politecnico di Milano, Italy and the INRIA Rocquencourt, France, under the supervision of Alfio Quarteroni. Nowadays, LifeV is concurrently developed and maintained by CMCS Lausanne (group coordinator), MOX di Milano, REO and ESTIME and the E(CM)2 group at the Department of Mathematics and Computer Science at Emory University, Atlanta (GA), USA.

As for now, the library includes solvers for incompressible fluid dynamics, (linear) structural problems, transport in porous media, fluid-structure interaction, electrical conduction in the heart. Even though this library is a research code oriented to the development and test of new numerical methods and algorithms, it is intended to be an effective tool for solving complex "real-life" engineering problems. One of the main field of applications (although not the only one) is cardiovascular mathematics.

The code is distributed under the LGPL license and is downloadable from the lifev-release repository.
There are two distributed versions of LifeV, one is parallel, for complex three dimensional engineering problems, the other is serial, for one, two and three dimensional problems (prototyping, testing). These pages review the parallel version.
For other details, see the LifeV web site.

Overview of LifeV

In the following we briefly describe the main features of LifeV.

Boundary Conditions

LifeV provides classes and methods to prescribe the most common boundary conditions (Dirichlet, Neumann, Robin). Normal and tangential boundary conditions are also allowed for vectorial (3D) fields. In addition, a few kinds of boundary conditions specific for flow problems are available. Boundary conditions are prescribed by modifying the system matrix and the right-hand side after the assembling phase. The parameters of the boundary condition can be defined as functions of the space and time, or as finite element fields. The regions where to apply boundary conditions are determined by markers associated to the boundary faces of the mesh. Boundary conditions settings are stored in the BCHandler class (BCHandler.hpp), whereas the file BCManage.hpp contains the routines used to prescribe the conditions. The BCInterface class (BCInterface.hpp) contains tools to set the boundary conditions directly from data files.

Time discretization

LifeV provides the class TimeAdvance to integrate in time a generic non-linear PDE with derivates in time of order m = 1, 2.
This class is a virtual class, that defines the main features of a generic time advancing scheme:

  • it stores the unknown and its first, and second if m=2, derivatives;
  • it provides methods for the extrapolation (in time) of the unknown, and of its first derivative if m=2 ;
  • it computes the right-hand side associated to the discretization of the first derivative, and of the second derivative if m=2;
  • it provides methods to update the states of the stored unknown.

The needed coefficients, variables and methods are specified in derived classes.
LifeV provides two different implementations, namely:

  • Backward Differentiation Formulae (BDF) schemes (TimeAdvanceBDF.hpp) of order p (with p<6) for m=1,2;
  • the family of methods obtained from the Newmark schemes for second order problems ( m=2), and the theta-methods for the first order problems (m=1) (TimeAdvanceNewmark.hpp).

Space discretization

LifeV provides classes to perform easily and quickly the assembly of the most common problems (e.g. advection-diffusion-reaction, Stokes and Navier-Stokes). These classes are called Assemblers and can be considered as building blocks that can be combined at will. The user has moreover access to lower level structures and instructions in order to provide the maximal flexibility.

Algebraic solvers and preconditioners

Linear systems are solved using the preconditioned GMRES method. LifeV provides the following preconditioners:

  • Additive Schwarz;
  • Multilevel Schwarz;
  • Multigrid preconditioner;

It is also possible to develop new preconditioners using the abstract class Preconditioner (Preconditioner.hpp).

Physical solvers

In the following we briefly mention all the available physical solvers.

  • Advection Diffusion Reaction solver: this solver (ADRAssembler.hpp) deals with the simplest PDE usually studied, but also maybe the most widely used. Indeed, this is the PDE that governs phenomena where diffusion, transport and reaction are relevant. This solver is used to solve this kind of problems in a simple and efficient manner. It can also deal with time-dependent PDEs.

  • Darcy solver: phenomenological law which describes the flow of a fluid through a porous medium. The implementation of the solver (DarcySolver.hpp) uses the dual-mixed-hybrid formulation, entailing good approximation of the velocity field as well as of the pressure field. The global system in saddle point form is recast to an equivalent positive definite system, using the hybridization and static condensation procedure. The finite element spaces used are piecewise constant for the pressure and lowest order Raviart-Thomas for the velocity.

  • 1D Fluid-Structure Interaction solver: a solver for the Euler equations for blood flow is available (OneDFSISolver.hpp). It is based on a second order Taylor-Galerkin scheme, featuring excellent control of the dispersion error. In its current implementation, it can be used to study the pressure pulse wave propagation in an artery, assuming that the blood behaves as a Newtonian fluid, while the arterial wall behaves as a linearly elastic or viscoelastic structure. The presence of tapering in the arterial geometry can also be taken into account.

  • 3D Fluid-Structure Interaction solver: the FSI model consists of Navier-Stokes equations coupled with an elasticity equation by imposing the continuity of the velocity and of the forces at the interface. In LifeV both partitioned and monolithic FSI solver are implemented. For the formers the coupling obtained with separate fluid and structure solver iterations, while for the latters the fully coupled matrix is assembled and solved using a single "monolithic" solver (FSIMonolithic.hpp). Concerning the partitioned strategies the available choices are Dirichlet-Neumann and Robin-Neumann fixed–point algorithms, or the Newton algorithm applied to the "Dirichlet-Neumann" fixed–point formulation. Various monolithic solver variants are obtained depending on the way the various nonlinearities (due mainly to the convective term of the fluid equations and to the domain motion) are treated. The main difference is among the geometric explicit (GE), for which the geometry is extrapolated from the previous time steps, and the geometric implicit (GI). Many parallel preconditioners for the monolithic problem are available, featuring the splitting of the matrix into several factors.

  • Heart electrophysiological solver: both bidomain (HeartBidomainSolver.hpp) and monodomain (HeartMonodomainSolver.hpp) models are available as models for the electrophysiology behavior of cardiac tissue. These models consist on anisotropic reaction-diffusion equations governing the propagation of electrical potentials, coupled with a system of ODEs describing the physics of the cellular membrane and time evolution of ionic quantities. Several variants for membrane models are already present in the library: Luo-Rudy phase I, Rogers-McCulloch and Mitchell-Schaeffer models. The solver currently employs piecewise linear finite elements for all involved fields in the coupling.

  • Venant-Kirchhoff solver: the structural model available in LifeV is a linear elastic constitutive law. It is the linear approximation of the nonlinear St. Venant-Kirchhoff model. It is implemented in the VenantKirchhoffSolver class (VenantKirchhoffSolver.hpp). It can be used both for purely structural dynamics problems (traction of a cube) or for coupled or multiscale problems. In fact, it has been integrated in the FSI (both segregated and monolithic) and in the Multiscale frameworks. At the moment, in the LifeV developers community there is a big effort to implement a general interface (i.e. a general solver) for solving structural mechanics problems. In particular, the efforts are focused on the implementation of other material laws and to exploit the general interface in the FSI and Multiscale frameworks.

Geometrical Multiscale Framework

The geometrical multiscale framework provides a general and abstract way to couple different dimensionally-heterogeneous physical solvers. In the framework, the local specific mathematical equations (partial differential equations, differential algebraic equations, etc.) and the numerical approximation (finite elements, finite differences, etc.) of the heterogeneous compartments are hidden behind generic operators. Consequently, the resulting global interface problem is formulated and solved in a completely transparent way. The coupling between models of different dimensional scale (three-dimensional, one-dimensional, etc.) and type (Navier–Stokes, fluid-structure interaction, etc.) is addressed writing the interface equations in terms of scalar quantities, i.e., area, flow rate, and mean (total) normal stress. In the resulting flexible framework the heterogeneous models are treated as black boxes, each one equipped with a specific number of compatible interfaces such that (i) the arrangement of the compartments in the network can be easily manipulated, thus allowing a high level of customization in the design and optimization of the global geometrical multiscale model, (ii) the parallelization of the solution of the different compartments is straightforward, leading to the opportunity to make use of the latest high-performance computing facilities, and (iii) new models can be easily added and connected to the existing ones.

At the present time the framework includes the following models

  1. Fluid3D
  2. FSI3D
  3. OneDimensional
  4. Multiscale
  5. Windkessel0D

which can be coupled through the following interface equations (or just closed by boundary conditions)

  1. BoundaryCondition
  2. MeanNormalStress
  3. MeanNormalStressArea
  4. MeanNormalStressValve
  5. MeanTotalNormalStress
  6. MeanTotalNormalStressArea

while the interface problem can be solved through the following algorithms

  1. Aitken
  2. Broyden
  3. Explicit
  4. Newton


In the following we briefly describe some of the main tools inside the library.

  • Importers and Exporters: LifeV can input mesh files stored in some common formats encountered in this field: GMSH, Inria, Netgen, mesh++. LifeV is designed with large parallel simulations in mind, which are usually performed on high performance computing hardware. In many such cases, the low amount of memory per compute node requires a change in the workflow. LifeV allows to perform the mesh partitioning phase offline, on a workstation where memory isn't an issue and use this data later, during online simulations on modern supercomputers. For postprocessing, it's possible to save data in the following formats, using the common interface provided in Exporter.hpp:

    All of them are supported by ParaView, on which we rely for creating high quality visualizations.

  • Grammar parser for algebraic expression: the class Parser (Parser.hpp)provides a general interface to parse any simple algebraic function given as a string. This tool is based on Spirit which is a set of C++ libraries for parsing and output generation implemented as Domain Specific Embedded Languages (DSEL) using Expression Templates and Template Meta-Programming.


LifeV is available for download under the terms of the GNU Lesser General Public License.


LifeV can be downloaded from the LifeV downloads page. For additional documentation about the LifeV architecture please check the LifeV documentation page.

Mailing lists

We recommend that users and developers subscribe to the following mailing lists as appropriate.

LifeV contributors

LifeV is the joint collaboration between four institutions:

  • École Polytechnique Fédérale de Lausanne (CMCS), Switzerland;
  • Politecnico di Milano (MOX), Italy;
  • INRIA (REO, ESTIME), France;
  • Emory University (Math&CS), U.S.A.

The following people are active developers:

  • Alessandro Melani, MOX - Politecnico di Milano
  • Alessandro Veneziani, Math&CS - Emory University
  • Alessio Fumagalli, MOX - Politecnico di Milano
  • Antonello Gerbi CMCS - École Polytechnique Fédérale de Lausanne
  • Antonio Cervone, MOX - Politecnico di Milano
  • Carlo de Falco, MOX - Politecnico di Milano
  • Christian Vergara, MOX - Politecnico di Milano
  • Gianmarco Mengaldo, MOX - Politecnico di Milano
  • Guido Iori, MOX - Politecnico di Milano
  • Huanhuan Yang, Math&CS - Emory University
  • Laura Cattaneo, MOX - Politecnico di Milano
  • Luca Bertagna, Math&CS - Emory University
  • Luca Formaggia, MOX - Politecnico di Milano
  • Luca Pegolotti CMCS - École Polytechnique Fédérale de Lausanne
  • Lucia Mirabella, CFM Lab - Georgia Institute of Technology
  • Matteo Pozzoli, MOX - Politecnico di Milano
  • Mauro Perego, Sandia National Laboratories
  • Michel Kern, ESTIME - INRIA
  • Niccolò Dal Santo CMCS - École Polytechnique Fédérale de Lausanne
  • Nur Fadel, MOX - Politecnico di Milano
  • Simone Deparis, CMCS - École Polytechnique Fédérale de Lausanne
  • Simone Pezzuto, MOX - Politecnico di Milano
  • Tiziano Passerini, Math&CS - Emory University
  • Umberto Emanuele Villa, Lawrence Livermore National Laboratory

The following people are former developers:

  • Alexandra Moura, formerly at MOX, Politecnico di Milano
  • Alexis Aposporidis, formerly at Math&CS - Emory University
  • Andrea Manzoni, formerly at CMCS - École Polytechnique Fédérale de Lausanne
  • Andreas Fischle
  • Christoph Winkelmann, formerly at CMCS, École Polytechnique Fédérale de Lausanne
  • Christophe Prud'homme, formerly at CMCS, École Polytechnique Fédérale de Lausanne
  • Claudia Colciago, CMCS - École Polytechnique Fédérale de Lausanne
  • Cristiano Malossi, CMCS - École Polytechnique Fédérale de Lausanne
  • Daniele A. Di Pietro, formerly at CMCS, École Polytechnique Fédérale de Lausanne
  • Fabio Nobile, CMCS - École Polytechnique Fédérale de Lausanne
  • Federico Bonelli
  • Gilles Fourestey, formerly at CMCS - École Polytechnique Fédérale de Lausanne
  • Gwenol Grandperrin, CMCS - École Polytechnique Fédérale de Lausanne
  • Jean Bonnemain, CMCS - École Polytechnique Fédérale de Lausanne
  • Jean-Frédéric Gerbeau - REO, INRIA
  • Laura Iapichino, CMCS - École Polytechnique Fédérale de Lausanne
  • Lorenzo Tamellini, CMCS - École Polytechnique Fédérale de Lausanne
  • Marco Discacciati, formerly at CMCS, École Polytechnique Fédérale de Lausanne
  • Mariarita de Luca, formerly at MOX, Politecnico di Milano
  • Marta D'Elia, formerly at Math&CS - Emory University
  • Martin Prosi, formerly at MOX, Politecnico di Milano
  • Matteo Astorino, CMCS - École Polytechnique Fédérale de Lausanne
  • Matteo Lesinigo, CMCS - École Polytechnique Fédérale de Lausanne
  • Miguel Ángel Fernández - REO, INRIA
  • Nicola Parolini, MOX - Politecnico di Milano
  • Paolo Crosetto, CMCS - École Polytechnique Fédérale de Lausanne
  • Paolo Ferrandi, formerly at MOX - Politecnico di Milano
  • Radu Popescu, CMCS - École Polytechnique Fédérale de Lausanne
  • Ricardo Ruiz Baier, CMCS - École Polytechnique Fédérale de Lausanne
  • Samuel Quinodoz, CMCS - École Polytechnique Fédérale de Lausanne
  • Sara Minisini, formerly at MOX - Politecnico di Milano
  • Simone Cassani
  • Simone Rossi, CMCS - École Polytechnique Fédérale de Lausanne
  • Susanna Carcano, MOX - Politecnico di Milano
  • Toni Lassila, CMCS - École Polytechnique Fédérale de Lausanne
  • Tricerri Paolo, CMCS - École Polytechnique Fédérale de Lausanne
  • Vincent Martin, formerly at MOX - Politecnico di Milano
  • Zhen Wang, Math&CS - Emory University

For other questions and comments...

Please visit the LifeV web site.