Section: New Software and Platforms

Platforms

FreeFem++ , http://www.freefem.org/ff++/

FreeFem++ is a PDE solver based on a flexible language that allows a large number of problems to be expressed (elasticity, fluids, etc) with different finite element approximations on different meshes. There are more than 2000 users, and on the mailing list there are 430 members. Among those, we are aware of at least 10 industrial companies, 8 french companies and 2 non-french companies. It is used for teaching at Ecole Polytechnique, Ecole Centrale, Ecole des Ponts, Ecole des Mines, University Paris 11, University Paris Dauphine, La Rochelle, Nancy, Metz, Lyon, etc. Outside France, it is used for example at universities in Japan (Tokyo, Kyoto, Hiroshima, there is a userguide FreeFem++ in japan), Spain (Sevilla, BCAM, userguide available in spanish), UK (Oxford), Slovenia, Switzerland (EPFL, ETH), China. For every new version, there are 350 regression tests, and we provide a rapid correction of reported bugs. The licence of FreeFem++ is LGPL.

Library for preconditioned iterative methods

In the project-team we develop a library that integrates the direction preserving and low rank approximation preconditioners for both approached factorizations and domain decomposition like methods. It will be available through FreeFem++ and also as a stand alone library, and we expect to have one version of this library available in 2014.

HPDDM , https://github.com/hpddm

HPDDM is an efficient implementation of various domain decomposition methods (DDM) such as one- and two-level Restricted Additive Schwarz methods, the Finite Element Tearing and Interconnecting (FETI) method, and the Balancing Domain Decomposition (BDD) method. These methods can be enhanced with deflation vectors computed automatically by the framework using methods developed by members of the team:

• Generalized Eigenvalue problems on the Overlap (GenEO), an approach first introduced in the PhD of Nicole Spillane.

• local Dirichlet-to-Neumann operators, an approach first introduced in a paper by Nataf et al. and recently revisited by Conen et al.

This code has been proven to be efficient for solving various elliptic problems such as scalar diffusion equations, the system of linear elasticity, but also frequency domain problems like the Helmholtz equation. A comparison with modern multigrid methods can be found in the thesis of Pierre Jolivet.

HPDDM is a header-only library written in C++11 with MPI and OpenMP for parallelism. While its interface relies on plain old data objects, it requires a modern C++ compiler: g++ 4.7.3 and above, clang++ 3.3 and above, icpc 15.0.0.090 and above. HPDDM has to be linked against BLAS and LAPACK (as found in OpenBLAS, in the Accelerate framework on OS X, in IBM ESSL, or in Intel MKL) as well as a direct solver like MUMPS, SuiteSparse, MKL PARDISO, or PaStiX. At compilation, just define before including HPDDM.hpp one of these preprocessor macros MUMPSSUB, SUITESPARSESUB, MKL_PARDISOSUB, or PASTIXSUB (resp. DMUMPS, DSUITESPARSE, DMKL_PARDISO, or DPASTIX) to use the corresponding solver inside each subdomain (resp. for the coarse operator). Additionally, an eigenvalue solver is recommended. There is an existing interface to ARPACK. Other (eigen)solvers can be easily added using the existing interfaces. For building robust two-level methods, an interface with a discretization kernel like FreeFem++ or Feel++ is also needed. It can then be used to provide, for example, elementary matrices, that the GenEO approach requires. As such HPDDM is not an algebraic solver, unless only looking at one-level methods. Note that for substructuring methods, this is more of a limitation of the mathematical approach than of HPDDM itself.