Section: Software

Simula+

Participant : Emmanuel Creusé [ correspondant ] .

See the web page http://www.lpmm.fr/collard/simula+.html

The project Simula+ involves the LAMAV laboratory of the Valenciennes and Hainaut-Cambrésis University (UVHC) and LPMM laboratory from University and engineering schools ENSAM and ENIM of Metz. The project Simula+ aims at constructing C++ libraries devoted to scientific computing.

The motivation of this project is to organize the sharing and development of numerical routines. The final goal is to reduce significantly the time that is necessary to write scientific codes, and instead use more time to develop original methods and simulate applied problems. More precisely, the library contains three kinds of routines :

• The MOL++ library. This library is composed of some basic procedures of numerical linear algebra (direct and iterative methods for large space linear systems). These routines are developed both by the LAMAV and the LPMM. The goal is not to develop a wide range of solvers (a lot of commercial and free codes already exist to do it), but to have the only needed “material” for the following applications we are interested in.

• The FEMOL++ library. This library is composed of some procedures related to mesh refinement, finite element calculations, and a posteriori error estimators. It is developed by the LAMAV. Once again, the goal is not to do the same as well-known commercial codes, but to develop a specific work. The partial differential equations to be solved come mainly from fluid mechanics problems. They are rather standard (Laplacian, Stokes, p- Laplacian), and the geometries of the domains are academic. The originality of this work relies on the a posteriori error estimators derivation, for conform as well as for non conform finite element methods, and for isotropic as well as for anisotropic meshes. This topic is a large part of the research made by E. Creusé and S. Nicaise. These estimators are proved to be efficient and reliable from the theoretical point of view. The FEMOL++ library allows to illustrate and to validate these theoretical results by numerical computations.

• The MateriOL++ library. This library is composed of some procedures relative to the modelling of the multi-physics behaviour of some intelligent materials. It is developed by the LPMM.

Simula+ is still used to illustrate some theoretical results about a posteriori error estimates (for example [30] ). Nevertheless, because of the recent leaving of several PhD students of the LAMAV laboratory previously involved in the development of Simula+, combined to the departure of E. Creusé from Valenciennes, functionalities should be from now developed in the GetFem++ software (author Yves Renard, INSA Lyon, see http://home.gna.org/getfem/ ). GetFem++ is, like Simula+, a C++ library which allows the use of a vast choice of finite elements for 2D and 3D simulations, and which is based on a complete linear algebra library (GMM++). The connection of this code to the SIMPAF project also relies on the fact that it will allow to develop several a posteriori error estimators related to fluid-mechanics problems. Moreover, finite element and mesh functionalities will naturally be used in the codes developed by the project. It is already the case for the C++ code developped for the simulation of the low-Mach number flows (see section 3.4).