A computational framework for certified reduced basis methods: applications to multiphysics problems

Vincent Chabannes (1) , Cécile Daversin (2) , Christophe Prud'Homme (3) , Abdoulaye Samake (1) , Christophe Trophime (2) , Stéphane Veys (1)

1 EDP - Equations aux Dérivées Partielles
2 LNCMI-G - Laboratoire national des champs magnétiques intenses - Grenoble
3 IRMA - Institut de Recherche Mathématique Avancée

Over the last few years we have been developing an open-source computational framework for certified reduced basis methods based on the Feel++ framework. The latter provides (i) a very wide range of arbitrary order Galerkin methods (fem, sem, cG, dG) in 1D, 2D and 3D (ii) an interface to modern linear algebra framework PETSc/SLEPc and Trilinos and (iii) a language embedded in C++ for Galerkin methods with a syntax following closely the mathematical one. Our recent advances in the former allow to (i) treat a wide range of problems as exercised later, (ii) provide an (almost) automated framework including the use of reduced basis element methods, hp reduced basis approximations, empirical interpolation method, the successive contraints methods, a posteriori error estimation for linear and non-linear parametrized partial differential equations.

Mots clés: certified reduced basis methods; reduced order modeling in multiphysics applications; automated computational framework

Domaines: Equations aux dérivées partielles [math.AP]

Vincent Chabannes, Cécile Daversin, Christophe Prud'Homme, Abdoulaye Samake, Christophe Trophime, et al.. A computational framework for certified reduced basis methods: applications to multiphysics problems. Eccomas'12 MS403-2 - Reduced order modeling strategies for parametrized PDEs, Sep 2012, Vienna, Austria. ⟨hal-00762449⟩