%0 Journal Article
%T Numerical Verification of Industrial Numerical Codes
%A Denis Christophe
%A Montan Sethy
%J ESAIM : Proceedings
%D 2012
%I EDP Sciences
%R 10.1051/proc/201235006
%X Several approximations occur during a numerical simulation: physical effects mapy be discarded, continuous functions replaced by discretized ones and real numbers replaced by finite-precision representations. The use of the floating point arithmetic generates round-off errors at each arithmetical expression and some mathematical properties are lost. The aim of the numerical verification activity at EDF R&D is to study the effect of the round-off error propagation on the results of a numerical simulation. It is indeed crucial to perform a numerical verification of industrial codes such as developped at EDF R&D even more for code running in HPC environments. This paper presents some recent studies around the numerical verification at EDF R&D. Le r¨¦sultat d¡¯un code de simulation num¨¦rique subit plusieurs approximations effectu¨¦es lors de la mod¨¦lisation math¨¦matique du probl¨¨me physique, de la discr¨¦tisation du mod¨¨le math¨¦matique et de la r¨¦solution num¨¦rique en arithm¨¦tique flottante. L¡¯utilisation de l¡¯arithm¨¦tique flottante g¨¦n¨¨re en effet des erreurs d¡¯arrondi lors de chaque op¨¦ration flottante et des propri¨¦t¨¦s math¨¦matiques sont perdues. Il existe ¨¤ EDF R&D une activit¨¦ transverse de v¨¦rification num¨¦rique consistant ¨¤ ¨¦tudier l¡¯effet de la propagation des erreurs d¡¯arrondi sur les r¨¦sultats des simulations. Il est en effet important de v¨¦rifier num¨¦riquement des codes industriels et ce d¡¯autant plus s¡¯ils sont ¨¦x¨¦cut¨¦s dans environnements de calcul haute performance. Ce papier pr¨¦sente des ¨¦tudes r¨¦centes autour de la v¨¦rification num¨¦rique ¨¤ EDF R&D.
%U http://dx.doi.org/10.1051/proc/201235006