Combining proper orthogonal decomposition and residual estimates for fast time integration of PDEs

Maria-Luisa Rapun (1) , Filippo Terragni (2) , Jose-Manuel Vega (1)

1 UPM - Universidad Politécnica de Madrid
2 UC3M - Universidad Carlos III de Madrid [Madrid]

A method to accelerate time-dependent solvers is presented. The method is based on the combination of a numerical code and a Galerkin system in a sequence of alternate time intervals. The governing equations are Galerkin projected onto a set of modes, obtained by performing POD on sets of snapshots calculated by the numerical code. The reduced model is integrated until an a priori error estimate indicates that the approximation is no longer accurate. High order modes truncation instabilities are prevented using an estimate of the residual.

Mots clés: Reduced order models; proper orthogonal decomposition; Galerkin projection; Low dimensional dynamics

Domaines: Analyse numérique [math.NA]; Mécanique [physics]; Sciences de l'ingénieur [physics]

Maria-Luisa Rapun, Filippo Terragni, Jose-Manuel Vega. Combining proper orthogonal decomposition and residual estimates for fast time integration of PDEs. 2nd ECCOMAS Young Investigators Conference (YIC 2013), Sep 2013, Bordeaux, France. ⟨hal-00855915⟩