Mohamed Hamdaoui: March 23, 2011

Energy Preserving POD based ROMs

Mohamed Hamdaoui, MAS Laboratory, Ecole Centrale Paris

Wednesday, March 23, 2:00 p.m. in the CERFACS conference room

Abstract:

Reduced order modelling is an expanding field of computational science. A ROM is an accurate and
low cost model used to approximate expensive functions that arise in various scientific fields. Among
the different methods to build a ROM, POD is a very popular method that relies, like other basis
methods, on the determination of a suited projection basis that minimizes the projection error.
Nevertheless, POD is not able to preserve the moments (energy for example) of the solutions it
approximates. A method (ePOD) to compute energy preserving coefficients for pre-computed POD
basis is developed and tested on the unsteady one dimensional heat equation for the conservation of
the H1 norm. The test case shows that the ePOD preserves the energy of the solutions while having
the same projection error as the POD method. An application of the method to a bidimensional
Navier-Stokes flow shows that the ePOD preserves the solutions H1 norm while having a similar
projection error to the POD method.