January 26th – Amina Benaceur: An improved reduced basis method for non-linear heat transfer

Amina Benaceur: January 26 at 3pm, A415 Inria Paris.

We address the reduced order modeling of parameterized transient non-linear and non-affine partial differential equations (PDEs). In practice, both the treatment of non-affine terms and non-linearities result in an empirical interpolation method (EIM) that may not be affordable although it is performed `offline’, since it requires to compute various nonlinear trajectories using the full order model. An alternative to the EIM that lessens its cost for steady non-linear problems has been recently proposed by Daversion and Prudhomme so as to alleviate the global cost of the `offline’ stage in the reduced basis method (RBM) by enriching progressively the EIM using the computed reduced basis functions. In the present work, we adapt the latter ideas to transient PDEs so as to propose an algorithm that solely requires as many full-model computations as the number of functions that span both the reduced basis and the EIM spaces. The computational cost of the procedure can therefore be substantially reduced compared to the standard strategy. Finally, we discuss possible variants of the present approach.

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