Re: [Libmesh-users] Question regarding the algorithm used in TransientRBSystem

[David K. <dav...@ak...>]

On Sat, Mar 17, 2018 at 3:50 AM, 吴家桦Gauvain <cau...@gm...> wrote:

> Hi all,
>
> In order to know the details about the POD-Greedy algorithm implemented
> in TransientRBSystem for reduced basis construction, I referred to the
> paper
>
> *B. Haasdonk, M. Ohlberger, Reduced basis method for finite volume
> approximations of parametrized evolution equations, M2AN (Math. Model.
> Numer. Anal.) 42 (2) (2008) 277–302.*
>
> invoked by
>
> *A high-performance parallel implementation of the certified reduced basis
> method **David J. Knezevic , John W. Peterson b*
>
> when the TransientRBSystem is discussed. However, the algorithms proposed
> by the former are PCA with fixspace and the selection of time index
> associate with the largest error bound change. Neither of them mentions the
> POD, which makes me confused. Could anyone give me more information on
> the  POD-Greedy
> algorithm used in libmesh? Thanks in advance.
>


That paper by Haasdonk and Ohlberger is the main reference for POD-Greedy.
I guess PCA is equivalent to POD in this context. You can refer to this
paper <https://dspace.mit.edu/openaccess-disseminate/1721.1/61956> (Section
4.2) for another description of the approach.

David