GEIM - Generalised Empirical Interpolation Method

The Generalised Empirical Interpolation Method was firstly presented in [16] and in literature several extension and additional studies are present. In this repository, the algorithm is implemented in OpenFOAM, to scalar field only.

There are 3 folders containing the version of the solver for scalar field:

• ScalarGEIM_Offline (generation of the magic function and points)

• ScalarGEIM_Online (online reconstruction of the field using synthetic data)

• ScalarTR-GEIM (online reconstruction of the field using synthetic data polluted by noise, regularised version)

Here we report the algorithm for scalar fields (without regularisation).

Tikhonov regularisation

As proved in [1], the GEIM algorithm is not robust in presence of random noise, hence stabilisation techniques are required. Following the work of [12] which adopts the Tikhonov regularisation to retrieve stability of the method, in this library this method is used to keep the error bounded and to retrieve robustness in presence of noisy data.