Olga Mula

A Generalized Empirical Interpolation Method: Application of Reduced Basis Techniques to Data Assimilation

This paper, written as a tribute to Enrico Magenes, a giant that has kindly and warmly supported generations of young researchers, introduces a generalization of the empirical interpolation method (EIM) and the reduced basis method (RBM) in order to allow their combination with data mining and data assimilation. The purpose is to be able to derive sound information from data and reconstruct information, possibly taking into account noise in the acquisition, that can serve as an input to models expressed by partial differential equations. The approach combines data acquisition (with noise) with domain decomposition techniques and reduced basis approximations.

Stabilization of (G)EIM in presence of measurement noise: application to nuclear reactor physics

The Empirical Interpolation Method (EIM) and its generalized version (GEIM) can be used to approximate a physical system by combining data measured from the system itself and a reduced model representing the underlying physics. In presence of noise, the good properties of the approach are blurred in the sense that the approximation error no longer converges but even diverges. We propose to address this issue by a least-squares projection with constrains involving a some a priori knowledge of the geometry of the manifold formed by all the possible physical states of the system. The efficiency of the approach, which we will call Constrained Stabilized GEIM (CS-GEIM), is illustrated by numerical experiments dealing with the reconstruction of the neutron flux in nuclear reactors. A theoretical justification of the procedure will be presented in future works.

The Parareal in Time Algorithm Applied to the Kinetic Neutron Diffusion Equation

The parareal in time algorithm is a time domain decomposition method for the approximation of transient problems. Its implementation in a parallel fashion allows for significant speed-ups in the computing time and opens the door to long time computations that involve accurate propagators. In this work, we first propose to overview the different strategies for the parallelization of the algorithm. We will then study the speed-up provided by parareal on a concrete example: the kinetic neutron diffusion equation in a nuclear reactor core. Implementations have been carried out with the MINOS solver, which is a tool developed at CEA in the framework of the APOLLO3Ⓡproject. As a conclusion, we will discuss the possibility of using neutron diffusion as a coarse propagator for neutron transport.

Greedy algorithms for optimal measurements selection in state estimation using reduced models

We consider the problem of optimal recovery of an unknown function

Sensor placement in nuclear reactors based on the generalized empirical interpolation method

u

The generalized Empirical Interpolation Method: stability theory on Hilbert spaces with an application to the Stokes equation

in a Hilbert space

Convergence analysis of the Generalized Empirical Interpolation Method

V

A priori convergence of the Generalized Empirical Interpolation Method.

from measurements of the form

The DUNE-DPG library for solving PDEs with Discontinuous Petrov–Galerkin finite elements

\ell_j(u)

Sensor placement in nuclear reactors

,