EOLIS project

Efficient Off-LIne numerical Strategies for multi-query problems

About

The EOLIS project is a joint math-AMsud project between LNCC from Brazil, UDEC and UCSC from Chile, and Inria from France. This work proposes to design, implement and analyze novel preprocessing and postprocessing strategies for solving multi-query partial differential equation problems with finite element methods. By multi-query, we mean applications, such as inverse problems, optimal design or uncertainty quantification, that require a set of solution to the related PDE problems with different parameters. Instead of focusing on one particular PDE solve, we strive to reduce the computational cost for the whole set of PDE problems and focus on three main strategies: hp-adaptivity, multiscale modelling, and preconditioning. The design of nanostructures for light manipulation and the quantification of uncertainties associated with media fields on fluid flows will be the main benchmarks we consider

Events

February 2023: F. Valentin and A.T. Gomes gave a PhD course on multiscale hybrid-mixed methods in Nice.
January 2023: the EOLIS closing meeting took place online.
January 2023: R. Araya visited in Nice for two weeks.
January 2022: D. Paredes visited in Nice for three weeks.
December 2021: the EOLIS kickoff meeting took place online.

Publications

T. Chaumont-Frelet, A. Ern, S. Lemaire and F. Valentin,
Bridging the multiscale hybrid-mixed and multiscale hybrid high-order methods.
ESAIM Math. Model. Numer. Anal. 56 no. 1, pp 261-285. 2021.
preprint. doi.

Prepublications

T. Chaumont-Frelet, D. Paredes and F. Valentin,
Flux approximation on unfitted meshes and application to multiscale hybrid-mixed methods.
preprint.
D. Paredes, F. Valentin and H. Versieux,
Revisiting the robustness of the multiscale hybrid-mixed method: The face-based strategy.
preprint.
G.R. Barrenechea, A.T. Gomes and D. Paredes,
A Multiscale hybrid method.
preprint.
L. Camargo, B. López-Rodríguez, M. Osorio and M. Solano,
An adaptive and quasi-periodic HDG method for Maxwell’s equations in heterogeneous media.
preprint.

Members

Some members of the project in Conception in 2019.