Project MATH-AMSUD-ANID 21-MATH-04
January 2021 - December 2021
Manuel Solano [P], Rodolfo Araya, Theophile Chaumont Frelet, Diego Paredes, Abner Poza, Frederic Valentin, Patrick Vega:
Efficient Off-LIne numerical Strategies for multi-query problems (EOLIS)
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.