Embedded domain Reduced Basis Models for the shallow water hyperbolic equations with the Shifted Boundary Method
Abstract
We consider fully discrete embedded finite element approximations for a shallow water hyperbolic problem and its reduced-order model. Our approach is based on a fixed background mesh and an embedded reduced basis. The Shifted Boundary Method for spatial discretization is combined with an explicit predictor/multi-corrector time integration to integrate in time the numerical solutions to the shallow water equations, both for the full and reduced-order model. In order to improve the approximation of the solution manifold also for geometries that are untested during the offline stage, the snapshots have been pre-processed by means of an interpolation procedure that precedes the reduced basis computation. The methodology is tested on geometrically parametrized shapes with varying size and position.
Cite
@article{arxiv.2201.09546,
title = {Embedded domain Reduced Basis Models for the shallow water hyperbolic equations with the Shifted Boundary Method},
author = {Xianyi Zeng and Giovanni Stabile and Efthymios N. Karatzas and Guglielmo Scovazzi and Gianluigi Rozza},
journal= {arXiv preprint arXiv:2201.09546},
year = {2022}
}