Hierarchical Model Reduction Techniques for Flow Modeling in a Parametrized Setting

TL;DR

This paper compares two hierarchical model reduction techniques, based on proper orthogonal decomposition and greedy algorithms, for efficiently solving parametrized PDEs, demonstrating their effectiveness on 2D test cases.

Contribution

It introduces and compares two novel hierarchical model reduction methods for parametrized PDEs, highlighting their differences and performance.

Findings

Both methods effectively reduce computational complexity.

The approaches are validated on 2D scalar and vector test cases.

Preliminary results show promising accuracy and efficiency.

Abstract

In this work we focus on two different methods to deal with parametrized partial differential equations in an efficient and accurate way. Starting from high fidelity approximations built via the hierarchical model reduction discretization, we consider two approaches, both based on a projection model reduction technique. The two methods differ for the algorithm employed during the construction of the reduced basis. In particular, the former employs the proper orthogonal decomposition, while the latter relies on a greedy algorithm according to the certified reduced basis technique. The two approaches are preliminarily compared on two-dimensional scalar and vector test cases.