# Projection-based reduced order models for a cut finite element method in parametrized domains

## TL;DR

This paper introduces a reduced order modeling approach based on CutFEM that efficiently handles large domain deformations without remeshing, enabling fast evaluations for parametrized elliptic and Stokes problems.

## Contribution

It combines embedded finite element methods with reduced order models to improve computational efficiency in parametrized domain problems, avoiding remeshing and reference domain complexities.

## Key findings

- Effective in linear elliptic problems
- Applicable to Stokes flow simulations
- Reduces computational costs significantly

## Abstract

This work presents a reduced order modelling technique built on a high fidelity embedded mesh finite element method. Such methods, and in particular the CutFEM method, are attractive in the generation of projection-based reduced order models thanks to their capabilities to seamlessly handle large deformations of parametrized domains. The combination of embedded methods and reduced order models allows us to obtain fast evaluation of parametrized problems, avoiding remeshing as well as the reference domain formulation, often used in the reduced order modelling for boundary fitted finite element formulations. The resulting novel methodology is presented on linear elliptic and Stokes problems, together with several test cases to assess its capability. The role of a proper extension and transport of embedded solutions to a common background is analyzed in detail.