A localized reduced basis approach for unfitted domain methods on parameterized geometries

This work introduces a reduced order modeling (ROM) framework for the solution of parameterized second-order linear elliptic partial differential equations formulated on unfitted geometries. The goal is to construct efficient projection-based ROMs, which rely techniques such as basis method and discrete empirical interpolation. presence geometrical parameters in domain discretizations entails challenges application standard ROMs. Therefore, this we propose methodology based (i) extension snapshots background mesh (ii) localization strategies decrease number functions. obtain computationally accurate, while it agnostic with respect underlying discretization choice. We test applicability proposed numerical experiments two model problems, namely Poisson elasticity problems. In particular, study several benchmarks two-dimensional, trimmed domains discretized splines observe significant reduction online computational cost compared ROMs same level accuracy. Moreover, show our three-dimensional geometry elastic problem.