A localized reduced basis approach for unfitted domain methods on parameterized geometries
arXiv:2212.11934 · doi:10.1016/j.cma.2023.115997
Abstract
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 on techniques such as the reduced basis method and discrete empirical interpolation. The presence of geometrical parameters in unfitted domain discretizations entails challenges for the application of standard ROMs. Therefore, in this work we propose a methodology based on i) extension of snapshots on the background mesh and ii) localization strategies to decrease the number of reduced basis functions. The method we obtain is computationally efficient and accurate, while it is agnostic with respect to the underlying discretization choice. We test the applicability of the proposed framework with numerical experiments on two model problems, namely the Poisson and linear elasticity problems. In particular, we study several benchmarks formulated on two-dimensional, trimmed domains discretized with splines and we observe a significant reduction of the online computational cost compared to standard ROMs for the same level of accuracy. Moreover, we show the applicability of our methodology to a three-dimensional geometry of a linear elastic problem.
arXiv comment35 pages, 19 figures, 5 tables. Preprint accepted in Computer Methods in Applied Mechanics and Engineering
References in corpus (17)
- Condition number analysis and preconditioning of the finite cell method
- The aggregated unfitted finite element method for elliptic problems
- Isogeometric Analysis on V-reps: first results
- A Localized Reduced-Order Modeling Approach for PDEs with Bifurcating Solutions
- CutIGA with Basis Function Removal
- A Reduced Basis approach for PDEs on parametrized geometries based on the Shifted Boundary Finite Element Method and application to a Stokes Flow
- A New Least Squares Stabilized Nitsche Method for Cut Isogeometric Analysis
- Reduction of Nonlinear Embedded Boundary Models for Problems with Evolving Interfaces
- A Reduced-Order Shifted Boundary Method for Parametrized incompressible Navier-Stokes equations
- Adaptive isogeometric analysis on two-dimensional trimmed domains based on a hierarchical approach
- A minimal stabilization procedure for Isogeometric methods on trimmed geometries
- Coupling of non-conforming trimmed isogeometric Kirchhoff-Love shells via a projected super-penalty approach
- Robust Numerical Integration on Curved Polyhedra Based on Folded Decompositions
- Embedded domain Reduced Basis Models for the shallow water hyperbolic equations with the Shifted Boundary Method
- Tensor train based isogeometric analysis for PDE approximation on parameter dependent geometries
- Discrete Empirical Interpolation and unfitted mesh FEMs: application in PDE-constrained optimization
- An a posteriori error estimator for isogeometric analysis on trimmed geometries