Work

On the effect of different samplings to the solution of parametric PDE eigenvalue problems

Year: 2024

Type: article

Abstract: The use of sparse sampling is a consolidated technique for the reduced order modeling of parametric PDEs. In this note we investigate the choice of sampling points within the framework of reduced order techniques for the approximation of eigenvalue problems originating from parametric PDEs. We use the standard proper orthogonal decomposition technique to obtain the basis of the reduced space and Galerkin orthogonal technique to get the reduced problem. We present some numerical results and observe that, as in the case of the source problem, also for eigenvalue problems the use of sparse sampling is a good idea and that, when the number of sampling points is assigned, sparse sampling provides better results than uniform sampling. In the spirit of the journal, we present our results in the form of examples and counterexamples.

Source: Examples and Counterexamples

DOI: 10.1016/j.exco.2024.100170

Authors: Daniele Boffi, Abdul Halim, Gopal Priyadarshi

Institutions: University of Pavia, King Abdullah University of Science and Technology, Memari College, Patliputra University

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $330

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", King Abdullah University of Science and Technology