Localized Model Reduction for Parametric PDEs

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Volume Title

School of Science | Master's thesis

Date

2024-09-27

Department

Major/Subject

Applied Mathematics

Mcode

SCI3053

Degree programme

Master's Programme in Mathematics and Operations Research

Language

en

Pages

42

Series

Abstract

This thesis develops a method for approximately solving a parametric diffusion equation by combining techniques from local model order reduction and the reduced basis greedy method. The approach relies on partitioning the domain into subdomains where local approximation spaces can be constructed and later combined. The unknown boundary conditions on the local subdomains are handled with a boundary-to-interior mapping and an extended subdomain. A reduced basis greedy algorithm is used for the parameter dependence of the problem. Each approximation step is accompanied by error analysis. Numerical results show convergence of the error in agreement with the theoretical predictions.

Description

Supervisor

Hannukainen, Antti

Thesis advisor

Hannukainen, Antti

Keywords

partial differential equations, model order reduction, reduced basis, finite element method, local approximation, numerical methods

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