Localized Model Reduction for Parametric PDEs
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School of Science |
Master's thesis
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Authors
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, AnttiThesis advisor
Hannukainen, AnttiKeywords
partial differential equations, model order reduction, reduced basis, finite element method, local approximation, numerical methods