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Reduced Basis Methods for Partial Differential Equations : Evaluation of multiple non-compliant flux-type output functionals for a non-affine electrostatics problem

A method for rapid evaluation of flux-type outputs of interest from solutions to partial differential equations (PDEs) is presented within the reduced basis framework for linear, elliptic PDEs. The central point is a Neumann-Dirichlet equivalence that allows for evaluation of the output through the bilinear form of the weak formulation of the PDE. Through a comprehensive example related to electrostatics, we consider multiple outputs, a posteriori error estimators and empirical interpolation treatment of the non-affine terms in the bilinear form. Together with the considered Neumann-Dirichlet equivalence, these methods allow for efficient and accurate numerical evaluation of a relationship mu->s(mu), where mu is a parameter vector that determines the geometry of the physical domain and s(mu) is the corresponding flux-type output matrix of interest. As a practical application, we lastly employ the rapid evaluation of s-> s(mu) in solving an inverse (parameter-estimation) problem.

Identiferoai:union.ndltd.org:UPSALLA1/oai:DiVA.org:ntnu-9732
Date January 2008
CreatorsEftang, Jens Lohne
PublisherNorges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, Institutt for matematiske fag
Source SetsDiVA Archive at Upsalla University
LanguageEnglish
Detected LanguageEnglish
TypeStudent thesis, info:eu-repo/semantics/bachelorThesis, text
Formatapplication/pdf
Rightsinfo:eu-repo/semantics/openAccess

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