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.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:ntnu-9732 |
| Date | January 2008 |
| Creators | Eftang, Jens Lohne |
| Publisher | Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, Institutt for matematiske fag |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
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