Abstract
In this thesis, a new solution strategy based on stochastic Galerkin finite element method is introduced for the complete electrode model of electrical impedance tomography. The method allows writing an analytical approximation for the solution to the inverse problem of electrical impedance tomography in the setting of Bayesian inversion with the help of multivariate orthogonal polynomials. If the measurement setting, i.e., geometry, priors, etc., is known (well) in advance, most computations required by the introduced method can be performed and stored before the actual measurement. The formation of the approximative solution to the inverse problem, i.e., the posterior probability density, is practically free of charge once the measurements are available. Subsequently, estimates for the quantities of interest can typically be obtained by either minimizing an explicitly known polynomial or integrating a known analytical expression. In addition, some advances in the development of numerical solvers for parametric partial differential equations in the setting of generalized Polynomial Chaos and stochastic Galerkin finite element method are presented.
Original language  English 

Qualification  Doctor's degree 
Awarding Institution 

Supervisors/Advisors 

Publisher  
Print ISBNs  9789526063805 
Electronic ISBNs  9789526063812 
Publication status  Published  2015 
MoE publication type  G5 Doctoral dissertation (article) 
Keywords
 inverse problems
 electrical impedance tomography
 complete electrode model
 stochastic Galerkin finite element method
 generalized Polynomial Chaos
 stochastic spectral methods
 Bayesian inversion
 stochastic elliptic partial differential equations
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Leinonen, M. (2015). On applying stochastic Galerkin finite element method to electrical impedance tomography. Aalto University.