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.
|Translated title of the contribution||Stokastinen Galerkinin elementtimenetelmä impedanssitomografiassa|
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|Publication status||Published - 2015|
|MoE publication type||G5 Doctoral dissertation (article)|
- 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