# On applying stochastic Galerkin finite element method to electrical impedance tomography

Research output: Thesis › Doctoral Thesis › Collection of Articles

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**On applying stochastic Galerkin finite element method to electrical impedance tomography.** / Leinonen, Matti.

Research output: Thesis › Doctoral Thesis › Collection of Articles

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*On applying stochastic Galerkin finite element method to electrical impedance tomography*. Aalto University.

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TY - THES

T1 - On applying stochastic Galerkin finite element method to electrical impedance tomography

AU - Leinonen, Matti

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

KW - inverse problems

KW - electrical impedance tomography

KW - complete electrode model

KW - stochastic Galerkin finite element method

KW - generalized Polynomial Chaos

KW - stochastic spectral methods

KW - Bayesian inversion

KW - stochastic elliptic partial differential equations

KW - inversio-ongelmat

KW - impedanssitomografia

KW - täydellinen elektrodimalli

KW - stokastinen Galerkinin elementtimenetelmä

KW - yleistetty polynomikaaos

KW - stokastiset spektraalimenetelmät

KW - bayesiläinen inversio

KW - stokastiset elliptiset osittaisdifferentiaaliyhtälöt

KW - inverse problems

KW - electrical impedance tomography

KW - complete electrode model

KW - stochastic Galerkin finite element method

KW - generalized Polynomial Chaos

KW - stochastic spectral methods

KW - Bayesian inversion

KW - stochastic elliptic partial differential equations

M3 - Doctoral Thesis

SN - 978-952-60-6380-5

T3 - Aalto University publication series DOCTORAL DISSERTATIONS

PB - Aalto University

ER -

ID: 18407547