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 -