Title: | On applying stochastic Galerkin finite element method to electrical impedance tomography Stokastinen Galerkinin elementtimenetelmä impedanssitomografiassa |
Author(s): | Leinonen, Matti |
Date: | 2015 |
Language: | en |
Pages: | 38 + app. 129 |
Department: | Matematiikan ja systeemianalyysin laitos Department of Mathematics and Systems Analysis |
ISBN: | 978-952-60-6381-2 (electronic) 978-952-60-6380-5 (printed) |
Series: | Aalto University publication series DOCTORAL DISSERTATIONS, 135/2015 |
ISSN: | 1799-4942 (electronic) 1799-4934 (printed) 1799-4934 (ISSN-L) |
Supervising professor(s): | Hyvönen, Nuutti, Prof., Aalto University, Department of Mathematics and Systems Analysis, Finland |
Thesis advisor(s): | Hyvönen, Nuutti, Prof., Aalto University, Department of Mathematics and Systems Analysis, Finland; Hakula, Harri, Dr, Aalto University, Department of Mathematics and Systems Analysis, Finland |
Subject: | Mathematics |
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, inversio-ongelmat, impedanssitomografia, täydellinen elektrodimalli, stokastinen Galerkinin elementtimenetelmä, yleistetty polynomikaaos, stokastiset spektraalimenetelmät, bayesiläinen inversio, stokastiset elliptiset osittaisdifferentiaaliyhtälöt |
Archive | yes |
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Abstract:Väitöskirjassa esitellään uusi stokastiseen Galerkinin elementtimenetelmään perustuva ratkaisutekniikka impedanssitomografian täydelliselle elektrodimallille. Tekniikka mahdollistaa analyyttisen approksimaation kirjoittamisen impedanssitomografian käänteisongelman bayesiläiselle ratkaisulle usean muuttujan ortogonaalipolynomien avulla. |
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Parts:[Publication 1]: Leinonen, M., Hakula, H., and Hyvönen, N. Application of stochastic Galerkin FEM to the complete electrode model of electrical impedance tomography. Journal of Computational Physics, Vol. 269, pp. 181–200, 2014. DOI:10.1016/j.jcp.2014.03.011 View at Publisher [Publication 2]: Hakula, H., Hyvönen, N., and Leinonen, M. Reconstruction algorithm based on stochastic Galerkin finite element method for electrical impedance tomography. Inverse Problems, Vol. 30 (6), 065006, 17 pp., 2014. DOI:10.1088/0266-5611/30/6/065006 View at Publisher [Publication 3]: Hyvönen, N., and Leinonen, M. Stochastic Galerkin finite element method with local conductivity basis for electrical impedance tomography. Accepted for publication in SIAM/ASA Journal on Uncertainty Quantification, 21 pp., 2015.[Publication 4]: Hakula, H., and Leinonen, M. On efficient construction of stochastic moment matrices. arXiv:1502.07562, 39 pp., 2015. |
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