Original title: Laplacian preconditioning of elliptic PDEs: Localization of the eigenvalues of the discretized operator
Authors: Gergelits, Tomáš ; Mardal, K.-A. ; Nielsen, B. F. ; Strakoš, Z.
Document type: Papers
Conference/Event: SNA´19 - Seminar on numerical analysis, Ostrava (CZ), 20190121
Year: 2019
Language: eng
Abstract: This contribution represents an extension of our earlier studies on the paradigmatic example of the inverse problem of the diffusion parameter estimation from spatio-temporal measurements of fluorescent particle concentration, see [6, 1, 3, 4, 5]. More precisely, we continue to look for an optimal bleaching pattern used in FRAP (Fluorescence Recovery After Photobleaching), being the initial condition of the Fickian diffusion equation maximizing a sensitivity measure. As follows, we define an optimization problem and we show the special feature (so-called complementarity principle) of the optimal binary-valued initial conditions.
Keywords: convergence of the conjugate gradient method; eigenvalues of the discretized preconditioned problem; Hall’s theorem; nodal values of the coefficient function; preconditioning by the inverse Laplacian; second order elliptic PDEs
Project no.: GC17-04150J (CEP)
Funding provider: GA ČR
Host item entry: SNA '19 - Seminar on numerical analysis, ISBN 978-80-86407-73-9

Institution: Institute of Computer Science AS ČR (web)
Document availability information: Fulltext is available in the digital repository of the Academy of Sciences.
Original record: http://hdl.handle.net/11104/0293164

Permalink: http://www.nusl.cz/ntk/nusl-391594


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