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Laplacian preconditioning of elliptic PDEs: Localization of the eigenvalues of the discretized operator
- 1.0501181 - ÚI 2020 RIV CZ eng K - Conference Paper (Czech conference)
Gergelits, Tomáš - Mardal, K.-A. - Nielsen, B. F. - Strakoš, Z.
Laplacian preconditioning of elliptic PDEs: Localization of the eigenvalues of the discretized operator.
SNA '19 - Seminar on numerical analysis. Ostrava: Institute of Geonics of the CAS, 2019 - (Blaheta, R.; Starý, J.; Sysalová, D.), s. 51-53. ISBN 978-80-86407-73-9.
[SNA´19 - Seminar on numerical analysis. Ostrava (CZ), 21.01.2019-25.01.2019]
Grant - others:GA ČR(CZ) GC17-04150J
Institutional support: RVO:67985807
Keywords : second order elliptic PDEs * preconditioning by the inverse Laplacian * eigenvalues of the discretized preconditioned problem * nodal values of the coefficient function * Hall’s theorem * convergence of the conjugate gradient method
OECD category: Pure mathematics
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.
Permanent Link: http://hdl.handle.net/11104/0293164
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