On the spectrum of stiffness matrices arising from isogeometric analysis |
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Authors: | Carlo Garoni Carla Manni Francesca Pelosi Stefano Serra-Capizzano Hendrik Speleers |
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Institution: | 1. Department of Science and High Technology, University of Insubria, Via Valleggio 11, 22100?, Como, Italy 2. Department of Mathematics, University of Rome ‘Tor Vergata’, Via della Ricerca Scientifica, 00133?, Rome, Italy 3. Department of Computer Science, University of Leuven, Celestijnenlaan 200A, 3001?, Heverlee (Leuven), Belgium
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Abstract: | We study the spectral properties of stiffness matrices that arise in the context of isogeometric analysis for the numerical solution of classical second order elliptic problems. Motivated by the applicative interest in the fast solution of the related linear systems, we are looking for a spectral characterization of the involved matrices. In particular, we investigate non-singularity, conditioning (extremal behavior), spectral distribution in the Weyl sense, as well as clustering of the eigenvalues to a certain (compact) subset of \(\mathbb C\) . All the analysis is related to the notion of symbol in the Toeplitz setting and is carried out both for the cases of 1D and 2D problems. |
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