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 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.

Garoni, C., Manni, C., Pelosi, F., Serra-Capizzano, S., Speleers, H. (2014). On the spectrum of stiffness matrices arising from isogeometric analysis. NUMERISCHE MATHEMATIK, 127(4), 751-799 [10.1007/s00211-013-0600-2].

On the spectrum of stiffness matrices arising from isogeometric analysis

Garoni, C;Manni, C;Pelosi, F;Speleers, H
2014-08-01

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 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.
ago-2014
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/08 - ANALISI NUMERICA
English
Con Impact Factor ISI
Galerkin discretization; isogeometric analysis; spectral analysis; stiffness matrices
Garoni, C., Manni, C., Pelosi, F., Serra-Capizzano, S., Speleers, H. (2014). On the spectrum of stiffness matrices arising from isogeometric analysis. NUMERISCHE MATHEMATIK, 127(4), 751-799 [10.1007/s00211-013-0600-2].
Garoni, C; Manni, C; Pelosi, F; Serra-Capizzano, S; Speleers, H
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/121992
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