We study the spectral properties of stiffnessmatrices 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.

On the spectrum of stiffness matrices arising from isogeometric analysis

Garoni, C.;SERRA CAPIZZANO, STEFANO;
2014-01-01

Abstract

We study the spectral properties of stiffnessmatrices 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.
2014
Isgeometric Analysis; Weyl spctral distribution; eig localization; conditioning
Garoni, C.; Manni, C.; Pelosi, F.; SERRA CAPIZZANO, Stefano; Speleers, H.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/1926722
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