On the spectrum of stiffness matrices arising from isogeometric analysis

• Published in: Numerische Mathematik Vol. 127; no. 4; pp. 751 - 799
• Main Authors: Garoni, Carlo, Manni, Carla, Pelosi, Francesca, Serra-Capizzano, Stefano, Speleers, Hendrik
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-08-2014
• Subjects: Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematics; Mathematics and Statistics; Numerical Analysis; Numerical and Computational Physics; Simulation; Theoretical; 15A12; 15B05; 15A69; 41A15; 65N30; 65L10; 15A18
• ISSN: 0029-599X; 0945-3245
• DOI: 10.1007/s00211-013-0600-2

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.