Volume 53, pp. 113-216, 2020.
Block generalized locally Toeplitz sequences: theory and applications in the multidimensional case
Giovanni Barbarino, Carlo Garoni, and Stefano Serra-Capizzano
Abstract
In computational mathematics, when dealing with a large linear discrete problem (e.g., a linear system) arising from the
numerical discretization of a partial differential equation (PDE), knowledge of the spectral distribution of the associated matrix has proved to be
useful information for designing/analyzing appropriate solvers–-especially, preconditioned Krylov and multigrid solvers–-for the considered problem.
Actually, this spectral information is of interest also in itself as long as the eigenvalues of the aforementioned matrix represent physical quantities of interest,
which is the case for several problems from engineering and applied sciences (e.g., the study of natural vibration frequencies in an elastic material).
The theory of multilevel generalized locally Toeplitz (GLT) sequences is a powerful apparatus for computing the asymptotic spectral distribution of matrices
Full Text (PDF) [1.3 MB], BibTeX , DOI: 10.1553/etna_vol53s113
Key words
asymptotic distribution of singular values and eigenvalues, multilevel block Toeplitz matrices, multilevel block generalized locally Toeplitz matrices, numerical discretization of partial differential equations, finite differences, finite elements, isogeometric analysis, discontinuous Galerkin methods, tensor products, B-splines
AMS subject classifications
15A18, 15B05, 47B06, 65N06, 65N30, 65N25, 15A60, 15A69, 65D07
Links to the cited ETNA articles
[8] | Vol. 53 (2020), pp. 28-112 Giovanni Barbarino, Carlo Garoni, and Stefano Serra-Capizzano: Block generalized locally Toeplitz sequences: theory and applications in the unidimensional case |
ETNA articles which cite this article
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