The theory of generalized locally Toeplitz (GLT) sequences is a powerful apparatus for computing the asymptotic spectral distribution of matrices Anarising from virtually any kind of numerical discretization of differential equations (DEs). Indeed, when the mesh fineness parameter n tends to infinity, these matrices Angive rise to a sequence (An)n, which often turns out to be a GLT sequence or one of its "relatives", i.e., a block GLT sequence or a reduced GLT sequence. In particular, block GLT sequences are encountered in the discretization of systems of DEs as well as in the higher-order finite element or discontinuous Galerkin approximation of scalar DEs. Despite the applicative interest, a solid theory of block GLT sequences has been developed only recently, in 2018. The purpose of the present paper is to illustrate the potential of this theory by presenting a few noteworthy examples of applications in the context of DE discretizations.

Block generalized locally Toeplitz sequences: From the theory to the applications

Mazza, Mariarosa;Serra-Capizzano, Stefano
2018-01-01

Abstract

The theory of generalized locally Toeplitz (GLT) sequences is a powerful apparatus for computing the asymptotic spectral distribution of matrices Anarising from virtually any kind of numerical discretization of differential equations (DEs). Indeed, when the mesh fineness parameter n tends to infinity, these matrices Angive rise to a sequence (An)n, which often turns out to be a GLT sequence or one of its "relatives", i.e., a block GLT sequence or a reduced GLT sequence. In particular, block GLT sequences are encountered in the discretization of systems of DEs as well as in the higher-order finite element or discontinuous Galerkin approximation of scalar DEs. Despite the applicative interest, a solid theory of block GLT sequences has been developed only recently, in 2018. The purpose of the present paper is to illustrate the potential of this theory by presenting a few noteworthy examples of applications in the context of DE discretizations.
2018
2018
www.mdpi.com/journal/axioms
B-splines; Curl-curl operator; Discontinuous Galerkin methods; Discretization of systems of differential equations; Finite difference methods; Generalized locally Toeplitz sequences; Higher-order finite element methods; Isogeometric analysis; Spectral (eigenvalue) and singular value distributions; Time harmonic Maxwell's equations and magnetostatic problems; Analysis; Algebra and Number Theory; Mathematical Physics; Logic; Geometry and Topology
Garoni, Carlo; Mazza, Mariarosa; Serra-Capizzano, Stefano
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2073479
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