Sie können Bookmarks mittels Listen verwalten, loggen Sie sich dafür bitte in Ihr SLUB Benutzerkonto ein.
Medientyp:
E-Artikel
Titel:
A systematic approach to reduced GLT
Beteiligte:
Barbarino, Giovanni
Erschienen:
Springer Science and Business Media LLC, 2022
Erschienen in:
BIT Numerical Mathematics, 62 (2022) 3, Seite 681-743
Sprache:
Englisch
DOI:
10.1007/s10543-021-00896-7
ISSN:
1572-9125;
0006-3835
Entstehung:
Anmerkungen:
Beschreibung:
AbstractThis paper concerns the spectral analysis of matrix-sequences that are generated by the discretization and numerical approximation of partial differential equations, in case the domain is a generic Peano–Jordan measurable set. It is observed that such matrix-sequences often present a spectral symbol, that is a measurable function describing the asymptotic behaviour of the eigenvalues. When the domain is a hypercube, the analysis can be conducted using the theory of generalized locally Toeplitz (GLT) sequences, but in case of generic domains, a different kind of matrix-sequences and theory has to be formalized. We thus develop in full detail the theory of reduced GLT sequences and symbols, presenting some application to finite differences and finite elements discretization for linear convection–diffusion–reaction differential equations.