The incompressible Navier–Stokes equations are solved in a channel, using a Discontinuous Galerkin method over staggered grids. We study the structure and the spectral features of the matrices of the linear systems arising from the discretization. They are of block type, each block showing Toeplitz-like, band, and tensor structure at the same time. After introducing new tools to study Toeplitz-like matrix sequences with rectangular symbols, a quite complete spectral analysis is presented, with the target of designing and analyzing fast iterative solvers for the associated large linear systems. Promising numerical results are presented, commented, and critically discussed for elongated two- and three-dimensional geometries.

A matrix-theoretic spectral analysis of incompressible Navier–Stokes staggered DG approximations and a related spectrally based preconditioning approach

Mazza M.;Semplice M.;Serra Capizzano S.;
2021-01-01

Abstract

The incompressible Navier–Stokes equations are solved in a channel, using a Discontinuous Galerkin method over staggered grids. We study the structure and the spectral features of the matrices of the linear systems arising from the discretization. They are of block type, each block showing Toeplitz-like, band, and tensor structure at the same time. After introducing new tools to study Toeplitz-like matrix sequences with rectangular symbols, a quite complete spectral analysis is presented, with the target of designing and analyzing fast iterative solvers for the associated large linear systems. Promising numerical results are presented, commented, and critically discussed for elongated two- and three-dimensional geometries.
2021
2021
Mazza, M.; Semplice, M.; Serra Capizzano, S.; Travaglia, E.
File in questo prodotto:
File Dimensione Formato  
Mazza2021_AMatrixtheoreticSpectralAnalysis.pdf

non disponibili

Tipologia: Versione Editoriale (PDF)
Licenza: DRM non definito
Dimensione 2.87 MB
Formato Adobe PDF
2.87 MB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2120286
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 4
social impact