Are the eigenvalues of the B‐spline isogeometric analysis approximation of −Δu = λu known in almost closed form?

DOI10.1002/nla.2198OpenAlexW2883998123MaRDI QIDQ4558731

Stefano Serra Capizzano, Sven-Erik Ekström, Hendrik Speleers, Carlo Garoni, Isabella Furci, Carla Manni

Publication date: 29 November 2018

Published in: Numerical Linear Algebra with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/nla.2198

zbMATH Keywords

eigenvalues and eigenvectorsmass and stiffness matricesLaplacian eigenvalue problemisogeometric analysis and B-splinespolynomial interpolation and extrapolationspectral symbol and asymptotic eigenvalue expansion

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Extrapolation to the limit, deferred corrections (65B05) Numerical interpolation (65D05) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Toeplitz, Cauchy, and related matrices (15B05)

Related Items (8)

Exact formulae and matrix-less eigensolvers for block banded symmetric Toeplitz matrices ⋮ Asymptotic spectra of large (grid) graphs with a uniform local structure. II: Numerical applications ⋮ Fractional Laplace operator in two dimensions, approximating matrices, and related spectral analysis ⋮ A low-rank isogeometric solver based on Tucker tensors ⋮ Eigenvalues and eigenvectors of tau matrices with applications to Markov processes and economics ⋮ Analysis of the spectral symbol associated to discretization schemes of linear self-adjoint differential operators ⋮ A matrix-less method to approximate the spectrum and the spectral function of Toeplitz matrices with real eigenvalues ⋮ Fast Toeplitz eigenvalue computations, joining interpolation-extrapolation matrix-less algorithms and simple-loop theory

This page was built for publication: Are the eigenvalues of the B‐spline isogeometric analysis approximation of −Δu = λu known in almost closed form?