Spectral analysis of matrices in Galerkin methods based on generalized B-splines with high smoothness

DOI10.1007/s00211-016-0796-zzbMath1361.65049OpenAlexW2340560612MaRDI QIDQ504172

Fabio Roman, Hendrik Speleers, Carla Manni

Publication date: 25 January 2017

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/2318/1621468

zbMATH Keywords

Galerkin methodasymptotic eigenvalue distributiongeneralized B-splineshyperbolic and trigonometric GB-splines

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Linear boundary value problems for ordinary differential equations (34B05) Toeplitz, Cauchy, and related matrices (15B05)

Related Items (9)

Outlier-free spline spaces for isogeometric discretizations of biharmonic and polyharmonic eigenvalue problems ⋮ Generalized B-Splines in Isogeometric Analysis ⋮ ON INTERPOLATION BY ALMOST TRIGONOMETRIC SPLINES ⋮ Block Generalized Locally Toeplitz Sequences: Topological Construction, Spectral Distribution Results, and Star-Algebra Structure ⋮ Isogeometric discretizations with generalized B-splines: symbol-based spectral analysis ⋮ Block generalized locally Toeplitz sequences: theory and applications in the unidimensional case ⋮ Block generalized locally Toeplitz sequences: theory and applications in the multidimensional case ⋮ Block generalized locally Toeplitz sequences: from the theory to the applications ⋮ Application of optimal spline subspaces for the removal of spurious outliers in isogeometric discretizations

Cites Work

• Unnamed Item
• Unnamed Item
• On the spectrum of stiffness matrices arising from isogeometric analysis
• Finite element and NURBS approximations of eigenvalue, boundary-value, and initial-value problems
• Some estimates for \(h\)-\(p\)-\(k\)-refinement in isogeometric analysis
• Generalized B-splines as a tool in isogeometric analysis
• Isogeometric analysis in advection-diffusion problems: Tension splines approximation
• On unitarily invariant norms of matrix-valued linear positive operators.
• The GLT class as a generalized Fourier analysis and applications
• The asymptotic properties of the spectrum of nonsymmetrically perturbed Jacobi matrix sequences
• Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
• Unified and extended form of three types of splines
• Isogeometric analysis of structural vibrations
• The rate of convergence of Toeplitz based PCG methods for second order nonlinear boundary value problems
• Multi-iterative methods
• Analysis of preconditioning strategies for collocation linear systems
• Robust and optimal multi-iterative techniques for Iga Galerkin linear systems
• Robust and optimal multi-iterative techniques for Iga collocation linear systems
• \(GB\)-splines of arbitrary order
• Generalized locally Toeplitz sequences: Spectral analysis and applications to discretized partial differential equations
• Critical length for design purposes and extended Chebyshev spaces
• A unifying approach to some old and new theorems on distribution and clustering
• Isogeometric collocation methods with generalized B-splines
• On a class of weak Tchebycheff systems
• Superlinear Convergence of Conjugate Gradients
• Spectral analysis and spectral symbol of matrices in isogeometric collocation methods
• Symbol-Based Multigrid Methods for Galerkin B-Spline Isogeometric Analysis
• Spectral analysis and spectral symbol of matrices in isogeometric Galerkin methods
• Isogeometric Analysis
• V-cycle Optimal Convergence for Certain (Multilevel) Structured Linear Systems
• A note on the spectral distribution of toeplitz matrices
• The Theory of Generalized Locally Toeplitz Sequences: a Review, an Extension, and a Few Representative Applications
• Cardinal exponential splines: part I - theory and filtering algorithms
• Convergence Analysis of Krylov Subspace Iterations with Methods from Potential Theory

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