Generalized Spectrum of Second Order Differential Operators

DOI10.1137/20M1316159zbMath1452.65066arXiv2002.00676MaRDI QIDQ5115709

Bjørn Fredrik Nielsen, Zdeněk Strakoš, Tomáš Gergelits

Publication date: 18 August 2020

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.00676

zbMATH Keywords

preconditioninggeneralized eigenvalue problemoperator spectrumsecond-order partial differential equations

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Boundary value problems for second-order elliptic equations (35J25) General topics in linear spectral theory for PDEs (35P05) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Preconditioners for iterative methods (65F08)

Related Items (4)

Numerical approximation of the spectrum of self-adjoint operators in operator preconditioning ⋮ Guaranteed two-sided bounds on all eigenvalues of preconditioned diffusion and elasticity problems solved by the finite element method. ⋮ Robust Superlinear Krylov Convergence for Complex Noncoercive Compact-Equivalent Operator Preconditioners ⋮ Accurate error estimation in CG

Uses Software

• FEniCS

Cites Work

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• Behavior of slightly perturbed Lanczos and conjugate-gradient recurrences
• An introduction to partial differential equations
• A robust multigrid method for isogeometric analysis in two dimensions using boundary correction
• Isogeometric Preconditioners Based on Fast Solvers for the Sylvester Equation
• Preconditioning by inverting the Laplacian: an analysis of the eigenvalues
• Robust Multigrid for Isogeometric Analysis Based on Stable Splittings of Spline Spaces
• Laplacian Preconditioning of Elliptic PDEs: Localization of the Eigenvalues of the Discretized Operator

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