Preconditioning by inverting the Laplacian: an analysis of the eigenvalues

DOI10.1093/imanum/drm018zbMath1167.65066OpenAlexW2081066113MaRDI QIDQ3600854

Bjørn Fredrik Nielsen, Aslak Tveito, Wolfgang Hackbusch

Publication date: 6 February 2009

Published in: IMA Journal of Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1093/imanum/drm018

zbMATH Keywords

preconditioningsecond-order elliptic equationinverse Laplacianelliptic differential equations: eigenvalues

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Numerical computation of matrix norms, conditioning, scaling (65F35) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items (8)

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. ⋮ A Simple Formula for the Generalized Spectrum of Second Order Self-Adjoint Differential Operators ⋮ Generalized Spectrum of Second Order Differential Operators ⋮ An optimal preconditioned FFT-accelerated finite element solver for homogenization ⋮ Decomposition into subspaces preconditioning: abstract framework ⋮ Laplacian Preconditioning of Elliptic PDEs: Localization of the Eigenvalues of the Discretized Operator ⋮ Optimized sparse approximate inverse smoothers for solving Laplacian linear systems

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