On the computation of a very large number of eigenvalues for selfadjoint elliptic operators by means of multigrid methods

DOI10.1016/S0021-9991(02)00043-8zbMath1016.65080MaRDI QIDQ1869854

Vincent Heuveline

Publication date: 28 April 2003

Published in: Journal of Computational Physics (Search for Journal in Brave)

zbMATH Keywords

numerical experimentsLanczos methodmultigrid methodeigenvalue problemsselfadjoint elliptic operators\(p\)-finite element methodQuantum billiards

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Estimates of eigenvalues in context of PDEs (35P15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

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Uses Software

• LAPACK
• HiFlow3
• Wesseling

Cites Work

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• Rational Krylov sequence methods for eigenvalue computation
• Asymptotic error expansion and Richardson extrapolation for linear finite elements
• The Lanczos phenomenon - An interpretation based upon conjugate gradient optimization
• A new look at the Lanczos algorithm for solving symmetric systems of linear equations
• Computing eigenvalues of very large symmetric matrices. An implementation of a Lanczos algorithm with no reorthogonalization
• Chaos in classical and quantum mechanics
• Isospectral plane domains and surfaces via Riemannian orbifolds
• Efficient solution of symmetric eigenvalue problems using multigrid preconditioners in the locally optimal block conjugate gradient method
• Integral equations. Theory and numerical treatment
• How to Implement the Spectral Transformation
• LAPACK Users' Guide
• The Spectral Transformation Lanczos Method for the Numerical Solution of Large Sparse Generalized Symmetric Eigenvalue Problems
• Predicting the Behavior of Finite Precision Lanczos and Conjugate Gradient Computations
• Parallel Implementation of the $hp$-Version of the Finite Element Method on a Shared-Memory Architecture
• Rate of Convergence Estimates for Nonselfadjoint Eigenvalue Approximations
• Spectral Approximation for Compact Operators
• Eigenmodes of Isospectral Drums
• Changing poles in the rational Lanczos method for the Hermitian eigenvalue problem
• Can One Hear the Shape of a Drum?
• Computational Variants of the Lanczos Method for the Eigenproblem
• Fully discrete \(hp\)-finite elements: Fast quadrature