Laplacian Preconditioning of Elliptic PDEs: Localization of the Eigenvalues of the Discretized Operator

DOI10.1137/18M1212458zbMath1495.65212arXiv1809.03790WikidataQ114074289 ScholiaQ114074289MaRDI QIDQ5232290

Kent-André Mardal, Bjørn Fredrik Nielsen, Tomáš Gergelits, Zdeněk Strakoš

Publication date: 2 September 2019

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

Full work available at URL: https://arxiv.org/abs/1809.03790

zbMATH Keywords

Hall's theoremsecond order elliptic PDEsconvergence of the conjugate gradient methodeigenvalues of the discretized preconditioned problemnodal values of the coefficient functionpreconditioning by the inverse Laplacian

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Preconditioners for iterative methods (65F08)

Related Items (14)

Elimination of ringing artifacts by finite-element projection in FFT-based homogenization ⋮ 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 ⋮ Preconditioners for Krylov subspace methods: An overview ⋮ 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 ⋮ Accurate error estimation in CG ⋮ Decomposition into subspaces preconditioning: abstract framework ⋮ Block Preconditioning of Stochastic Galerkin Problems: New Two-sided Guaranteed Spectral Bounds ⋮ On the cost of iterative computations ⋮ Optimized sparse approximate inverse smoothers for solving Laplacian linear systems ⋮ Operator Splitting and Finite Difference Schemes for Solving the EMI Model

Uses Software

• FEniCS

Cites Work

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