Comparison of two-level preconditioners derived from deflation, domain decomposition and multigrid methods
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Publication:618454
DOI10.1007/s10915-009-9272-6zbMath1203.65073OpenAlexW2114535880MaRDI QIDQ618454
J. M. Tang, Reinhard Nabben, Kees Vuik, Yogi A. Erlangga
Publication date: 16 January 2011
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10915-009-9272-6
domain decompositionmultigriddeflationconjugate gradientstwo-level preconditioningSPD matricestwo-grid schemestwo-level PCG methods
Iterative numerical methods for linear systems (65F10) Preconditioners for iterative methods (65F08)
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Cites Work
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- Comparison of two-level preconditioners derived from deflation, domain decomposition and multigrid methods
- Efficient deflation methods applied to 3-D bubbly flow problems
- Fast and robust solvers for pressure-correction in bubbly flow problems
- Preconditioned conjugate gradients for solving singular systems
- Additive and multiplicative multi-grid -- a comparison
- An efficient preconditioned CG method for the solution of a class of layered problems with extreme contrasts in the coefficients
- Twofold deflation preconditioning of linear algebraic systems. I: Theory
- Analysis of acceleration strategies for restarted minimal residual methods
- On deflation and singular symmetric positive semi-definite matrices
- Generalized Augmented Matrix Preconditioning Approach and its Application to Iterative Solution of Ill-Conditioned Algebraic Systems
- On the Construction of Deflation-Based Preconditioners
- Deflation of Conjugate Gradients with Applications to Boundary Value Problems
- A Comparison of Two-Level Preconditioners Based on Multigrid and Deflation
- Balancing domain decomposition
- On the Conjugate Gradient Solution of the Schur Complement System Obtained from Domain Decomposition
- Necessary and Sufficient Conditions for the Existence of a Conjugate Gradient Method
- Recent computational developments in Krylov subspace methods for linear systems
- Additive and Multiplicative Two-Level Spectral Preconditioning for General Linear Systems
- A comparison of abstract versions of deflation, balancing and additive coarse grid correction preconditioners
- Robust domain decomposition algorithms for multiscale PDEs
- Multilevel Projection-Based Nested Krylov Iteration for Boundary Value Problems
- Damped Jacobi Preconditioning and Coarse Grid Deflation for Conjugate Gradient Iteration on Parallel Computers
- Iterative Methods by Space Decomposition and Subspace Correction
- An Iterative Solution Method for Linear Systems of Which the Coefficient Matrix is a Symmetric M-Matrix
- Multi-Level Adaptive Solutions to Boundary-Value Problems
- A Deflated Version of the Conjugate Gradient Algorithm
- A Comparison of Deflation and Coarse Grid Correction Applied to Porous Media Flow
- Balancing domain decomposition for problems with large jumps in coefficients
- The Construction of Preconditioners for Elliptic Problems by Substructuring. I
- Balancing Neumann-Neumann methods for incompressible Stokes equations
- Schwarz methods of neumann‐neumann type for three‐dimensional elliptic finite element problems
- A Restarted GMRES Method Augmented with Eigenvectors
- A Comparison of Deflation and the Balancing Preconditioner
- A Comparative Study of Iterative Solvers Exploiting Spectral Information for SPD Systems
- Methods of conjugate gradients for solving linear systems