A Hierarchical Low Rank Schur Complement Preconditioner for Indefinite Linear Systems
DOI10.1137/17M1143320zbMath1392.65027OpenAlexW2883768998MaRDI QIDQ3174789
Yousef Saad, Vassilis Kalantzis, Yuanzhe Xi, G. Dillon
Publication date: 18 July 2018
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/17m1143320
multileveldomain decompositionKrylov subspace methodsSchur complementslow rank approximationblock preconditionernested dissection ordering
Computational methods for sparse matrices (65F50) Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Iterative numerical methods for linear systems (65F10) Parallel numerical computation (65Y05) Preconditioners for iterative methods (65F08)
Related Items
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Hybrid reordering strategies for ILU preconditioning of indefinite sparse matrices
- Preconditioning Helmholtz linear systems
- Block preconditioning and domain decomposition methods. II
- A sparse matrix arithmetic based on \({\mathfrak H}\)-matrices. I: Introduction to \({\mathfrak H}\)-matrices
- Experimental study of ILU preconditioners for indefinite matrices
- On swapping diagonal blocks in real Schur form
- Preconditioning techniques for large linear systems: A survey
- A sparse \({\mathcal H}\)-matrix arithmetic. II: Application to multi-dimensional problems
- Preconditioning of discrete Helmholtz operators perturbed by a diagonal complex matrix
- A Note on Preconditioning Nonsymmetric Matrices
- An Algebraic Multilevel Preconditioner with Low-Rank Corrections for Sparse Symmetric Matrices
- Computing Partial Spectra with Least-Squares Rational Filters
- On the Stability of Some Hierarchical Rank Structured Matrix Algorithms
- A New Approximate Block Factorization Preconditioner for Two-Dimensional Incompressible (Reduced) Resistive MHD
- Divide and Conquer Low-Rank Preconditioners for Symmetric Matrices
- Block Preconditioners for Coupled Physics Problems
- Superfast and Stable Structured Solvers for Toeplitz Least Squares via Randomized Sampling
- Preconditioning discretizations of systems of partial differential equations
- On the purely algebraic data-sparse approximation of the inverse and the triangular factors of sparse matrices
- Fast Sparse Selected Inversion
- Schur complement-based domain decomposition preconditioners with low-rank corrections
- The university of Florida sparse matrix collection
- Fast algorithms for hierarchically semiseparable matrices
- Numerical solution of saddle point problems
- Why Finite Element Discretizations Can Be Factored by Triangular Hierarchical Matrices
- Spectral Analysis of the Discrete Helmholtz Operator Preconditioned with a Shifted Laplacian
- A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
- Orderings for Incomplete Factorization Preconditioning of Nonsymmetric Problems
- Parallel Preconditioning with Sparse Approximate Inverses
- Approximate Inverse Techniques for Block-Partitioned Matrices
- A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems
- Approximate Inverse Preconditioners via Sparse-Sparse Iterations
- A Note on Preconditioning for Indefinite Linear Systems
- An Approximate Minimum Degree Ordering Algorithm
- ILUM: A Multi-Elimination ILU Preconditioner for General Sparse Matrices
- Block preconditioners for finite element discretization of incompressible flow with thermal convection
- Matrix Reordering Using Multilevel Graph Coarsening for ILU Preconditioning
- A Rational Function Preconditioner For Indefinite Sparse Linear Systems
- A Flexible Inner-Outer Preconditioned GMRES Algorithm
- ARMS: an algebraic recursive multilevel solver for general sparse linear systems
- A Parallel Multistage ILU Factorization Based on a Hierarchical Graph Decomposition
- Algorithm 837
- A Novel Multigrid Based Preconditioner For Heterogeneous Helmholtz Problems
- Block Preconditioners Based on Approximate Commutators
- Nested Dissection of a Regular Finite Element Mesh
- The principle of minimized iterations in the solution of the matrix eigenvalue problem