Journal ArticleDOI
Fine-Grained Parallel Incomplete LU Factorization
Edmond Chow,Aftab Patel +1 more
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TLDR
Numerical tests show that very few sweeps are needed to construct a factorization that is an effective preconditioner, and the amount of parallelism is large irrespective of the ordering of the matrix, and matrix ordering can be used to enhance the accuracy of the factorization rather than to increase parallelism.Abstract:
This paper presents a new fine-grained parallel algorithm for computing an incomplete LU factorization. All nonzeros in the incomplete factors can be computed in parallel and asynchronously, using one or more sweeps that iteratively improve the accuracy of the factorization. Unlike existing parallel algorithms, the amount of parallelism is large irrespective of the ordering of the matrix, and matrix ordering can be used to enhance the accuracy of the factorization rather than to increase parallelism. Numerical tests show that very few sweeps are needed to construct a factorization that is an effective preconditioner.read more
Citations
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Proceedings ArticleDOI
10M-core scalable fully-implicit solver for nonhydrostatic atmospheric dynamics
Chao Yang,Wei Xue,Haohuan Fu,Hongtao You,Xinliang Wang,Yulong Ao,Fangfang Liu,Lin Gan,Ping Xu,Lanning Wang,Guangwen Yang,Weimin Zheng +11 more
TL;DR: An ultra-scalable fully-implicit solver is developed for stiff time-dependent problems arising from the hyperbolic conservation laws in nonhydrostatic atmospheric dynamics and a highly efficient hybrid domain-decomposed multigrid preconditioner is proposed that can greatly accelerate the convergence rate at the extreme scale.
Journal ArticleDOI
ViennaCL---Linear Algebra Library for Multi- and Many-Core Architectures
Karl Rupp,Philippe Tillet,Florian Rudolf,Josef Weinbub,Andreas Morhammer,Tibor Grasser,Ansgar Jüngel,Siegfried Selberherr +7 more
TL;DR: This work presents the linear algebra library ViennaCL, which is built on top of all three programming models, thus enabling computational scientists to interface to a single library, yet obtain high performance for all three hardware types.
Book ChapterDOI
A Synchronization-Free Algorithm for Parallel Sparse Triangular Solves
TL;DR: This paper proposes a novel approach for SpTRSV in which the ordering between components is naturally enforced within the solution stage, and is an order of magnitude faster for the preprocessing stage than existing methods.
Book ChapterDOI
Iterative Sparse Triangular Solves for Preconditioning
TL;DR: This work proposes using an iterative approach for solving sparse triangular systems when an approximation is suitable, and demonstrates the performance gains that this approach can have on GPUs in the context of solving sparse linear systems with a preconditioned Krylov subspace method.
Journal ArticleDOI
Incomplete Sparse Approximate Inverses for Parallel Preconditioning
Hartwig Anzt,Hartwig Anzt,Thomas Huckle,Jürgen Bräckle,Jack Dongarra,Jack Dongarra,Jack Dongarra +6 more
TL;DR: A new preconditioning method that can be seen as a generalization of block-Jacobi methods, or as a simplification of the sparse approximate inverse (SAI) preconditionsers is proposed.
References
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Book
Iterative Methods for Sparse Linear Systems
TL;DR: This chapter discusses methods related to the normal equations of linear algebra, and some of the techniques used in this chapter were derived from previous chapters of this book.
Book
Iterative Solution of Nonlinear Equations in Several Variables
J.M. Ortega,Werner C. Rheinboldt +1 more
TL;DR: In this article, the authors present a list of basic reference books for convergence of Minimization Methods in linear algebra and linear algebra with a focus on convergence under partial ordering.
Journal ArticleDOI
An iterative solution method for linear systems of which the coefficient matrix is a symmetric -matrix
TL;DR: A particular class of regular splittings of not necessarily symmetric M-matrices is proposed, if the matrix is symmetric, this splitting is combined with the conjugate-gradient method to provide a fast iterative solution algorithm.
MonographDOI
Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators
Lloyd N. Trefethen,Mark Embree +1 more
TL;DR: In this article, the authors introduce pseudospectra and non-normal matrices, and describe the behavior of nonsymmetric eigenproblems in non-hermitian systems.
Journal ArticleDOI
A flexible inner-outer preconditioned GMRES algorithm
TL;DR: A variant of the GMRES algorithm is presented that allows changes in the preconditioning at every step, resulting in a result of the flexibility of the new variant that any iterative method can be used as a preconditionser.