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Managing data-movement for effective shared-memory parallelization of out-of-core sparse solvers

Haim Avron, Anshul Gupta
2012 2012 International Conference for High Performance Computing, Networking, Storage and Analysis  
We analyze the data-movement costs and memory versus parallelism trade-offs in a sharedmemory parallel out-of-core linear solver for sparse symmetric systems.  ...  We propose an algorithm that uses a novel memory management scheme and adaptive task parallelism to reduce the data-movement costs.  ...  Accordingly, we devised a memory management scheme for dynamically apportioning the available main memory between contribution and factor blocks, and a task parallelization strategy that self-adapts based  ... 
doi:10.1109/sc.2012.74 dblp:conf/sc/AvronG12 fatcat:xxkfgi3r5nhxriavrdab4n3m3e

New Parallel Sparse Direct Solvers for Multicore Architectures

Jonathan Hogg, Jennifer Scott
2013 Algorithms  
In the last few years, there have been many new developments, and a number of new modern parallel general-purpose sparse solvers have been written for inclusion within the HSL mathematical software library  ...  In this paper, we introduce and briefly review these solvers for symmetric sparse systems.  ...  his role as a co-author of HSL MA77 and HSL MA87 and for invaluable advice on Fortran.  ... 
doi:10.3390/a6040702 fatcat:7au67fmi5bcflgt3xtrmrfdfmu

The design and implementation of a new out-of-core sparse cholesky factorization method

Vladimir Rotkin, Sivan Toledo
2004 ACM Transactions on Mathematical Software  
For example, the code can factor AUDIKW, currenly the largest matrix in any matrix collection (factor size over 10 GB), in a little over an hour, and can factor a matrix whose graph is a 140-by-140-by-  ...  We describe a new out-of-core sparse Cholesky factorization method.  ...  Thanks to Didi Bar-David for configuring the operating system on the test machines and for telling us about zcav.  ... 
doi:10.1145/974781.974783 fatcat:aldqmfcgu5e35ea5tvlic4cldm

An out-of-core sparse Cholesky solver

John K. Reid, Jennifer A. Scott
2009 ACM Transactions on Mathematical Software  
The code, which is written in Fortran and called HSL MA77, implements a multifrontal algorithm. The first release is for positivedefinite systems and performs a Cholesky factorization.  ...  Indeed, the first author of this article wrote an out-of-core multifrontal solver for finite-element systems more than 20 years ago [Reid 1984] and the HSL mathematical software library [HSL 2007] has  ...  We are also grateful to Jean-Yves L'Excellent of LIP-ENS Lyon and Abdou Guermouche of LaBRI, Bordeaux, for helpful discussions on their work on the efficient implementation of multifrontal algorithms.  ... 
doi:10.1145/1499096.1499098 fatcat:ttt2ruuhn5h3tknywli5bx47oa

A direct finite element solver of linear complexity for large-scale 3-D circuit extraction in multiple dielectrics

Bangda Zhou, Haixin Liu, Dan Jiao
2013 Proceedings of the 50th Annual Design Automation Conference on - DAC '13  
Numerical experiments demonstrate a clear advantage of the proposed solver as compared with existing finite-element solvers that employ state-of-theart direct sparse matrix solutions.  ...  We develop a direct finite-element solver of linear (optimal) complexity to extract broadband circuit parameters such as S-parameters of arbitrarily shaped 3-D interconnects in inhomogeneous dielectrics  ...  both the multifrontal based solver and the H-matrix based solver.  ... 
doi:10.1145/2463209.2488906 dblp:conf/dac/ZhouLJ13 fatcat:trqgt2pv3rabpgnhgtmz4blwzy

A survey of direct methods for sparse linear systems

Timothy A. Davis, Sivasankaran Rajamanickam, Wissam M. Sid-Lakhdar
2016 Acta Numerica  
A glimpse of the breadth of applications relying on sparse solvers can be seen in the origins of matrices in published matrix benchmark collections (Duff and Reid 1979a , Duff, Grimes and Lewis 1989a ,  ...  Wilkinson defined a sparse matrix as one with enough zeros that it pays to take advantage of them. 1 This informal yet practical definition captures the essence of the goal of direct methods for solving  ...  Acknowledgments We would like to thank Iain Duff for his comments on a draft of this paper.  ... 
doi:10.1017/s0962492916000076 fatcat:u4dqyjkjqnelll5e3ywm7lqkca

Implementing Multifrontal Sparse Solvers for Multicore Architectures with Sequential Task Flow Runtime Systems

Emmanuel Agullo, Alfredo Buttari, Abdou Guermouche, Florent Lopez
2016 ACM Transactions on Mathematical Software  
Implementing multifrontal sparse solvers for multicore architectures with Sequential Task Flow runtime systems.  ...  Implementing multifrontal sparse solvers for multicore architectures with Sequential Task Flow runtime systems ACM Trans. Math.  ...  Faverge as well as the reviewers for their constructive suggestions on a preliminary version of this manuscript.  ... 
doi:10.1145/2898348 fatcat:mos5jdb5crfbffzzp4a3ut4yye

A fast direct solver for elliptic problems on general meshes in 2D

Phillip G. Schmitz, Lexing Ying
2012 Journal of Computational Physics  
Linear time complexity is shown for a quasi-regular grid and demonstrated via numerical results for the adaptive algorithm.  ...  We present a variant of that approach with additional hierarchical structure, extend it to quasi-uniform meshes, and detail an adaptive decomposition procedure for general meshes.  ...  Lexing Ying is also partially supported by a Sloan Research Fellowship.  ... 
doi:10.1016/j.jcp.2011.10.013 fatcat:dy766mrwrrfbbft2qigpddp7hi

Using Mixed Precision for Sparse Matrix Computations to Enhance the Performance while Achieving 64-bit Accuracy

Alfredo Buttari, Jack Dongarra, Jakub Kurzak, Piotr Luszczek, Stanimir Tomov
2008 ACM Transactions on Mathematical Software  
These ideas can be applied to sparse multifrontal and supernodal direct techniques and sparse iterative techniques such as Krylov subspace methods.  ...  By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many sparse linear algebra algorithms can be significantly enhanced while maintaining the 64-bit accuracy of the  ...  It forces the virtual memory system to swap pages to disk resulting in a considerable loss of performance.  ... 
doi:10.1145/1377596.1377597 fatcat:5hrp5k5zy5buzlksp6jgirwrxi

The Design of Sparse Direct Solvers using Object-Oriented Techniques [chapter]

Florin Dobrian, Gary Kumfert, Alex Pothen
2000 Lecture Notes in Computational Science and Engineering  
We describe our experience in designing object-oriented software for sparse direct solvers.  ...  While several direct solvers are currently available, most of them are designed as black b o xes"|di cult to understand and adapt to new situations.  ...  Finally, w e thank David Keyes for his enthusiasm and support.  ... 
doi:10.1007/978-3-642-57172-5_3 fatcat:mhkpgsfb4bfndndwr4dknywcta

Multifrontal parallel distributed symmetric and unsymmetric solvers

P.R. Amestoy, I.S. Duff, J.-Y. L'Excellent
2000 Computer Methods in Applied Mechanics and Engineering  
A new parallel distributed memory multifrontal approach is described.  ...  To handle numerical pivoting e ciently, a parallel asynchronous algorithm with dynamic scheduling of the computing tasks has been developed.  ...  Acknowledgment We w ould like to thank John Reid of the Rutherford Appleton Laboratory for helpful comments on an earlier draft.  ... 
doi:10.1016/s0045-7825(99)00242-x fatcat:gp4ugjqoejcfzjkl7hxzrw7m7e

Parallelising a simulator for the analysis of electromagnetic radiation using MUMPS library

R. Rico López, V. Escuder Cabañas, R. Durán Díaz, L.E. García-Castillo, I. Gómez-Revuelto, J.A. Acebrón
2009 Proceedings of the 4th International ICST Conference on Performance Evaluation Methodologies and Tools  
For factorising the matrix with MUMPS, two different ordering methods have been considered.  ...  After the analysis of a test case, two steps were carried out: firstly, a "hand-crafted" code parallelisation was developed within the kernel of the simulator.  ...  ACKNOWLEDGEMENTS As per usage conditions, we kindly acknowledge the use of HSL 2002 ( [2] ) as a tool to achieve part of the results reported in this paper.  ... 
doi:10.4108/icst.valuetools2009.7456 dblp:conf/valuetools/LopezCDGGA09 fatcat:y2ri6746e5hb3jmesnfcpufnj4

An out-of-core sparse symmetric-indefinite factorization method

Omer Meshar, Dror Irony, Sivan Toledo
2006 ACM Transactions on Mathematical Software  
We present a new out-of-core sparse symmetric-indefinite factorization algorithm. The most significant innovation of the new algorithm is a dynamic partitioning method for the sparse factor.  ...  This partitioning method results in very low I/O traffic and allows the algorithm to run at high computational rates, even though the factor is stored on a slow disk.  ...  ACKNOWLEDGMENTS Thanks to Anders Ekroth, Ismail Bustany, and Olaf Schenk for sending us test matrices. Thanks to Didi Bar-David for configuring the disks of the test machine.  ... 
doi:10.1145/1163641.1163645 fatcat:idwavqm6efh3tevbifeqtkcfwu

Fine-Grained Multithreading for the Multifrontal $QR$ Factorization of Sparse Matrices

Alfredo Buttari
2013 SIAM Journal on Scientific Computing  
This work describes a new parallelization strategy for the multifrontal QR factorization that is capable of achieving very high efficiency and speedup on modern multicore computers.  ...  This work presents an approach to the parallelization of the multifrontal method for the QR factorization of sparse matrices specifically designed for multicore based systems.  ...  Acknowledgments I wish to express my gratitude to the members of the MUMPS team for the countless advices they gave me on the implementation of multifrontal methods and to Chiara Puglisi for sharing with  ... 
doi:10.1137/110846427 fatcat:nvwrihy4tvhbzmfkepm74btdfi

Fast alternating bi-directional preconditioner for the 2D high-frequency Lippmann-Schwinger equation [article]

Leonardo Zepeda-Núñez, Hongkai Zhao
2016 arXiv   pre-print
This paper presents a fast iterative solver for Lippmann-Schwinger equation for high-frequency waves scattered by a smooth medium with a compactly supported inhomogeneity.  ...  The iterative solver has two levels, the outer level in which a sparsifying preconditioner for the Lippmann-Schwinger equation is constructed, and the inner level, in which the resulting sparsified system  ...  We would like to thank Lexing Ying, and Leslie Greengard for fruitful discussions; Antoine Cerfon for his help with the plasma example, and Laurent Demanet for computational resources.  ... 
arXiv:1602.07652v2 fatcat:l66i27pxvvcqxerqtlf3fas3ci
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