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A domain-decomposing parallel sparse linear system solver

Murat Manguoglu
2011 Journal of Computational and Applied Mathematics  
In this paper we introduce a new parallel hybrid sparse linear system solver for distributed memory architectures that contains both direct and iterative components.  ...  Comparisons to well-known direct and iterative solvers on a parallel architecture are provided.  ...  Acknowledgments The author would like to thank Ahmed Sameh, Ananth Grama, David Kuck, Eric Cox, Faisal Saied, Henry Gabb, Kenji Takizawa, and Tayfun Tezduyar for the numerous discussions and for their  ... 
doi:10.1016/j.cam.2011.07.017 fatcat:pghvfrrev5djxht5vljmbae3nm

Parallel Solution of Sparse Linear Systems [chapter]

Murat Manguoglu
2012 High-Performance Scientific Computing  
It is a well known fact that the cost of the simulation process is almost always governed by the solution of the linear systems especially for largescale problems.  ...  We presented two alternative variations of DS factorization based methods for solution of sparse linear systems on parallel computing platforms.  ...  Acknowledgements I would like to thank Ahmed Sameh, Ananth Grama, Faisal Saied, Eric Cox, Kenji Takizawa, Madan Sathe, Mehmet Koyuturk, Olaf Schenk, and Tayfun Tezduyar for their help and many useful discussions  ... 
doi:10.1007/978-1-4471-2437-5_8 fatcat:o5lcbme7tvfwdepmr7daf7gyma

Parallel preconditioning for spherical harmonics expansions of the Boltzmann transport equation

Karl Rupp, Tibor Grasser, Ansgar Jungel
2011 2011 International Conference on Simulation of Semiconductor Processes and Devices  
method which requires the solution of a linear system of equations.  ...  For the typically employed iterative solvers, preconditioners are required to obtain good convergence rates.  ...  The slightly larger number of solver iterations for third order expansions is due to the higher number of unknowns in the linear system.  ... 
doi:10.1109/sispad.2011.6034963 fatcat:sl3vpshbcne6nc6qzlsqbdf3jy

A GPU-Accelerated Parallel Preconditioner for the Solution of the Boltzmann Transport Equation for Semiconductors [chapter]

Karl Rupp, Ansgar Jüngel, Tibor Grasser
2012 Lecture Notes in Computer Science  
This work presents a parallel preconditioning scheme for a state-ofthe-art semiconductor device simulator and allows for the acceleration of the iterative solution process of the resulting system of linear  ...  The solution of large systems of linear equations is typically achieved by iterative methods.  ...  Execution times of the iterative BiCGStab solver are compared for a single CPU core using ILUT for the full system matrix, and for the proposed parallel scheme using multiple CPU cores of a quad-core Intel  ... 
doi:10.1007/978-3-642-30397-5_13 fatcat:huv3fhdtrfhs5ho3i3xxoh6dqm

A GPU-based preconditioned Newton-Krylov solver for flexible multibody dynamics

Radu Serban, Daniel Melanz, Ang Li, Ilinca Stanciulescu, Paramsothy Jayakumar, Dan Negrut
2015 International Journal for Numerical Methods in Engineering  
The implicit numerical integration method adopted relies on a Newton-Krylov methodology and a parallel direct sparse solver to precondition the underlying linear system.  ...  PRECONDITIONED NEWTON-KRYLOV SOLVER FOR FLEXIBLE MULTIBODY DYNAMICS 17 ¶ As discussed in section §5.1, although the cost of a preconditioner update is relatively high compared with that of a preconditioner  ...  ACKNOWLEDGEMENTS Financial support has been provided in part by a US Army TARDEC ARO grant under Contract No.  ... 
doi:10.1002/nme.4876 fatcat:jkjjpn3dtva2dboa4pyvjylm5u

ShyLU: A Hybrid-Hybrid Solver for Multicore Platforms

Sivasankaran Rajamanickam, Erik G. Boman, Michael A. Heroux
2012 2012 IEEE 26th International Parallel and Distributed Processing Symposium  
We present ShyLU, a "hybrid-hybrid" solver for general sparse linear systems that is hybrid in two ways: First, it combines direct and iterative methods.  ...  In the latter case, it should be used as a subdomain solver.  ...  ACKNOWLEDGMENT Sandia is a multiprogram laboratory operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin, for the United States Department of Energy's National Nuclear Security Administration  ... 
doi:10.1109/ipdps.2012.64 dblp:conf/ipps/RajamanickamBH12 fatcat:2asj5tfvgbecnn3ic62ycpylhe

Variable-Size Batched LU for Small Matrices and Its Integration into Block-Jacobi Preconditioning

Hartwig Anzt, Jack Dongarra, Goran Flegar, Enrique S. Quintana-Orti
2017 2017 46th International Conference on Parallel Processing (ICPP)  
sparse linear systems.  ...  The development of these kernels is motivated by the need for tackling this embarrasingly-parallel scenario in the context of block-Jacobi preconditioning that is relevant for the iterative solution of  ...  linear solvers" (d65).  ... 
doi:10.1109/icpp.2017.18 dblp:conf/icpp/AnztDFQ17 fatcat:sryw4eagnnf3zbuzllaxhm3ebm

On some parallel banded system solvers

Jack J. Dongarra, Ahmed H. Sameh
1984 Parallel Computing  
This paper describes algorithms for solving narrow banded systems and the Helmholtz difference equations that are suitable for multiprocessing systems.  ...  The organization of the algorithms highlight the large grain parallelism inherent in the problems.  ...  Acknowledgements We would like to thank the people at CRAY Research, especially Chris Hsiung and Tom Hewitt, for helping with the runs on the CRAY X-MP-4 and Ken Hillstrom at Argonne for help with the  ... 
doi:10.1016/s0167-8191(84)90165-0 fatcat:ecggvwwpxfhj5nnuqd7kie73zm

A tearing-based hybrid parallel banded linear system solver

Maxim Naumov, Ahmed H. Sameh
2009 Journal of Computational and Applied Mathematics  
A new parallel algorithm for the solution of banded linear systems is proposed.  ...  Our proposed algorithm is a hybrid scheme that combines direct and iterative methods for solving a single banded system of linear equations on parallel architectures.  ...  Conclusion In this paper we have developed a parallel hybrid algorithm for the solution of banded linear systems.  ... 
doi:10.1016/j.cam.2008.08.019 fatcat:7oppsjmakreyjjqsymrpszfxnm

Parallel iterative solvers for boundary value methods

P. Amodio, F. Mazzia
1996 Mathematical and computer modelling  
A parallel variant of the block Gauss-Seidel iteration for the solution of block-banded linear systems is presented.  ...  The parallel algorithm is applied to the solution of block-banded linear systems arising from the numerical discretization of initial value problems by means of Boundary Value Methods (BVMs).  ...  In [3] , a parallel variant of the block Gauss-Seidel iteration for tridiagonal systems is introduced and compared to multicoloring schemes for the solution of linear systems arising from PDEs.  ... 
doi:10.1016/0895-7177(96)00027-1 fatcat:g2ozorhwpnhevawddmporn4hgq

Recent advances in sparse linear solver technology for semiconductor device simulation matrices

O. Schenk, M. Hagemann, S. Rollin
2003 International Conference on Simulation of Semiconductor Processes and Devices, 2003. SISPAD 2003.  
This paper discusses recent advances in the development of robust direct and iterative sparse linear solvers for general unsymmetric linear systems of equations.  ...  Reliability, a low memory-footprint, and a short solution time are important demands for the linear solver. Currently, no black-box solver exists that can satisfy all criteria.  ...  SOLVERS FOR SPARSE LINEAR SYSTEMS OF EQUATIONS In this section the algorithms and strategies that are used in the direct and preconditioned iterative linear solvers in the numerical experiments are discussed  ... 
doi:10.1109/sispad.2003.1233648 fatcat:bevsymsdubcsrmtgeqk5r2mgse

Evaluation and FPGA Implementation of Sparse Linear Solvers for Video Processing Applications

Pierre Greisen, Marian Runo, Patrice Guillet, Simon Heinzle, Aljoscha Smolic, Hubert Kaeslin, Markus Gross
2013 IEEE transactions on circuits and systems for video technology (Print)  
In this work, we address sparse linear solvers for real-time video applications.  ...  We investigate several solver techniques, discuss hardware trade-offs, and provide FPGA architectures and implementation results of a Cholesky direct solver and of an iterative BiCGSTAB solver.  ...  SPARSE LINEAR SOLVERS There exists a variety of algorithms for solving linear systems [9] , [10] .  ... 
doi:10.1109/tcsvt.2013.2244797 fatcat:fpiw7zccbbcfflla3hevmq4fyi

Preface

John C. Butcher, Jeff R. Cash, Pieter J. van der Houwen
1993 Journal of Computational and Applied Mathematics  
Our final selection consists of eighteen papers which can be classified into four groups: analysis of (i) initial-value problem (IVP) solvers, (ii) boundary value problem (BVP) solvers, (iii) parallel  ...  Cash and Silva examine the efficiency of deferred correction based on mono-implicit RK methods for first-order systems of nonlinear two-point BVPs and in particular look at singular problems.  ...  and Paprzycki report numerical results of a new level 3 BLAS algorithm for almost block diagonal systems when implemented on a CRAY Y-MP.  ... 
doi:10.1016/0377-0427(93)90259-e fatcat:slzwy6kyxzcqjnbjb5klfxonce

A Robust Hierarchical Solver for Ill-conditioned Systems with Applications to Ice Sheet Modeling [article]

Chao Chen, Leopold Cambier, Erik G. Boman, Sivasankaran Rajamanickam, Raymond S. Tuminaro, Eric Darve
2018 arXiv   pre-print
A hierarchical solver is proposed for solving sparse ill-conditioned linear systems in parallel.  ...  As a result, the new solver achieves linear computational complexity under mild assumptions and excellent parallel scalability.  ...  ., for the U.S.  ... 
arXiv:1811.11248v2 fatcat:thimfc3zejfanmpellorz7jx7i

Low cost high performance uncertainty quantification

C. Bekas, A. Curioni, I. Fedulova
2009 Proceedings of the 2nd Workshop on High Performance Computational Finance - WHPCF '09  
Second, for this linear system we developed a novel, mixed precision, iterative refinement scheme, which uses iterative solvers instead of matrix factorizations.  ...  First, we turned to stochastic estimation of the diagonal. This allowed us to cast the problem as a linear system with a relatively small number of multiple right hand sides.  ...  Thomas Lippert and the Jülich Supercomputing Center for kindly granting access to their 72 rack BG/P cluster.  ... 
doi:10.1145/1645413.1645421 dblp:conf/sc/BekasCF09 fatcat:xsdwvupqc5gvnns5jcugixedrm
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