An implementation of direct linear equation solver using a many-core CPU for mechanical dynamic analysis
This research proposes an effective implementation of linear equation solver for an implicit integration on a many-core CPU. Although this implementation is applied to a flexible body simulation in mechanical dynamics, it could be also utilized in a wide range of other fields. BFS-based nested disse...
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| Published in | Journal of mechanical science and technology Vol. 31; no. 10; pp. 4637 - 4645 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Seoul
Korean Society of Steel Construction
01.10.2017
Springer Nature B.V 대한기계학회 |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1738-494X 1976-3824 |
| DOI | 10.1007/s12206-017-0910-x |
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| Abstract | This research proposes an effective implementation of linear equation solver for an implicit integration on a many-core CPU. Although this implementation is applied to a flexible body simulation in mechanical dynamics, it could be also utilized in a wide range of other fields. BFS-based nested dissection and its numerical factorization enables adaptive control of setting operational range as well as positive parallelization compared with traditional DFS-based nested dissection. It brings better parallel efficiency when various sized separators are divided into blocks under a certain size. This study presents an experiment to identify an optimal maximum block size. Sparse matrices from mechanical dynamics software are numerically factorized, and the time results show that CACHE memory mode is appropriate for a better performance than FLAT mode. And it is recommended to split the operational region in accordance with MCDRAM size in this experiment. Our research shows fairly similar performance to DSS included in MKL and speeds up the time approximately 8 - 14 times in comparison with CHOLMOD, a part of SuiteSparse. |
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| AbstractList | This research proposes an effective implementation of linear equation solver for an implicit integration on a many-core CPU. Although this implementation is applied to a flexible body simulation in mechanical dynamics, it could be also utilized in a wide range of other fields. BFS-based nested dissection and its numerical factorization enables adaptive control of setting operational range as well as positive parallelization compared with traditional DFS-based nested dissection. It brings better parallel efficiency when various sized separators are divided into blocks under a certain size. This study presents an experiment to identify an optimal maximum block size. Sparse matrices from mechanical dynamics software are numerically factorized, and the time results show that CACHE memory mode is appropriate for a better performance than FLAT mode. And it is recommended to split the operational region in accordance with MCDRAM size in this experiment. Our research shows fairly similar performance to DSS included in MKL and speeds up the time approximately 8 - 14 times in comparison with CHOLMOD, a part of SuiteSparse. This research proposes an effective implementation of linear equation solver for an implicit integration on a many-core CPU. Although this implementation is applied to a flexible body simulation in mechanical dynamics, it could be also utilized in a wide range of other fields. BFS-based nested dissection and its numerical factorization enables adaptive control of setting operational range as well as positive parallelization compared with traditional DFS-based nested dissection. It brings better parallel efficiency when various sized separators are divided into blocks under a certain size. This study presents an experiment to identify an optimal maximum block size. Sparse matrices from mechanical dynamics software are numerically factorized, and the time results show that CACHE memory mode is appropriate for a better performance than FLAT mode. And it is recommended to split the operational region in accordance with MCDRAM size in this experiment. Our research shows fairly similar performance to DSS included in MKL and speeds up the time approximately 8 - 14 times in comparison with CHOLMOD, a part of SuiteSparse. KCI Citation Count: 0 |
| Author | Bae, Dae-Sung Jung, Ji-Hyun |
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| Cites_doi | 10.1007/978-0-387-09766-4_86 10.1145/1391989.1391995 10.1007/s12206-014-0928-2 10.1145/992200.992201 10.1016/S0045-7825(00)00372-8 10.1007/978-3-319-41321-1_18 10.1137/S0895479801385037 10.1007/s12206-015-0508-0 10.1137/1.9780898718003 10.1080/08905459908915692 10.1016/j.compstruc.2015.05.010 10.1007/s12206-017-0322-y 10.1007/s11227-012-0825-3 10.1109/TMAG.2011.2179527 10.1016/j.compstruc.2014.05.009 10.1137/1.9780898718881 10.1109/JPROC.2008.917757 10.1007/s12206-014-1129-8 |
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| Copyright | The Korean Society of Mechanical Engineers and Springer-Verlag GmbH Germany 2017 The Korean Society of Mechanical Engineers and Springer-Verlag GmbH Germany 2017. |
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| Keywords | Linear equation solver Nested dissection Mechanical dynamics Implicit integration Knights landing |
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| References | ChenY.DavisT. A.HagerW. W.RajamanickamS.Algorithm 887: CHOLMOD, supernodal sparse Cholesky factorization and update/downdateACM Transactions on Mathematical Software (TOMS)200835322273820910.1145/1391989.1391995 BaeD. S.KimH. W.YooH. H.SuhM. S.A decoupling solution method for implicit numerical integration of constrained mechanical systemsMechanics of Structures and Machines1999272129141170568810.1080/08905459908915692 YeralanS. N.DavisT. A.RankaS. A. N. J. A. Y.Algorithm 9xx: Sparse QR Factorization on the GPUACM Transactions on Mathematical Software201511128 ShinS.CherguiJ.JuricD.A solver for massively parallel direct numerical simulation of three-dimensional multiphase flowsJournal of Mechanical Science and Technology20173141739175110.1007/s12206-017-0322-y HeineckeA.BreuerA.BaderM.DubeyP.High order seismic simulations on the intel xeon phi processor (Knights landing)International Conference on High Performance Computing2016343362 KarypisG.KumarV.METIS-A software package for partitioning unstructured graphs, partitioning meshes, and computing fill-reducing orderings of sparse matrices Version 5.1.02013 KimH. W.BaeD. S.ChoiK. K.Configuration design sensitivity analysis of dynamics for constrained mechanical systemsComputer Methods in Applied Mechanics and Engineering2001190405271528210.1016/S0045-7825(00)00372-80997.70007 L'ExcellentJ. Y.Multifrontal methods: Parallelism, memory usage and numerical aspects2012 IntelIntel Math Kernel Library Reference Manual 2017201716771690 OwensJ. D.HoustonM.LuebkeD.GreenS.StoneJ. E.PhillipsJ. C.GPU computingProceedings of the IEEE200896587989910.1109/JPROC.2008.917757 Virtual Motion, IncDAFUL 5.1 User’s Manual2015 KoricA.LuQ.GuleryuzE.Evaluation of massively parallel linear sparse solvers on unstructured finite element meshesComputers & Structures2014141192510.1016/j.compstruc.2014.05.009 RodriguesA. W. O.Guyomarc'hF.DekeyserJ. L.Le MenachY.Automatic multi-GPU code generation applied to simulation of electrical machinesIEEE Transactions on Magnetics201248283183410.1109/TMAG.2011.2179527 DuffI. S.ScottJ. A.A parallel direct solver for large sparse highly unsymmetric linear systemsACM Transactions on Mathematical Software (TOMS)200430295117207597610.1145/992200.9922011072.65038 LiR.SaadY.GPU-accelerated preconditioned iterative linear solversThe Journal of Supercomputing201363244346610.1007/s11227-012-0825-3 BrainmanI.ToledoS.Nested-dissection orderings for sparse LU with partial pivotingSIAM Journal on Matrix Analysis and Applications20022349981012192093010.1137/S08954798013850371011.65012 GaikwadA.TokeI. M.Parallel iterative linear solvers on GPU: A financial engineering caseParallel, Distributed and Network-Based Processing (PDP), 18th Euromicro International Conference on IEEE2010607614 JungJ. H.BaeD. S.Optimization of operating and assembling mass properties of solid elements on heterogeneous platforms using OpenCL frameworkJournal of Mechanical Science and Technology20152972631263710.1007/s12206-015-0508-0 TangZ.HuangH.JiangH.LiB.MIC-based preconditioned conjugate gradient method for solving large sparse linear equations201611231129 SodaniA.Knights landing (KNL): 2nd Generation Intel® Xeon Phi processorHot Chips 27 Symposium (HCS), 2015 IEEE2015 SeoI. S.KimJ. H.ShinJ. H.ShinS. W.LeeS. H.Particle behaviors of printing system using GPU-based discrete element methodJournal of Mechanical Science and Technology201428125083508710.1007/s12206-014-1129-8 Martínez-FrutosJ.Martínez-CastejónP. J.Herrero-PérezD.Fine-grained GPU implementation of assembly-free iterative solver for finite element problemsComputers & Structures201515791810.1016/j.compstruc.2015.05.010 DuranA.CelebiM. S.AkaydinB.TuncelM.ÖztoprakaF.Analysis of SuperLU_DIST and SuperLU_ MCDT on Intel® Xeon Phi™ ArchitecturePartnership for Advanced Computing in Europe2013 GuptaA.JoshiM.KumarV.WSMP: A highperformance shared-and distributed-memory parallel sparse linear equation solver2001 ChrysosG.Intel® Xeon Phi™ Coprocessor-the Architecture2014 HorowitzE.Fundamentals of data structures in C++2006 DavisT. A.Direct methods for sparse linear systems200610.1137/1.97808987188811119.65021 KangD. K.KimC. W.YangH. I.GPU-based parallel computation for structural dynamic response analysis with CUDAJournal of Mechanical Science and Technology201428104155416210.1007/s12206-014-0928-2 PaduaD.Encyclopedia of parallel computing20111209121610.1007/978-0-387-09766-41231.68001 SaadY.Iterative methods for sparse linear systems200310.1137/1.97808987180031031.65046 DavisT. A.User guide for CHOLMOD: A sparse Cholesky factorization and modification package2016Gainesville, FL, USADepartment of Computer and Information Science and Engineering, University of Florida A. Heinecke (910_CR21) 2016 J. Y. L'Excellent (910_CR28) 2012 I. S. Duff (910_CR7) 2004; 30 Y. Chen (910_CR17) 2008; 35 E. Horowitz (910_CR24) 2006 A. Gupta (910_CR6) 2001 A. Sodani (910_CR20) 2015 T. A. Davis (910_CR31) 2016 Y. Saad (910_CR1) 2003 D. Padua (910_CR27) 2011 R. Li (910_CR10) 2013; 63 G. Karypis (910_CR26) 2013 G. Chrysos (910_CR9) 2014 T. A. Davis (910_CR2) 2006 S. Shin (910_CR5) 2017; 31 S. N. Yeralan (910_CR18) 2015; 1 J. D. Owens (910_CR8) 2008; 96 D. S. Bae (910_CR22) 1999; 27 Virtual Motion, Inc (910_CR29) 2015 A. Koric (910_CR4) 2014; 141 A. Duran (910_CR19) 2013 Z. Tang (910_CR11) 2016 I. S. Seo (910_CR12) 2014; 28 A. W. O. Rodrigues (910_CR15) 2012; 48 D. K. Kang (910_CR13) 2014; 28 J. Martínez-Frutos (910_CR14) 2015; 157 J. H. Jung (910_CR3) 2015; 29 H. W. Kim (910_CR23) 2001; 190 Intel (910_CR30) 2017 A. Gaikwad (910_CR16) 2010 I. Brainman (910_CR25) 2002; 23 |
| References_xml | – reference: Virtual Motion, IncDAFUL 5.1 User’s Manual2015 – reference: SaadY.Iterative methods for sparse linear systems200310.1137/1.97808987180031031.65046 – reference: GuptaA.JoshiM.KumarV.WSMP: A highperformance shared-and distributed-memory parallel sparse linear equation solver2001 – reference: DavisT. A.User guide for CHOLMOD: A sparse Cholesky factorization and modification package2016Gainesville, FL, USADepartment of Computer and Information Science and Engineering, University of Florida – reference: Martínez-FrutosJ.Martínez-CastejónP. J.Herrero-PérezD.Fine-grained GPU implementation of assembly-free iterative solver for finite element problemsComputers & Structures201515791810.1016/j.compstruc.2015.05.010 – reference: LiR.SaadY.GPU-accelerated preconditioned iterative linear solversThe Journal of Supercomputing201363244346610.1007/s11227-012-0825-3 – reference: GaikwadA.TokeI. M.Parallel iterative linear solvers on GPU: A financial engineering caseParallel, Distributed and Network-Based Processing (PDP), 18th Euromicro International Conference on IEEE2010607614 – reference: BrainmanI.ToledoS.Nested-dissection orderings for sparse LU with partial pivotingSIAM Journal on Matrix Analysis and Applications20022349981012192093010.1137/S08954798013850371011.65012 – reference: ShinS.CherguiJ.JuricD.A solver for massively parallel direct numerical simulation of three-dimensional multiphase flowsJournal of Mechanical Science and Technology20173141739175110.1007/s12206-017-0322-y – reference: PaduaD.Encyclopedia of parallel computing20111209121610.1007/978-0-387-09766-41231.68001 – reference: HeineckeA.BreuerA.BaderM.DubeyP.High order seismic simulations on the intel xeon phi processor (Knights landing)International Conference on High Performance Computing2016343362 – reference: RodriguesA. W. O.Guyomarc'hF.DekeyserJ. L.Le MenachY.Automatic multi-GPU code generation applied to simulation of electrical machinesIEEE Transactions on Magnetics201248283183410.1109/TMAG.2011.2179527 – reference: SodaniA.Knights landing (KNL): 2nd Generation Intel® Xeon Phi processorHot Chips 27 Symposium (HCS), 2015 IEEE2015 – reference: DuffI. S.ScottJ. A.A parallel direct solver for large sparse highly unsymmetric linear systemsACM Transactions on Mathematical Software (TOMS)200430295117207597610.1145/992200.9922011072.65038 – reference: KoricA.LuQ.GuleryuzE.Evaluation of massively parallel linear sparse solvers on unstructured finite element meshesComputers & Structures2014141192510.1016/j.compstruc.2014.05.009 – reference: IntelIntel Math Kernel Library Reference Manual 2017201716771690 – reference: JungJ. H.BaeD. S.Optimization of operating and assembling mass properties of solid elements on heterogeneous platforms using OpenCL frameworkJournal of Mechanical Science and Technology20152972631263710.1007/s12206-015-0508-0 – reference: ChrysosG.Intel® Xeon Phi™ Coprocessor-the Architecture2014 – reference: KangD. K.KimC. W.YangH. I.GPU-based parallel computation for structural dynamic response analysis with CUDAJournal of Mechanical Science and Technology201428104155416210.1007/s12206-014-0928-2 – reference: ChenY.DavisT. A.HagerW. W.RajamanickamS.Algorithm 887: CHOLMOD, supernodal sparse Cholesky factorization and update/downdateACM Transactions on Mathematical Software (TOMS)200835322273820910.1145/1391989.1391995 – reference: KarypisG.KumarV.METIS-A software package for partitioning unstructured graphs, partitioning meshes, and computing fill-reducing orderings of sparse matrices Version 5.1.02013 – reference: KimH. W.BaeD. S.ChoiK. 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| SubjectTerms | Adaptive control Central processing units Computer memory Computer simulation Control CPUs Dissection Dynamical Systems Engineering Flexible bodies Industrial and Production Engineering Linear equations Mechanical Engineering Separators Sparse matrices Vibration 기계공학 |
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| Title | An implementation of direct linear equation solver using a many-core CPU for mechanical dynamic analysis |
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