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Accelerating the GMRES Solver with Block ILU (K) Preconditioner on GPUs in Reservoir Simulation

Hui Liu Bo Yang
2015 Journal of Geology & Geosciences  
These techniques also work with an arbitrary level k for the block ILU (k) preconditioner. Numerical experiments show that the GPU-based linear solver GMRES (m) is much faster than its CPU version.  ...  This paper studies the parallelization of the restarted GMRES solver, GMRES (m), and the block ILU (k) preconditioner on GPUs used in petroleum reservoir simulations.  ...  Acknowledgements The support of Department of Chemical and Petroleum Engineering, University of Calgary and Reser-voir Simulation Group is gratefully acknowledged.  ... 
doi:10.4172/2329-6755.1000199 fatcat:kwi7pcfg3beirjqjorowabpafa

Accelerating advanced preconditioning methods on hybrid architectures

Ernesto Dufrechou
2021 CLEI Electronic Journal  
Additionally we enhance existing task-parallel versions of ILUPACK for shared- and distributed-memory systems with the inclusion of GPU acceleration.  ...  This dissertation targets the use of GPUs to enhance the performance of the solution of sparse linear systems using iterative methods complemented with state-of-the-art preconditioned techniques.  ...  Acknowledgments Special thanks to the advisors of the thesis, Dr. Pablo Ezzatti (Universidad de la República, Uruguay) and Dr. Enrique Quintana-Ortí (Universitat Politècnica de València, Spain).  ... 
doi:10.19153/cleiej.24.1.6 doaj:cf900516b6334e27afbe4102fa203079 fatcat:ohhmcgyrl5hgfaib7hb2rdyhom

Parallel Sparse Approximate Inverse Preconditioning on Graphic Processing Units

M. M. Dehnavi, D. M. Fernandez, J. Gaudiot, D. D. Giannacopoulos
2013 IEEE Transactions on Parallel and Distributed Systems  
Accelerating numerical algorithms for solving sparse linear systems on parallel architectures has attracted the attention of many researchers due to their applicability to many engineering and scientific  ...  We propose a GPU accelerated SAI preconditioning technique called GSAI, which parallelizes the computation of this preconditioner on NVIDIA graphic cards.  ...  to compute the preconditioner on GTX480 (GPU-SAI) and TESLA M2070 using the GSAI preconditioning algorithm (ParaSails-Total is computed by adding ParaSails-Setup and ParaSails-Preconditioner).  ... 
doi:10.1109/tpds.2012.286 fatcat:v5u6f5v7hbctpfadovqy5thbfq

3D Bubbly Flow Simulation on the GPU - Iterative Solution of a Linear System Using Sub-domain and Level-Set Deflation

R. Gupta, M. B. van Gijzen, C. Vuik
2013 2013 21st Euromicro International Conference on Parallel, Distributed, and Network-Based Processing  
Solving an ill-conditioned linear system with a two level preconditioned Conjugate Gradient method on the GPU presents many options.  ...  Our results exhibit up to an order of magnitude speedup on the GPU.  ...  This is very useful for solving such ill-conditioned systems since preconditioning is required in order to solve them in a realistic time-frame.  ... 
doi:10.1109/pdp.2013.58 dblp:conf/pdp/GuptaGV13 fatcat:jorzcizmsfcbzdd7b72d4ki3fe

CPU and GPU Performance of Large Scale Numerical Simulations in Geophysics [chapter]

Ali Dorostkar, Dimitar Lukarski, Björn Lund, Maya Neytcheva, Yvan Notay, Peter Schmidt
2014 Lecture Notes in Computer Science  
These packages provide toolboxes with state-of-the-art implementations of iterative solution methods and preconditioners for multicore computer platforms and GPU.  ...  The efficiency of solving systems of the latter type is crucial as it is to be embedded in a time-evolution procedure, where systems with matrices of similar type have to be solved repeatedly many times  ...  Acknowledgments, This work has been supported by the Linnaeus center of excellence UPMARC, Uppsala Programming for Multicore Architectures Research Center.  ... 
doi:10.1007/978-3-319-14325-5_2 fatcat:gm6ukwbp6bbv5oedbjx7fv5eqe

Parallel multigrid preconditioning on graphics processing units (GPUs) for robust power grid analysis

Zhuo Feng, Zhiyu Zeng
2010 Proceedings of the 47th Design Automation Conference on - DAC '10  
This work presents an efficient GPU-based multigrid preconditioning algorithm for robust power grid analysis.  ...  Existing preconditioned iterative methods that require incomplete matrix factorizations can not be effectively accelerated on GPU due to its limited hardware resource as well as data parallel computing  ...  Cholmod [6] ), especially when dealing with ill-conditioned problems.  ... 
doi:10.1145/1837274.1837443 dblp:conf/dac/FengZ10 fatcat:cgflmgnmr5bbrajd7sdl24fq74

GPU-Accelerated Finite Element Method for Modelling Light Transport in Diffuse Optical Tomography

Martin Schweiger
2011 International Journal of Biomedical Imaging  
We introduce a GPU-accelerated finite element forward solver for the computation of light transport in scattering media.  ...  The GPU forward solver uses a CUDA implementation that evaluates on the graphics hardware the sparse linear system arising in the finite element formulation of the diffusion equation.  ...  However, at very high absorption and scattering parameter values, the linear system may become increasingly ill-conditioned and no longer converge with single-precision arithmetic.  ... 
doi:10.1155/2011/403892 pmid:22013431 pmcid:PMC3195519 fatcat:6rmq2zxuwbbxno2ueigsnd7mii

GPU implementation of a Helmholtz Krylov solver preconditioned by a shifted Laplace multigrid method

H. Knibbe, C.W. Oosterlee, C. Vuik
2011 Journal of Computational and Applied Mathematics  
The results show that preconditioned Bi-CGSTAB on GPU as well as preconditioned IDR(s) on GPU is about 30 times faster than on CPU for the same stopping criterion.  ...  The implementation of the preconditioned solver on CPU (Central Processing Unit) is compared to an implementation on GPU (Graphics Processing Units or graphics card) using CUDA (Compute Unified Device  ...  The linear system is symmetric but indefinite, non-Hermitian and ill-conditioned which brings difficulties when solving with basic iterative methods.  ... 
doi:10.1016/j.cam.2011.07.021 fatcat:5ewml7w6xzdi7g57zkircv5j3i

A Comparative Study on Different Parallel Solvers for Nonlinear Analysis of Complex Structures

Lei Zhang, Guoxin Zhang, Lixiang Wang, Zhaosong Ma, Shihai Li
2013 Mathematical Problems in Engineering  
preconditioned Krylov subspace solver based on MPI, (3) a parallel sparse equation solver based on OpenMP, and (4) a parallel GPU equation solver.  ...  The parallelization of 2D/3D software SAPTIS is discussed for nonlinear analysis of complex structures. A comparative study is made on different parallel solvers.  ...  Acknowledgments The authors would like to acknowledge the financial support of the National Natural Science Foundation of China  ... 
doi:10.1155/2013/764237 fatcat:ftigdfgnq5fwnprcyqr7qxi36e

Toward a GPU-aware comparison of explicit and implicit CFD simulations on structured meshes

Mohamed Aissa, Tom Verstraete, Cornelis Vuik
2017 Computers and Mathematics with Applications  
Then we introduce a classification of basic CFD operations, found on the degree of parallelism they expose, and study the potential of GPU acceleration for every class.  ...  A computational Fluid Dynamics (CFD) code for steady simulations solves a set of non-linear partial differential equations using an iterative time stepping process, which could follow an explicit or an  ...  We are also grateful to NVIDIA for the hardware donation.  ... 
doi:10.1016/j.camwa.2017.03.003 fatcat:nurf52bzifcydbtit6gznzfsly

Survey on Efficient Linear Solvers for Porous Media Flow Models on Recent Hardware Architectures

Ani Anciaux-Sedrakian, Peter Gottschling, Jean-Marc Gratien, Thomas Guignon
2014 Oil & Gas Science and Technology  
Our results demonstrate that using GPGPUs becomes now a real alternative to multi-core nodes for solving ill-conditioned linear systems with Krylov solvers in reservoir simulation.  ...  This table shows that for the ill conditioned Spe10 system, the hybrid CPU +GPU offers a better performance, even if the number of solver iterations is more important, due to the graphcoloring, than the  ... 
doi:10.2516/ogst/2013184 fatcat:zdxhrlm5nvdujn7stynit4vyg4

The Design of Fast and Energy-Efficient Linear Solvers: On the Potential of Half-Precision Arithmetic and Iterative Refinement Techniques [chapter]

Azzam Haidar, Ahmad Abdelfattah, Mawussi Zounon, Panruo Wu, Srikara Pranesh, Stanimire Tomov, Jack Dongarra
2018 Lecture Notes in Computer Science  
In this work, we present a novel design and implementation of an energyefficient solution for dense linear systems of equations, which are at the heart of large-scale HPC applications.  ...  The proposed energy-efficient linear system solvers are based on two main components: (1) iterative refinement techniques, and (2) reduced-precision computing features in modern accelerators and coprocessors  ...  Department of Energy Office of Science and the National Nuclear Security Administration. The work was also partially supported by NVIDIA and NSF grant No. OAC-1740250.  ... 
doi:10.1007/978-3-319-93698-7_45 fatcat:huozvhdhk5fqlhskmih4cpkyne

Co-processor acceleration of an unmodified parallel solid mechanics code with FEASTGPU

Dominik Goddeke, Hilmar Wobker, Robert Strzodka, Jamaludin Mohd Yusof, Patrick McCormick, Stefan Turek
2009 International Journal of Computational Science and Engineering (IJCSE)  
We present accuracy experiments, a scalability test and acceleration results for different elastic objects under load.  ...  With the extension FeastGPU the authors have previously demonstrated that significant speed-ups in the solution of the scalar Poisson problem can be achieved by the addition of GPUs as scientific co-processors  ...  Also thanks to NVIDIA and AMD for donating hardware that was used in developing the serial version of the GPU backend.  ... 
doi:10.1504/ijcse.2009.029162 fatcat:apmjkuwxc5bufjipmr2jwnpja4

GPU acceleration of an unmodified parallel finite element Navier-Stokes solver

Dominik Goddeke, Sven H.M. Buijssen, Hilmar Wobker, Stefan Turek
2009 2009 International Conference on High Performance Computing & Simulation  
linear solver.  ...  In this paper we explore the limitations of our approach by accelerating a Navier-Stokes solver.  ...  The 'minimally invasive' concept of co-processor acceleration has been developed in close collaboration with Robert Strzodka, Jamaludin Mohd-Yusof and Patrick McCormick.  ... 
doi:10.1109/hpcsim.2009.5191718 dblp:conf/ieeehpcs/GoddekeBWT09 fatcat:mm4tch3fjnc3vgmh7hxkdnrq6u

A Study of Mixed Precision Strategies for GMRES on GPUs [article]

Jennifer A. Loe, Christian A. Glusa, Ichitaro Yamazaki, Erik G. Boman, Sivasankaran Rajamanickam
2021 arXiv   pre-print
We present a study of mixed precision strategies for accelerating this kernel on an NVIDIA V100 GPU with a Power 9 CPU.  ...  In this paper, we focus on preconditioned sparse iterative linear solvers, a key kernel in several CSE applications.  ...  We focus on one of the expensive portions of solving PDEs, the sparse linear solve. While there are several approaches for solving sparse linear systems, we focus on sparse iterative linear solvers.  ... 
arXiv:2109.01232v1 fatcat:celwzxytdnaupad2zffcuivzw4
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