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GPU-based power flow analysis with Chebyshev preconditioner and conjugate gradient method

Xue Li, Fangxing Li
2014 Electric power systems research  
This work implemented a polynomial preconditioner Chebyshev preconditioner with graphic processing unit (GPU), and integrated a GPU-based conjugate gradient solver.  ...  Preconditioner, used for preconditioning the linear system for a better convergence rate in iterative computations, is an indispensable part of iterative solving process.  ...  In this work, a polynomial preconditioner Chebyshev preconditioner with graphic processing unit (GPU) will be implemented and integrated with a GPU-based conjugate gradient solver for linearized DC power  ... 
doi:10.1016/j.epsr.2014.05.005 fatcat:ekb7abwty5ablj4s2s4y5we7c4

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  
Leveraging the power of nowadays graphics processing units for robust power grid simulation remains a challenging task.  ...  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  ...  Recently, there has been ever increasing interest in circuit simulations on data parallel computing platforms, such as graphics processing units [2, 3] .  ... 
doi:10.1145/1837274.1837443 dblp:conf/dac/FengZ10 fatcat:cgflmgnmr5bbrajd7sdl24fq74

Parallel preconditioned conjugate gradient algorithm on GPU

Rudi Helfenstein, Jonas Koko
2012 Journal of Computational and Applied Mathematics  
We propose a parallel implementation of the Preconditioned Conjugate Gradient algorithm on a GPU platform. The preconditioning matrix is an approximate inverse derived from the SSOR preconditioner.  ...  As compared to CPU implementation of the conjugate gradient algorithm, our GPU preconditioned conjugate gradient implementation is up to 10 times faster (8 times faster at worst).  ...  Introduction In the last years, Graphics Processing Units (GPU) have evolved into a very flexible and powerful many-core processor.  ... 
doi:10.1016/j.cam.2011.04.025 fatcat:celrnv3bavccfmitrnxg63ji5e

Single and Dual-GPU Generalized Sparse Eigenvalue Solvers for Finding a Few Low-Order Resonances of a Microwave Cavity Using the Finite-Element Method

A. Dziekonski, M. Mrozowski
2018 Radioengineering  
The computations are expedited by using one or two graphical processing units (GPUs) as accelerators.  ...  To find a few loworder resonances, the locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm with null-space deflation is applied.  ...  Also, the preconditioned conjugate-gradient algorithm involves a sparse matrix-vector product (SpMV). This is typical of all iterative techniques based on Krylov-spaces.  ... 
doi:10.13164/re.2018.0930 fatcat:oxssj7clwra73homyuqt5u7l44

A PCG Implementation of an Elliptic Kernel in an Ocean Global Circulation Model Based on GPU Libraries [article]

Salvatore Cuomo, Pasquale De Michele, Raffaele Farina, Marta Chinnici
2012 arXiv   pre-print
Finally, we describe an easy-to-implement version of the solver on the Graphical Processing Units (GPUs) by means of scientific computing libraries and we discuss its performance.  ...  The inverse preconditiong technique is adopted in order to efficiently compute the numerical solution of the elliptic kernel by using the Conjugate Gradient (CG) method.  ...  In this paper we propose a new solver based on preconditioned conjugate gradient (PCG) method with an approximate inverse preconditioner AINV [7] for the numerical solution of the elliptic sea-surface  ... 
arXiv:1210.1878v1 fatcat:act3344l3vhqtg7t5jub3cumwy

Updated sparse cholesky factors for corotational elastodynamics

Florian Hecht, Yeon Jin Lee, Jonathan R. Shewchuk, James F. O'brien
2012 ACM Transactions on Graphics  
conjugate gradients.  ...  Coupled with an algorithm for incremental updates to a sparse Cholesky factorization, the method realizes the stability and scalability of a sparse direct method without the need for expensive refactorization  ...  ACKNOWLEDGMENTS We thank Xiaoye Li and James Demmel for helpful discussions and commentary about sparse direct solvers.  ... 
doi:10.1145/2231816.2231821 fatcat:iujvmlw6fjgh7jfox7c5rhsbde

A smart GPU implementation of an elliptic kernel for an ocean global circulation model

R. Farina, S. Cuomo, P. De Michele, F. Piccialli
2013 Applied Mathematical Sciences  
Finally, we present an easy-toimplement version of the solver on the Graphics Processing Units (GPUs).  ...  In this paper, the preconditioning technique of an elliptic Laplace problem in a global circulation ocean model is analyzed.  ...  We introduce a Factored Sparse Approximate Inverse (FSAI) preconditioner P =ZZ t [5, 3] , computed by means of a conjugate-orthogonalization procedure.  ... 
doi:10.12988/ams.2013.13266 fatcat:yuu6uzbaazgddf7fa4cgqvcd7a

Evaluation of the deflated preconditioned CG method to solve bubbly and porous media flow problems on GPU and CPU

R. Gupta, D. Lukarski, M. B. van Gijzen, C. Vuik
2015 International Journal for Numerical Methods in Fluids  
Through our experiments, we show that it is possible to achieve a computationally fast solver on a graphics processing unit.  ...  Through this work, we want to show that for bubbly and porous media flow, we can use deflation with preconditioning to accelerate convergence on the graphics processing units (GPUs).  ...  of Applied Mathematics for providing the matrices for porous media flow problems and Kees Verstoep at DAS-4 cluster Vrije University site for valuable help and suggestions for running the experiments on  ... 
doi:10.1002/fld.4170 fatcat:hcogynaw7rhgtndcitgpe36n4q

Locally adapted hierarchical basis preconditioning

Richard Szeliski
2006 ACM Transactions on Graphics  
This paper develops locally adapted hierarchical basis functions for effectively preconditioning large optimization problems that arise in computer vision, computer graphics, and computational photography  ...  applications such as surface interpolation, optic flow, tone mapping, gradient-domain blending, and colorization.  ...  However, the advantages of LAHBF over conjugate gradient still remain quite dramatic. We also compared the time taken with our solver against the sparse linear solver in MatLab.  ... 
doi:10.1145/1141911.1142005 fatcat:y36p64vx5rc6lmmynnk3rwjbzi

Locally adapted hierarchical basis preconditioning

Richard Szeliski
2006 ACM SIGGRAPH 2006 Papers on - SIGGRAPH '06  
This paper develops locally adapted hierarchical basis functions for effectively preconditioning large optimization problems that arise in computer vision, computer graphics, and computational photography  ...  applications such as surface interpolation, optic flow, tone mapping, gradient-domain blending, and colorization.  ...  However, the advantages of LAHBF over conjugate gradient still remain quite dramatic. We also compared the time taken with our solver against the sparse linear solver in MatLab.  ... 
doi:10.1145/1179352.1142005 fatcat:gewgayqoizbh5jm3xl6o566q5y

Krylov Subspace Methods for Big Data Analysis of Large Computational Electromagnetics Applications

Bruno Carpentieri
2021 International Conference on Modern Management based on Big Data  
In this paper we present some computational techniques based on the class of preconditioned Krylov subspace methods that enable us to carry out large-scale, big data simulations of Computational Electromagnetics  ...  This analysis requires the solution of large linear systems that cannot be afforded by conventional direct methods (based on variants of the Gaussian elimination algorithm) due to their high memory costs  ...  Acknowledgements The author is a member of the Gruppo Nazionale per il Calcolo Scientifico (GNCS) of the Istituto Nazionale di Alta Matematica (INdAM) and this work was partially supported by INdAM-GNCS  ... 
doi:10.3233/faia210232 dblp:conf/mmbd/Carpentieri21 fatcat:pcwvruj6zrf7discjugsxxmevy

GPU Accelerated High Accuracy Surface Modelling

C.Q. Yan, T.X. Yue, G. Zhao
2012 Procedia Environmental Sciences  
This paper presents HASM-GA, a Graphic Processor Unit (GPU) accelerated High Accuracy Surface Modelling, to construct surface with a significant boost performance.  ...  The results show that one order of magnitude speedupcan be achieved by fully using the parallel processing power of theGPU compared with the traditional CPU method.  ...  Other forms include the Sparse Approximate Inverse preconditioner, Incomplete Cholesky factorization, Incomplete LU factorization, Successive overrelaxation, etc.  ... 
doi:10.1016/j.proenv.2012.01.046 fatcat:ruztz4nuc5as3o4e3464wzawri

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

Martin Schweiger
2011 International Journal of Biomedical Imaging  
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.  ...  A comparison with a CPU-based implementation shows significant performance gains of the graphics accelerated solution, with improvements of approximately a factor of 10 for double-precision computations  ...  Real-valued problems were solved with a conjugate gradient solver, complex problems with a biconjugate gradient stabilised solver.  ... 
doi:10.1155/2011/403892 pmid:22013431 pmcid:PMC3195519 fatcat:6rmq2zxuwbbxno2ueigsnd7mii

Adaptive precision in block-Jacobi preconditioning for iterative sparse linear system solvers

Hartwig Anzt, Jack Dongarra, Goran Flegar, Nicholas J. Higham, Enrique S. Quintana-Ortí
2018 Concurrency and Computation  
We assess the effects of the adaptive-precision preconditioner on the iteration count and data transfer cost of a preconditioned conjugate gradient solver.  ...  A preconditioned conjugate gradient method is, in general, a memory-bound algorithm, and therefore its execution time and energy consumption are largely dominated by the costs of accessing the problem's  ...  ACKNOWLEDGEMENT We thank Matthias Bollhöfer for fruitful discussions on flexible variants of Krylov solvers allowing for nonconstant preconditioning operators and for pointing us to the flexible version  ... 
doi:10.1002/cpe.4460 fatcat:vkh3zx2l75bbvpvnjakollnowu

Fast Fourier-Based Phase Unwrapping on the Graphics Processing Unit in Real-Time Imaging Applications

Sam Jeught, Jan Sijbers, Joris Dirckx
2015 Journal of Imaging  
By executing the parallel implementation of a single-step Fourier-based phase unwrapping algorithm on the graphics processing unit of a standard graphics card, we were able to reduce the total processing  ...  In addition, we expand upon this technique by inserting the obtained solution as a preconditioner in the conjugate gradient technique.  ...  using a preconditioned conjugate gradient algorithm.  ... 
doi:10.3390/jimaging1010031 fatcat:opwlqu552rbgvi7aeepdt2vrce
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