Modeling of GPU computing using difference schemes
D.G. Vorotnikova, A.V. Kochurov, D.L. Golovashkin
Samara State Aerospace University, Samara, Russia,
Image Processing Systems Institute, Russian Academy of Sciences, Samara, Russia
Full text of article: Russian language.
PDF
Abstract:
We propose models of GPU (graphics processing unit) computing that can be recommended for implementation of explicit and implicit difference schemes on GPUs. In particular, these are models for selecting an optimal vector length in the 'long-vector' algorithms and for finding an optimal pyramid height in corresponding parallel algorithms.
Keywords:
computational modeling, GPU, difference scheme, CUDA.
Citation:
Vorotnikova DG, Kochurov AV, Golovashkin DL. Modeling of GPU using difference schemes. Computer Optics 2015; 39(5): 801-807. DOI: 10.18287/0134-2452-2015-39-5-801-807.
References:
- Krilov AN. Lectures on approximate calculations [In Russian]. Ìoscow: State publishing house technical and theoretical literature; 1954.
- Samarskii ÀÀ. About the works in the theory of difference schemes [In Russian]. International Congress of Mathematicians (Nice); 1972.
- Samarskii AA, Mihajlov AP. Mathematical modeling: Ideas. Methods. Examples [In Russian]. Moscow: «Fizmatlit» Publisher; 2001.
- Ortega J. Introduction to Parallel and Vector Solution of Linear Systems. NY: Plenum Press; 1987.
- Golub GH, Van Loan ChF. Matrix Computations. JHU Press; 1989.
- Karpov VE. Introduction to the parallelization of algorithms and programs [In Russian]. Computer Research and Modeling 2010; 3: 231-72.
- Frolov V. Introduction to CUDA technology. Electronic magazine “Computer graphics and multimedia”. Source: http://cgm.computergraphics.ru/issues/issue16/cuda .
- Foster I. Designing and Building Parallel Programs. Addison Wesley; 1995.
- Voevodin VV, Voevodin VlV. Parallel computations [In Russian]. St.-Petersburg: “BHV-Petersburg” Publisher; 2002.
- Horoshevskii VG. Architecture of Computer Systems [In Russian]. Moscow: Publisher of Bauman Moscow State Technical University; 2008.
- Boreskov AV, Harlamov AA. Basics of CUDA technology [In Russian]. Moscow: “DMK Press” Publisher; 2010.
- Vorotnikova DG, Golovashkin DL. Long vector algorithms for solving grid equations of explicit difference scheme. Computer Optics 2015; 39(1): 87-93.
- Golovashkin DL, Kochurov AV. Solving finite-difference equations on GPU. The pyramid method [In Russian]. Computational Technologies 2012; 17(3): 55-69.
- van der Steen AJ, Dongarra JJ. Overview of Recent Supercomputers. Source http://www.netlib.org/utk/papers/advanced-computers/overview.html .
- Voevodin VlV. Lectures “Parallel processing”. Systems of parallel programming on Linda [In Russian]. Source: http://parallel.ru/vvv/lec7.html .
- Antonov AS. Textbook: Parallel programming technology OpenMP [In Russian]. Moscow: MSU Press; 2009.
- Golub GH, Van Loan ChF. Matrix Computations. 3rd ed. Baltimor: JHU Press; 1996.
- Golub GH, Ortega JM. Scientific Computing and Differential Equations: An Introduction to Numerical Methods. California: Academic Press; 1992.
- Lindholm E, Nickolls J, Oberman S, Montrym J. NVIDIA Tesla: A Unified Graphics and Computing Architecture. Micro, IEEE 2008; 28(2): 39-55.
- Lelchuk TI, Marchuk AG. Description language of computing systems functional architecture (models and general principles) [In Russian]. Novosibirsk: Preprint of the Computing Center of the USSR Academy, JS 258; 1981.
- Chrzeszczyk A, Chrzeszczyk J. Matrix computation on the GPU. CUBLAS and MAGMA by examples. Source: https://developer.nvidia.com/sites/default/files/akamai/cuda/files/Misc/mygpu.pdf .
- Golovashkin DL, Vorotnokova DG, Kochurov AV, Malysheva SA. Solving finite-difference equations for diffractive optics problems using graphics processing units. Optical Engeneering 2013; 52(9): 091719. DOI: 10.1117/1.OE.52.9.091719.
- Barillo A. NVIDIA CUDA – non-graphical computing on GPUs. Source: http://www.ixbt.com/video3/cuda-1.shtml .
- Kochurov A, Golovashkin D. GPU implementation of Jacobi Method and Gauss-Seidel Method for Data Arrays that Exceed GPU-dedicated Memory Size. JMMA 2015; DOI: 10.1007/s10852-015-9272-5.
- Jin G, Endo T, Matsuoka T. A parallel optimization method for stencil computation on the domain that is bigger than memory capacity of GPUs. Cluster Computing (CLUSTER). 2013 IEEE International Conference 2013; 1-8.
© 2009, IPSI RAS
151, Molodogvardeiskaya str., Samara, 443001, Russia; E-mail: journal@computeroptics.ru ; Tel: +7 (846) 242-41-24 (Executive secretary), +7 (846) 332-56-22 (Issuing editor), Fax: +7 (846) 332-56-20