Author : Mr. Akshay A. Jadhav 1
Date of Publication :9th August 2017
Abstract: The performance and use of parallel computing in the field of differential calculus is increased tremendously opening up new avenues for applying these in the field of numerical computation for high speed performance. The computation time required to find analytical as well as numerical solution is tested and compared. In this work we have harnessed this property of GPU to accelerate the grid point calculations for numerical calculations and the performance of numerical method using CPU and GPU is compared. The numerical Methods for integer order PDE are studied, analyzed and implemented on GPU using parallel computing toolbox of MATLAB. The finite difference methods of PDE like explicit, implicit method are tested for the results, for parabolic, hyperbolic and elliptical type of PDE’s. The positive speed up is achieved for elliptical type of PDE. The verification of results with the analytical solution is made by the mean square error.
Reference :
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[1] Farlow, Stanley J. Partial differential equations for scientists and engineers. Courier Corporation, 1993.
[2] Smith, Gordon D. Numerical solution of partial differential equations: finite difference methods. Oxford university press, 1985. [3] Lindfield, George, and John Penny. Numerical methods: using MATLAB. Academic Press, 2012.
[4] Ames, William F. Numerical methods for partial differential equations. Academic press, 2014.
[5] Peaceman, Donald W., and Henry H. Rachford, Jr. “The numerical solution of parabolic and elliptic differential equations.” Journal of the Society for Industrial and Applied Mathematics 3.1 (1955): 28-41.
[6] Arnold, Douglas N. “Stability, consistency, and convergence of numerical discretizations.” Encyclopedia of Applied and Computational Mathematics. Springer Berlin Heidelberg, 2015. 1358- 1364.
[7] John, Volker. “Numerical methods for partial differential equations.” Lecture notes (2013).
[8] Trangenstein, John. “Numerical solution of hyperbolic conservation laws.”Cambridge University Press, (2009).
[9] Urroz, G. E. “Numerical Solution of Laplace Equation.” Utah State University paper (2004).
[10] Peter Knabner, Lutz Angermann. “Numerical Methods for Elliptic and Parabolic Partial Differential Equations” Springer-Verlag,New York Berlin Heidelberg,2000.
[11] Arnold, Douglas N. “Lecture notes on Numerical Analysis of Partial Differential Equations.” (2012)
[12] Chun-Hasiang Han, “Introduction to Matlab GPU Acceleration for COmputational Finance.” Natational Tsing-Hua University,Taiwan, December 26, 2013.
[13] “Partial Differential Equation”. En.Wikipedia.Org, 2017, https:// en.wikipedia .org/ wiki/ Partial-differential-equation
[14] “NVIDIA On GPU Computing And The Difference Between Gpus And Cpus”. Nvidia.Com, 2017, http://www.nvidia.com/object/what-isgpucomputing.html.
[15] “Graphics Processing Unit”. En.Wikipedia.Org, 2017, https://en .wikipedia .org /wiki / Graphicsprocessing -unit.