### PARALLEL COMPUTING TECHNOLOGIES IN THE FINITE ELEMENT METHOD

*S. V. Choporov*

#### Abstract

Nowadays engineers and researchers are faced with solving very complex problems in a mathematical modeling and design. Numerical analysis naturally finds applications in all fields of engineering and the physical sciences. The finite element method is a powerful tool for the numerical simulation of a wide range of problems. Implementation of the finite element method in CAD systems on the basis of modern computers allows researchers to solve large scale problems. The finite element method uses a discretization of a continuum domain into a mesh as the starting point. The discretization of complex domains may give large numbers of elements, thus increasing the requirements of computer memory and speed. Modern parallel computers use multiple processing elements simultaneously to solve a problem. Thus implementation of parallel computing into the finite element method is urgent direction of the research. In the finite element method for the numerical solution of partial differential equations, the stiffness matrix represents the system of linear equations that must be solved in order to ascertain an approximate solution to the differential equation. Therefore the article describes parallel algorithms for assembly of stiffness matrix and for solution of linear equations. Also this article contains two numerical experiments: 1) Dirichlet problem on the complex domain (gear); 2) Elasticity problem of three-layer shell. In the end of the article author compares the speed of a solution of these problems with one, two and four parallel cores and makes discussion about the effectiveness of parallel finite element processing.

#### Keywords

finite element method, parallel computing technologies, mathematical model, numerical method.

#### References

Zienkiewicz O. Z., Taylor R.L. The Finite Element Method. V. 1: The Basis. Oxford, Butterworth-Heinemann, 2000, 689 p.

Smith I. M., Griffits D. V. Programming the finite element method. Chichester, Wiley, 2004, 628 p.

Ahmad A. Parallel Programming in the Finite Element Methos, In. Proceedings of Failure of engineering Materials and Structures, UET Taxila, October 2007, pp. 87–93.

Thompson J. F., Bharat K. Soni, Nigel P. Weatheril. Hand book of grid generation. New York, CRC Press, 1999, 1200 p.

Gergel’ V. P., Strongin R. G. Osnovy parallel’nyx vychislenij dlya mnogoprocessornyx vychislitel’nyx system. Nizhnij Novgorod, NNGU im. N. I. Lobachevskogo, 2003, 184 p.

DOI:

https://doi.org/10.15588/1607-3274-2013-2-15
Copyright (c) 2014 S. V. Choporov

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