Keywords: grid computing, dynamic relaxation method, finite element analysis, Globus toolkit, MPICH-G2, Windows OS.

Grid computing [1] is innovative technology that obtains computing power by using many computers connected by a network, and is low price because it is constructed by the use of existing computer resources, local area networks, and internet technology. Grid computing has several kinds of application, for example, one is a computational grid [2] which means high-performance computing, and the other is a data grid which deals with large amounts of distributed data.

It seems that the study of the computational grid is limited to a field in which it is unnecessary to consider the calculated results of the next domain such as genetic algorithms. Therefore it seems to be easy to apply grid technologies to these themes. However, the parallel computation of finite element analysis is effective when using the substructure method. It is necessary to consider some techniques for the numerical method because of the large amount of communications to the next domain in grid computing.

In this paper, a virtual grid computing system was constructed in our laboratory using the Globus toolkit [3]. It contains several Linux and Windows PCs as computing nodes. It is necessary to consider the use of existing Windows PCs in some companies or educational facilities. The Globus toolkit which is the middleware of grid computing seems to be favourable on Linux PCs and unfavourable on Windows PCs for computing grid, while, the virtual machine software is used for Windows PCs. Therefore, the Linux environment for the Globus Toolkit could be constructed on Windows PCs. Moreover, MPICH-G2 [4] which is the grid-enabled implementation of the message passing interface (MPI), was also applied in this system.

Next, the numerical method is described in detail. The parallel computation of the finite element analysis using dynamic relaxation as iterative technique was achieved. Dynamic relaxation method was suggested by Day [5], and developed by Otter [6], and widely used for analyzing various problem [7]. It has been usually based on the finite difference method in terms of both time and shape of elements, and is an efficient iterative technique, while the finite element method can be applicable to arbitary shapes of elements [8,9,10]. Moreover, some study of parallel computation for dynamic relaxation method has been performed [11], however, it does not seem to consider the substructure method.

Finally, numerical results were investigated. By using this technique, the parallel computation by grid computing was achieved and the convergence of solutions was examined for a practical finite element model. From the numerical results, the parallel efficiency for the use of Windows PCs for the computing nodes was also discussed.

1

I. Foster, C. Kesselman, S. Tuecke: The Anatomy of the Grid, Enabling Scalable Virtual Organizations, IJSA, 2001.

2

Seminar on Advances in Computational Mechanics in Civil Engineering, JSCE, 2005.8.

3

http://www.globus.org/

4

http://www3.niu.edu/mpi/

5

Day, A.S.: An Introduction to dynamic relaxation, Engineer, Vol.219, pp.218-221, Jan.,1965.

6

Otter, J.R.H.: Dynamic relaxation compared with other iterative finite diffirence methods, nuclear Engineering and Design, Vol.3, No.1, pp.183-185, 1966. doi:10.1016/0029-5493(66)90157-9

7

Mikami, I., Watanabe, E., and Tanaka, K.: Large deflection analysis of elasto-plastic cylindrical panels using vector processor, Theoretical and Applied Mechanics, Vol.38, Univ. of Tokyo Press, pp.3-14, Mar., 1990.

8

Al-Shawi, F.A.N.: Dynamic relaxation technique for the solution of finite element equations in structural analysis, Bull. Coll. Engng., Vol.5, pp.155-177, 1981.

9

Al-Shawi, F.A.N., and Mardirosian, A.H.: An improved dynamic relaxation method for the analysis of plate bending problems, Computer and Structures, Vol.27, No.2, pp.237-240, 1987. doi:10.1016/0045-7949(87)90091-5

10

Lynch, R.D., Kelsey, S., and Saxe, H.C.: The Application of Dynamic Relaxation to the Finite Element Methods of Structural Analysis, Theoretical Report No.themis-und-68-1, Univ. of Notre Dame, 1968.

11

Takehara, K., Mikami, I., Kano, T., Hamatani, S : The Application of Finite Element Method to Dynamic Relaxation Method for Nonlinear Analysis of Large Structures Using PC Cluster, Proceedings of the 9th East Asia-Pacific Conference On Structural Engineering and Construction (EASEC9), Bali, Indonesia, 2003.12.

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