This paper presents an application of cluster computing in finite element programming. A cluster of eight PCs of different configurations was developed and used in the present work. Three parallel solvers of Gauss-Seidel Method (GSM), Gauss Elimination Method (GEM) and Matrix Inversion Method (MIM) were developed and implemented on this cluster to achieve a reduction in the computational time in getting the solution of a system of linear equations. The performances of these solvers were compared and the most suitable solver was implemented in a finite element software developed on Windows NT platform to analyze the structural components. A typical problem of stress analysis in the anchorage zone in a prestressed, post-tensioned concrete beam was analyzed using a developed software on the developed cluster and the variation in different components of computational time was obtained. By computing speedup and efficiency, the performance of the developed software was presented. It was found in the present study that the optimum number of computers required to form the cluster varied between three and five. It was also observed that an excessive increase in the number of computers resulted in an increase in the total time due to increase in communication time.

In the past few years, advancement in the field of computer technology has provided faster computing techniques. Now, it is possible to solve large time-consuming problems in a reduced time frame on PCs. A solution to structural analysis problems using finite element method requires reasonably high computational time due to the implementation of iterative techniques. Therefore, super computers could be employed to solve such problems in lesser time. Mackerle (1992) shows that parallel solvers are essential to carry out finite element analysis on super computers within a reduced time frame. In the development of parallel solvers, parallel computing technique is used (Quinn, 1994). In this technique, the total computational job is distributed among several processors. Every processor operates simultaneously that results in saving computational time without interfering with the accuracy of the required results.

Since supercomputers are expensive as compared to the PCs, PC clusters could be used in the place of supercomputers as an inexpensive alternative (Sterling, 2001). Very little work has been reported on the implementation of PC cluster to carry out the finite element analysis. Thiagarajan and Aravamuthan (2002) discussed the implementation of high-performance FORTRAN on 32-node Pentium II 350 MHz Linux cluster. They used two different parallelization strategies on a preconditioned conjugate gradient solver for linear elastic finite element analysis. They found that initially the total time reduces with increase in the number of computers, but after a certain number of computers, the total time increases with further increase in the number of computers. They found that the variation of total time with increasing number of computers is not smooth. The number of computers at which the measured total time is minimum was called optimal number of processors. They concluded that this optimal number of processors depends on the problem size. They also discussed the performance of the developed code by measuring the speedup and found that the speedup increases curvilinearly with increasing number of computers.

Khan and Topping (1996) developed a parallel solver using modified parallel Jacobi-conditioned conjugate gradient method for solving linear elastic finite element system of equations. They employed an element-by-element approach and diagonally conditioned approach in their solver and implemented on distributed memory Multiple-Instruction Multiple Data (MIMD) architectures. They analyzed two finite element domains discretized using 794 and 1172 Constant Strain Triangular (CST) elements. The global stiffness matrices of size 934 and 1294 were solved using multiple processors from 1 to 14. They found that the total time reduces considerably with increase in the number of processors and speedup increases almost linearly with increase in the number of processors.

Structural Engineering Journal, Windows Nt Cluster, Cluster Computing, Finite Element Analysis, Anchorage Zone, Constant Strain Triangular Elements, Multiple-Instruction Multiple Data, MIMD, Gauss-Seidel Method, GSM, Gauss Elimination Method, GEM, Matrix Inversion Method, MIM, Finite Element Method, Computer Technology, Parallel Computing Techniques.