N.H.M. Ali, T.C. Shien, and C.C. Hau (Malaysia)

Numerical methods, biharmonic equation, high performance computing, parallel algorithm.

In this paper, we consider the parallel development on group iterative scheme based on rotated(cross) five-point finite difference discretisation in solving a fourth order elliptic partial differential equation (p.d.e). This type of discretisation was firstly introduced by Abdullah [1] in solving the second order elliptic p.d.e.'s where the resulting algorithm was found to be more superior than the common existing methods based on the standard five point finite difference discretisation. This is due to the fact that this type of discretisation will lead to lower computational complexities since the iterative procedure need only involve nodes on half of the total grid points in the solution domain. The method was then shown to be viable elliptic solver on a shared memory parallel computer where almost linear speedups were achieved in almost all of the cases tested ([2], [3]). In this work, we describe the parallel implementation of this method in solving the biharmonic equation on a distributed parallel system, specifically on a cluster of workstations using PVM programming environment: the results of some computational experiments are reported.

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