Abstract
In this paper we describe the 3-D Telegraph Equation (3-DTEL) with the use of Alternating Direction Implicit (ADI) method on Geranium Cadcam Cluster (GCC) with Message Passing Interface (MPI) parallel software. The algorithm is presented by the use of Single Program Multiple Data (SPMD) technique. The implementation is discussed by means of Parallel Design and Analysis with the use of Domain Decomposition (DD) strategy. The 3-DTEL with ADI scheme is implemented on the GCC cluster, with an objective to evaluate the overhead it introduces, with ability to exploit the inherent parallelism of the computation. Results of the parallel experiments are presented. The Speedup and Efficiency from the experiments on different block sizes agree with the theoretical analysis.
Highlights
Parallel computing has greatly motivated the research works on the parallel design and analysis of the 3-D Telegraph Equation (3-DTEL) in parallel cluster system
We presented a detailed study of using parallel design and analysis on 3-DTEL, and solved by the use of Alternating Direction Implicit (ADI) method on a Geranium Cadcam Cluster (GCC) cluster Message Passing Interface (MPI)
The 3-DTEL with ADI scheme is implemented on the GCC cluster, with an objective to evaluate the overhead it introduces with ability to exploit the inherent parallelism of the computation
Summary
Parallel computing has greatly motivated the research works on the parallel design and analysis of the 3-DTEL in parallel cluster system. Design and analysis for finite difference DD for 2-D heat equation has been discussed in [23], and the parallelization for 3-DTEL on parallel virtual machine with DD [8] show effective load scheduling over various mesh sizes, which produce the expected inherent speedups. The theoretical properties of the 3-D ADI algorithm with the parallel design approach employing SPMD model with DD are promising, achieving good performance as to what was done by [7] in practice can be challenging. We presented a detailed study of using parallel design and analysis on 3-DTEL, and solved by the use of ADI method on a GCC cluster MPI. The SPMD model is employed with DD to enhance overlapping communication with computation that resulted in significant improved speedup, effectiveness, and efficiency across varying mesh sizes as compared to [7].
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