Abstract
High performance computing is the branch of parallel computing dealing with very large problems and large parallel computers that can solve those problems in a reasonable amount of time. This paper will describe the parallelization of the Keller-box method using the high performance computing on heterogeneous cluster of workstations. The problem statement is based on the equation of boundary-layer flow due to a moving flat plate. The objective is to develop the parallel algorithm of the Keller-box method in purpose to solve a large size of matrix. The parallelization is based on the domain decomposition, where the upper and lower matrices will be splitting into a number of blocks, which then will be compute concurrently on the parallel computers. The experiment was run using 200, 2000, and 20000 size of matrices and using 10 number of processors. The comparison was made from the results obtained from that various size of matrices by doing the analysis based on the performance measurement in terms of time execution, speedup, and effectiveness.
Highlights
The box method reported by Keller (1970) and known as Keller-box method has become popular for obtaining nonsimilar solutions for boundary layer problems [1]
Parallel computing is a form of computing in which many instructions are carried out simultaneously [2]
The problem statement of this paper is based on the equation of boundary-layer flow due to a moving flat plate
Summary
The box method reported by Keller (1970) and known as Keller-box method has become popular for obtaining nonsimilar solutions for boundary layer problems [1]. The problem statement of this paper is based on the equation of boundary-layer flow due to a moving flat plate. The boundary layer theory is often the case for streamlined bodies that these layers are extremely thin, so we can neglect them entirely in computing the irrotational main flow. Once the irrotational flow has been established, we can compute the boundary layer thickness and velocity profile in the boundary layer, by first finding the pressure distributions evaluated from irrotational flow theory. The parallel algorithm is implemented to the tridiagonal matrix obtained after the calculation using the Keller-Box method. The parallel algorithm is based on the block LU decomposition
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