Pembinaan dan pelaksanaan algoritma selari bagi kaedah kelas TTHS dan TTKS dalam menyelesaikan persamaan parabolik pada sistem komputer selari ingatan teragih

Abstract

This thesis encompasses studies on recent advances in the development of parallel algorithmic techniques to solve large-scale problems involving the solution of systems of linear equations. An analysis of the computational aspect of the various classes of methods demonstrates that limited parallelism by using block partitioning can be effective in reducing data storage accesses and cost communication in a distributed memory parallel computer system. In the thesis is described the formulation of new iterative methods and the implementation of their parallel analogues in the numerical solution of parabolic equations on a distributed parallel computer system containing 20 PCs Intel Pentium IV with a speed of 1.6 GHz and employing the PVM (Parallel Virtual Machine) application program interface. These schemes are found to be convergent and possess unconditional stability, higher order accuracy and above all explicitly which is highly favorable for numerical parallel processing. New variants of the IADE (Iterative Alternating Decomposition Explicit) and AGE (Alternating Group Explicit) class of methods are developed based on the AD1 fractional splitting strategy. Numerical experiments on multi-dimensional model problems confirm the convergence and accuracies of these schemes. To effect parallel implementation, a number of parallel strategies are suggested. A comparison of the sequential performance of the various methods provides us the following order of increased accuracy and rapid convergence in the IADE class : SUB (Subdomain), SOR (Successive Over-relaxation), RB (Red Black), MULTI (multicaloring), VECTOR and MF (Michell-Fairweather) . Between the two classes, however AGE has the edge over IADE in terms of speedup and efficiency because of the ability of the processors to perform independently due to the presence of non-overlapping subdomain and the nature of the implicit block which can be easily be converted to an explicit form. A comparison of the parallel performance measurements of the two classes of methods also indicate that the communication cost when AGE is used is minimum compared to new IADE (IADEN) and IADE with SUB strategy. The compatibility of the parallel implementation of AGE on the distributed parallel computer system is also discussed. We find that there is a marked improvement in terms of convergence, accuracy, time executions, speedup, efficiency, effectiveness and temporal performance when the AGE concept is extended for application to higher dimensions in cartesian, cylindrical and spherical coordinate systems as exhibited by the newly developed AGE-BRIAN variant. Finally, the CG method is adapted into the IADE class on one-space dimension and the AGE class on one- , two- and three-space dimensions. The parallel and sequential performance measurements of IADE-CG and AGE-CG classes as an alternative to AGE and IADE classes are analyzed. In the thesis, we also consider the communication activities and work balance of the CG method in the context of a distributed parallel computer system. In this paper, element stiffness matrix is formed by groups in each processor related by classes as an alternative to AGE and IADE classes are analyzed. In the thesis, we also consider the communication activities and work balance of the CG method in the context of a d~str~buted parallel computer system.