| In this paper, we study parallel of generalized minimal residual algorithm (GMRES) in fast multipole boundary element method (FM-BEM), present the discretization of the boundary integral equation and numerical application of parallel algorithm, then improve on the conventional QR decomposition in order to reduce the problem solution process seriously. Due to its high efficiency and low computing memory demanding, the above method makes the large-scale computing possible.The paper includes four chapters. Chapter 1 is introduction, which summarizes the research and development of BEM, FMM, fast multipole-BEM and parallel algorithm, then presented the source, significance of the task and the major work of the paper.In chapter 2, we introduce basic theory knowledge of the fast multipole boundary element method, and it establishes the foundation of the multipole expansion method fuses with BEM form and the followlling to studied multipole expansion BEM, also we discuss the multipole expansion method's suitable scope, this method renews the traditional BEM theory and calculation structure, it is suitable for big scale operate project problem.In chapter 3, we introduce the basic theory of parallel computer, put forward to the parallel algorithm design and simple assemble language of numerical analysis, then discuss some opertions of dense matrix especially, including matrix transpose, matrix-vector product, matrix multiplication and so on. At last, we conclude the advantage of parallel algorithm.In chapter 4, new QR decomposition is presented and its superiority to the conventional QR decomposition is analysed. Then we present the parallel QR decomposition, which has less communication speeding and more speedup ratio. Theory analysis and numerical example show that it is suitable to use in the cluster systems.
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