Design Of Parallel IGMRES(m) Algorithm In Multipole Boundary Element Method

We study the Designing Parallel Algorithms for GMRES(m) in the FM-BEM in this paper, and bring forward Householder Reduction Methods of QR decomposition,and give designing the parallel algorithm at computer's system .At the same time,it was named the Parallel Incomplete Generalized Minimal Residual Method (IGMRES(m)), which was based on the Program-iteration pattern Fast Multipole Method(FMM).We gave Parallel IGMRES(m) in the parallel thinking.Due to its high efficiency and low computing memory demanding,the above method improve the speeding and makes the large-scale computing possible.The paper includes five chapters.Chapter 1 is introduction, which summarizes the research and development of BEM, FMM 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 we discuss the multipole expansion method's suitable scope,and it establishes the foundation of the multipole expansion method fuses with BEM. these are basis to our research parallel FM-BEM.In chapter 3, we describe the designing method of the parallel computer and the parallel algorithm. We also illustrate the related concepts of parallel program, the computation model and evaluation of its algorithm performance. All of these are basis to our research parallel FM-BEM in the following of this paper.In chapter 4,For the three dimension elasticity problem ,we give it's the disperse equation.Secondly, on basis of the designing method of data division of the intersected strategy, We study the Designing Parallel Algorithms for GMRES(m) at the couputer's system. Finally ,.we give Householder Reduction Methods the parallel algorithm of QR decomposition and design the parallel algorithm,and give numerical exemple.it prove that parallel GMRES(m) algorithm improve the speeding and makes the large-scale computing possible.In chapter 5, It was named the Parallel Incomplete Generalized Minimal Residual Method (IGMRES(m)), which was based on the Program-iteration pattern Fast Multipole Method(FMM).We gave Parallel IGMRES(m) in the parallel thinking.It could accelerate the speed of solution and enlarge the scale of the problem with ensured numerical accuracy.