Studies On Parallel Algorithm Based On Multinomial Preprocessing Conjugate Gradient Method

The improvement of the function of microcomputer processing chip and the high-speed development of computer network provided a good network base for parallel computation. Meanwhile, with the development of commercial hardware and software, computer network was provided with computation of high price ratio and high usability. This is called parallel computers system. It has been a hot spot of studies in academic, commercial and other fields.Parallel Virtual Machine (PVM) is a kind of software system combining a group of loose connected computers into one to do parallel computation. With this kind of computing power and internal storage, many computation problems can be solved with lower cost. PVM has owned large quantity of users and has become a standard of distributed computing of the world because of its transplantability, low price ration, compatability and wide-range of operation.This article tried to apply parallel computing system to solving electrical prospecting and large-scale linear equations caused by using Finite Element Method. Finite Element Method is an important means of engineering subject and has been proved to be a common method in many subjects. However, disadvantages still remained. During the structural analysis, large amount of high-order units were used in order to ensure the precision of arithmetic solution when using Finite Element Method to do discrete processing. This will cause high order of coefficient matrix of corresponding equation group. The basic point of analyzing by Finite Element Method processing structure is to discretize the field (lattice or model). This is similar to that of parallel computing system. Thus, nodal code of Finite Element Method can be parallelized and operated in the connecting point of different groups of PVM. Programming can be done with C++, PVM can be accessed through calling functions in PVM base. Linear equations caused by Finite Element Method can be solved by Multinomial Preprocessing ConjugateGradient Method. There is natural link between these two, both of them use similar minimizing process. The high-vectorization of Multinomial Preprocessing Conjugate Gradient Method makes it be effectively realized in large-scale parallel structure.