Research And Implementation On Parallelization Of Wu’s Method

As a critical milestone in the process of mathematics mechanization in China, Wu’s method has been of great value in various fields of science, technology and engineering. As the application of Wu’s method becomes wider, its target problems are getting much more complicated than ever before. It is usually the case that many problems may take a few hours or even days to get their solutions on a single computing resource, or that the limited memory makes computation impossible. In addition, Wu’s method is based on symbolic computing which is more compute-intensive than numerical computing, so Wu’s method has a very high computational intensity. Therefore, how to improve the efficiency of Wu’s method has already become an urgent need. Undoubtedly, high performance computing has gradually become the third scientific research method following theoretical science and experimental science for human beings to understand and transform the world after the development of more than half a century. Therefore, high performance computing provides a very good chance to improve the efficiency of Wu’s method.Characteristic set algorithm is the core of Wu’s method, so it is chosen as our research focus. This paper firstly analyzes the process of computing polynomial groups’ characteristic set series on the basis of characteristic set algorithm, then studies Guoliang Chen’s integrated parallel computing research method which combines structure, algorithm, programming and application tightly as a body, and finally puts forward an integrated parallel computing scheme to compute characteristic set series. In this scheme, this paper designs a hybrid multi-granularity parallel algorithm grounded upon factorization and zero points deconstruction, proposes a hybrid parallel programming model under Maple based on grid computing toolbox and task programming model, and chooses SMP cluster which has distributed memory structure and shared memory structure at the same time. As proved by the experiment, this integrated parallel computing scheme works very well by gaining a good acceleration and expands well as the quantity of computing resources increases when the given polynomials can be factorized.