Parallel Algorithm Research Of The Laplace Transform And Its Application Based On MPI

Parallel and distributed technology is a very important way of implementing high performance computing. High-performance computer technology is a crucial method for modern scientific research, engineering technology research and massive data processing. Quite a lot of complex computing problems and transactional dealings will not be finished at proper time without high-performance computers. Also a system with only one computer makes it difficult to meet the need of applications. Under such conditions, large-scale parallel computing systems have become the main architecture and research area of current high-performance computing system. Application systems based on parallel and distributed computing are working effectively on apartments such as finance、transportation、industry、 scientific researches、national defense、government, etc.Parallel algorithms refer to the methods and steps to solve problems by using many computers which work with each other,, researches on it occupies quite an important position in parallel computing technology,and it determines the parallel efficiency. It is urgent to measure properly the performance of new parallel computers’ system architecture, develop parallel algorithm design and analysis in many application fields. Message passing is the main programming model for developing parallel applications. MPI (message passing interface) is a kind of message passing interface which is published on May,1994, and it is a standard of message passing programming, built by industry、scientific researches and government departments together all the world., With such features as flexible support for parallel algorithm implementation, high performance and good portability, It aids to provide an effective and scalable programming environment for parallel programming based on message passing.The Laplace transform is the focus of this article. which is developed from operator method invented by an British engineer named Heaviside in later19th century, whose mathematical essence comes from Laplace, meanwhile, It improves from Fourier transform. It inherits many good characteristic of Fourier transform on one hand, and on the other hand it overcomes many shortcomings of Fourier transform, so Laplace transform is a integral transform which has a more wide application than Fourier transform. . In this paper, first, the author introduces some basic theories on parallel computing and parallel algorithm, following them is parallel procedure design knowledge of MPI, and then knowledge related Laplace transform and its inversion are summarized and analysed systematically,furthermore, some applications are introduced, finally the writer concludes this article and explores prospect for the possible application. The main contributions of this article can be summarized as follows:under the programming environment for parallel programming based on MPI, the writer gives a detailed analysis of feasibility about realization of parallel algorithm on Laplace transform computing, the most important is that the author presents some viewpoints and gives some suggestions,also some algorithms are proposed.it is a attempt for me.