| In many fields of science and technology and complex engineering problems,the format of the numerical solution of partial differential equations is expressed by algebraic equations.Solving large algebraic equations is very computationally intensive,and the general computer takes a long time.The so-called parallel algorithm is proposed to solve such problems,in order to take advantage of the current popularity of computers to distribute the workload of the approximate solution of partial differential equations to multiple computers to achieve the purpose of reducing the calculation time.This article first discusses the form of algebraic equations and parallel algorithms that are convenient for parallelism.On this basis,when constructing the numerical discrete format of differential equations,we should consider the requirement of parallelization as much as possible,and analyze and discuss the method of facilitating the construction of parallel computing format.A specific equation is taken as an example to illustrate the parallel algorithm.The innovative results of this work are as follows:The parallel Lawrie Sameh algorithm is improved on the condition that the coefficient matrix is a three-diagonal block matrix,and a kind of parallel algorithm with a more general sparse matrix equation system is obtained.And compare the number of operations of such algorithms with traditional algorithms.Taking the boundary value problem of Laplace equation as an example,the problem of using the difference method and the variable limit integral method to construct the numerical format with the above-mentioned convenient parallel calculation under a fixed step is discussed.The numerical format of the Laplace equation that varies with the step size and is convenient for parallelization is given,and an approximate solution sequence that converges to the exact solution is obtained.And gives a complete set of selection methods how to construct a convenient parallel format. |
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