Parallel decoupling algorithm for solving the block tri-diagonal linear equations

摘要

In this paper, the parallel decoupling algorithm is given to solve the block tri-diagonal linear equations. The solution process of the algorithm are as follows: Firstly, decoupling method is used to decompose the huge block tri-diagonal linear equations to even number small block tri-diagonal ones with balancing loadings, and sum of the small blocks tri-diagonal linear equations equals the number of processors in the cluster that are composed of multiple computers. Secondly, the parallel computing model of the single program multiple data is employed to solve each small blocks tri-diagonal linear equations by the pursuit method in each processor. Lastly, the main processor collects the results from different processors and calculates the final solution of the large block tri-diagonal linear equations.