Abstract:

Numerical analyses by the explicit scheme of the finite difference method greatly reduce the number of known variables that are needed to solve an unknown variable in comparison with the implicit methods. This fact means that the amount of communications decreases among each node of the computer cluster on parallel computing. Generally, on the parallel computing of the distributed memory system, the communicating time occupies most of the total calculating time. Therefore, the reduction to the amount of the communication directly causes the reduction of the calculating time. The parallel computing by the explicit scheme of the finite difference method can enable the building up of high-performance algorithms. In order to reduce the amount of communication among each node, one has proposed a method to divide the field of numerical analyses. It is called the ``bread slicing method.'' With this method, the fields must be divided into pieces parallel to the section that has the least area. The results showed that the method in this study enabled the total amount of communication in the computer cluster to be reduced and the geometries of communication to be made simpler.