A partitioned parallel Runge-Kutta method for weakly coupled ordinary differential equations

✍ Scribed by R. P. Mattione; I. N. Katz; M. A. Franklin

• Publisher: John Wiley and Sons
• Year: 1978
• Tongue: English
• Weight: 642 KB
• Volume: 12
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620120208

✦ Synopsis

Abstract

In many systems it is known a priori, that some states are ony weakly coupled with others. If such systems are solved on parallel processor it is possible to partition the states in such a way that one set of states is assigned to one processor and the other set of weakly coupled states to another. Computations can then be done in parallel. Because of the weak coupling it may not be necessary for information from the two sets to be communicated to each other for many integration steps. This can result in significant cost savings. In this paper, a partitined Runge—Kutta scheme is formulated for use on weakly coupleld systems of ordinary differential equations. An error expression is derived which provides a means for predicting the number of step sizes over which the partitioned formulas can be used in terms of a prespecified error tolerance. Numerical examples are presented both to verify the error expressions and to compare solutions using partitioned and unpartitioned schemes.