A parallel adaptive coupling algorithm for systems of differential equations

In this paper we address the challenge of metacomputing with two distant parallel computers linked by a slow network and running the numerical approximation of two sets of coupled PDEs. Several software tools are available for coupling codes, and large-scale computing on a network of parallel computers seems to be mature from a computer science point of view. From an algorithmic point of view, the key to obtaining parallel efficiency is the ability to overlap communication with computation: a priori, the speed of communication between the processors that run the two different codes must be of the same order as that between processors that run the same code in parallel. However, a local network of processors is still faster than a long distant network used for metacomputing by one or two orders of magnitude at least. In this paper, to overcome this limitation, we study some new adaptive time-marching schemes for coupling codes so that efficient metacomputing may be obtained. We will focus on stability and accuracy issues in order to minimize the communication processes and define under which conditions our schemes are numerically efficient. We give several examples of applications chosen as representative test cases for the numerical validation of our algorithms. Finally, efficient metacomputing with two distanced computers linked by a slow network is demonstrated for an application in combustion.