An adaptive parallel-in-time method with application to a membrane problem

Abstract

In a previous work (Nassif et al., In: V.A. al (ed.) ICCS 06. Computer Science, pp. 148–155. Springer, New York, 2006), we introduced an approach for solving the initial value problem in a time-parallel way. The main feature of the method is its capacity to automatically generate a non-regular time grid, adapted to the behavior of the solution. Parallel integration is made possible by introducing a “shooting function” that partitions the problem into a sequence of shooting value problems, each defined on a time slice of the coarse grid. After rescaling the variables on each slice, a prediction data model that permits accurate predictions of the solution at the beginning of every slice, leads to an Adaptive Parallel Time Integration (APTI) algorithm. In this paper, the method is applied to a membrane problem having oscillatory and unbounded solutions on (0, ∞).