Topic/Type: 2.5 Adaptative & multi-scale methods, Poster

### Parallel High Order Time Integrators

B.W. Ong1, A.J. Christlieb1, C.B. Macdonald2

1 Department of Math, Michigan State University, East Lansing, USA
2 Department of Math, University of Oxford, Oxford, UK

In this work we discuss a class of parallel high order time integrators, ideally suited for developing methods which can be order adaptive in time. The method is based on Integral Deferred Correction (IDC), which was itself motivated by Spectral Deferred Correction (SDC) by Dutt, Greengard and Rokhlin (BIT-2000). The method presented here is a revised formulation of explicit IDC, dubbed Revisionist IDC, which can achieve $\small p^{th}$-order accuracy in ?wall-clock time? comparable to a single forward Euler simulation, on problems where the time to evaluate the right hand side of a system of differential equations is greater than latency costs of inter-processor communication, such as in the case of the $\small N$-body problem. The key idea is to re-write the defect correction framework so that, after initial startup costs, each correction loop can be lagged behind the previous correction loop in a manner that facilitates running the predictor and correctors in parallel. Various RIDC schemes are shown to be significantly faster than the popular fourth-order Runge--Kutta method on an example $\small N$-body calculation. The ideas behind RIDC extend to implicit and semi-implicit IDC and have high potential in this area.