ParEx: A Parallel Extrapolation Solver for Initial-Value ODEs [2015]

State-of-the-art extrapolation-based solvers for ordinary differential equations (ODEs) are implemented sequentially. In my undergraduate research internship with Professor David Ketcheson of applied mathematics at King Abdullah University of Science and Technology, I exploited the fact that under certain conditions, high-order extrapolation methods naturally admit an efficient multi-processor implementation. Thus, I developed ParEx, an efficient shared-memory parallel implementation of explicit extrapolation methods for solving initial-value ODEs. Using a novel optimal load-balancing algorithm with adaptive step size and order control, ParEx outperforms state-of-the-art solvers on a range of test problems where the derivative evaluation is moderately expensive.