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- W4286233243 abstract "Numerically solving ordinary differential equations (ODEs) is a naturally serial process and as a result the vast majority of ODE solver software are serial. In this manuscript we developed a set of parallelized ODE solvers using extrapolation methods which exploit parallelism within the method so that arbitrary user ODEs can be parallelized. We describe the specific choices made in the implementation of the explicit and implicit extrapolation methods which allow for generating low overhead static schedules to then exploit with optimized multi-threaded implementations. We demonstrate that while the multi-threading gives a noticeable acceleration on both explicit and implicit problems, the explicit parallel extrapolation methods gave no significant improvement over state-of-the-art even with a multi-threading advantage against current optimized high order Runge-Kutta tableaus. However, we demonstrate that the implicit parallel extrapolation methods are able to achieve state-of-the-art performance (2x-4x) on standard multicore x86 CPUs for systems of $<200$ stiff ODEs solved at low tolerance, a typical setup for a vast majority of users of high level language equation solver suites. The resulting method is distributed as the first widely available open source software for within-method parallel acceleration targeting typical modest compute architectures." @default.
- W4286233243 created "2022-07-21" @default.
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- W4286233243 date "2022-07-17" @default.
- W4286233243 modified "2023-10-18" @default.
- W4286233243 title "Parallelizing Explicit and Implicit Extrapolation Methods for Ordinary Differential Equations" @default.
- W4286233243 doi "https://doi.org/10.48550/arxiv.2207.08135" @default.
- W4286233243 hasPublicationYear "2022" @default.
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