A nonlinear domain decomposition (DD) solver is considered with respect to improved energy efficiency. In this method, nonlinear problems are solved using Newton’s method on the subdomains in parallel and in asynchronous iterations. The method is compared to the more standard Newton-Krylov approach, where a linear domain decomposition solver is applied to the overall nonlinear problem after linearization using Newton’s method. It is found that in the nonlinear domain decomposition method, making use of the asynchronicity, some processor cores can be set to sleep to save energy and to allow better use of the power and thermal budget. Energy savings up to 77% are observed compared to the more traditional Newton-Krylov approach, which is synchronous by design, using up to 5120 Intel Broadwell (Xeon E5-2630v4) cores. The total time to solution is not affected. On the contrary, remaining cores of the same processor may be able to go to turbo mode, thus reducing the total time to solution slightly. Last, we consider the same strategy for the ASPIN (Additive Schwarz Preconditioned Inexact Newton) nonlinear domain decomposition method and observe a similar potential to save energy.

中文翻译：

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非线性域分解方法的能量效率

非线性域分解 (DD) 求解器被认为是为了提高能量效率。在这种方法中，非线性问题使用牛顿方法在子域上并行和异步迭代地解决。将该方法与更标准的 Newton-Krylov 方法进行比较，后者在使用 Newton 方法线性化之后将线性域分解求解器应用于整体非线性问题。发现在非线性域分解方法中，利用异步性，可以将一些处理器内核设置为休眠以节省能量并允许更好地利用功率和热预算。与更传统的 Newton-Krylov 方法相比，观察到的能源节省高达 77%，后者在设计上是同步的，使用多达 5120 个英特尔 Broadwell (Xeon E5-2630v4) 内核。解决的总时间不受影响。相反，同一处理器的剩余内核可能会进入 turbo 模式，从而稍微减少解决的总时间。最后，我们考虑了 ASPIN（加性施瓦茨预处理不精确牛顿）非线性域分解方法的相同策略，并观察到类似的节能潜力。