粒子加速器中粒子胞模型数值解参数的全局灵敏度分析
Global Sensitivity Analysis on Numerical Solver Parameters of Particle-In-Cell Models in Particle Accelerator Systems
摘要：
每个计算机模型都依赖于数值输入参数，这些参数是根据大多数保守但严格的数值或经验估计选择的。这些参数例如可以是时间积分器的步长、伪随机数生成器的种子、阈值或离散计算域的网格点的数量。在数值模型用新算法和建模技术增强的情况下，数值对感兴趣的量的影响、运行时间以及精度通常最初是未知的。通常，参数的选择是在试错的基础上，忽略了计算成本与精度方面。因此，每次模拟的成本可能不必要地高，这浪费了计算资源。因此，有必要确定最关键的数值参数，并系统地分析它们对结果的影响，以尽量减少求解时间，而不会显着损失精度。相关参数是通过全球敏感性研究确定的，其中Sobol指数是常用的衡量标准。这些灵敏度是由基于多项式混沌展开的代理模型得到的。本文首先介绍了不确定性量化的一般方法。然后，我们展示了他们的使用数值求解器参数，以减少计算成本，并讨论进一步的模型改进的敏感性分析的基础上。的灵敏度进行评估现有的PSI注入器II和PSI环，以及拟议的代达罗斯注入器回旋加速器和模拟的阿尔贡尾场加速器的射频电子枪的相邻的一束模拟。
英文摘要：
Every computer model depends on numerical input parameters that are chosen according to mostly conservative but rigorous numerical or empirical estimates. These parameters could for example be the step size for time integrators, a seed for pseudo-random number generators, a threshold or the number of grid points to discretize a computational domain. In case a numerical model is enhanced with new algorithms and modelling techniques the numerical influence on the quantities of interest, the running time as well as the accuracy is often initially unknown. Usually parameters are chosen on a trial-and-error basis neglecting the computational cost versus accuracy aspects. As a consequence the cost per simulation might be unnecessarily high which wastes computing resources. Hence, it is essential to identify the most critical numerical parameters and to analyze systematically their effect on the result in order to minimize the time-to-solution without losing significantly on accuracy. Relevant parameters are identified by global sensitivity studies where Sobol' indices are common measures. These sensitivities are obtained by surrogate models based on polynomial chaos expansion. In this paper, we first introduce the general methods for uncertainty quantification. We then demonstrate their use on numerical solver parameters to reduce the computational costs and discuss further model improvements based on the sensitivity analysis. The sensitivities are evaluated for neighbouring bunch simulations of the existing PSI Injector II and PSI Ring as well as the proposed Daedalus Injector cyclotron and simulations of the rf electron gun of the Argonne Wakefield Accelerator.
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