Global sensitivity analysis on numerical solver parameters of Particle-In-Cell models in particle accelerator systems

Abstract

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 analyse 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 DAE$\delta$ALUS Injector cyclotron and simulations of the rf electron gun of the Argonne Wakefield Accelerator.