  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.
