On the computation of solution spaces in high dimensions

A stochastic algorithm that computes box-shaped solution spaces for nonlinear, high-dimensional and noisy problems with uncertain input parameters has been proposed in Zimmermann and von Hoessle (Int J Numer Methods Eng 94(3):290-307, 2013). This paper studies in detail the quality of the results and the efficiency of the algorithm. Appropriate benchmark problems are specified and compared with exact solutions that were derived analytically. The speed of convergence decreases as the number of dimensions increases. Relevant mechanisms are identified that explain how the number of dimensions affects the performance. The optimal number of sample points per iteration is determined in dependence of the preference for fast convergence or a large volume.