  As uncertainty and sensitivity analysis of complex models grows ever more
important, the difficulty of their timely realizations highlights a need for
more efficient numerical operations. Non-intrusive Polynomial Chaos methods are
highly efficient and accurate methods of mapping input-output relationships to
investigate complex models. There is substantial potential to increase the
efficacy of the method regarding the selected sampling scheme. We examine
state-of-the-art sampling schemes categorized in space-filling-optimal designs
such as Latin Hypercube sampling and L1-optimal sampling and compare their
empirical performance against standard random sampling. The analysis was
performed in the context of L1 minimization using the least-angle regression
algorithm to fit the GPCE regression models. Due to the random nature of the
sampling schemes, we compared different sampling approaches using statistical
stability measures and evaluated the success rates to construct a surrogate
model with relative errors of $<0.1$\%, $<1$\%, and $<10$\%, respectively. The
sampling schemes are thoroughly investigated by evaluating the y of surrogate
models constructed for various distinct test cases, which represent different
problem classes covering low, medium and high dimensional problems. Finally,
the sampling schemes are tested on an application example to estimate the
sensitivity of the self-impedance of a probe that is used to measure the
impedance of biological tissues at different frequencies. We observed strong
differences in the convergence properties of the methods between the analyzed
test functions.
