In this paper, we present a reconstruction of climate conditions during the Last Glacial Maximum on a karst plateau Snežnik, which lies in Dinaric Mountains (southern Slovenia) and bears evidence of glaciation. The reconstruction merges geomorphological ice limits, classified as either clear or unclear, and a computer modelling approach based on the Parallel Ice Sheet Model (PISM). Based on extensive numerical experiments where we studied the agreements between simulated and geomorphological ice extent, we propose using a combination of a high-resolution precipitation model that accounts for orographic precipitation combined with a simple elevation-based temperature model. The geomorphological ice extent can be simulated with climate to be around 6 °C colder than the modern day and with a lower-than-modern-day amount of precipitation, which matches other state-of-the art climate reconstructions for the era. The results indicate that an orographic precipitation model is essential for the accurate simulation of the study area, with moist southern winds from the nearby Adriatic Sea having a predominant effect on the precipitation patterns. Finally, this study shows that transforming climate conditions towards wetter and warmer or drier and colder does not significantly change the conditions for glacier formation.

We present an algorithm for hp-adaptive collocation-based mesh-free numerical analysis of partial differential equations. Our solution procedure follows a well-established iterative solve–estimate–mark–refine paradigm. The solve phase relies on the Radial Basis Function-generated Finite Differences (RBF-FD) using point clouds generated by advancing front node positioning algorithm that supports variable node density. In the estimate phase, we introduce an Implicit-Explicit (IMEX) error indicator, which assumes that the error relates to the difference between the implicitly obtained solution (from the solve phase) and a local explicit re-evaluation of the PDE at hand using a higher order approximation. Based on the IMEX error indicator, the modified Texas Three Step marking strategy is used to mark the computational nodes for h-, p- or hp-(de-)refinement. Finally, in the refine phase, nodes are repositioned and the order of the method is locally redefined using the variable order of the augmenting monomials according to the instructions from the mark phase. The performance of the introduced hp-adaptive method is first investigated on a two-dimensional Peak problem and further applied to two- and three-dimensional contact problems. We show that the proposed IMEX error indicator adequately captures the global behaviour of the error in all cases considered and that the proposed hp-adaptive solution procedure significantly outperforms the non-adaptive approach. The proposed hp-adaptive method stands for another important step towards a fully autonomous numerical method capable of solving complex problems in realistic geometries without the need for user intervention.

When solving partial differential equations on scattered nodes using the radial basis function generated finite difference (RBF-FD) method, one of the parameters that must be chosen is the stencil size. Focusing on Polyharmonic Spline RBFs with monomial augmentation, we observe that the stencil size affects the approximation accuracy in a particularly interesting way - the solution error dependence on stencil size has several local minima. We find that we can connect this behaviour with the spatial dependence of the signed approximation error. Based on this observation we are then able to introduce a numerical quantity that indicates whether a given stencil size is close to one of those local minima.

Transmission system operators (TSOs) in recent years have faced challenges in order to ensure maximum transmission capacity of the system to satisfy market needs, while maintaining operational safety and permissible impact on the environment. A great help in the decision-making process was introduced with the Dynamic Thermal Rating (DTR) - an instrument to monitor and predict the maximal allowed ampacity of the power grid based on weather measurements and forecast. However, the introduction of DTR raises a number of questions related to the accuracy and uncertainty of the results of thermal assessment and the level of acceptable risk and its management. In this paper, we present a solution for estimating DTR uncertainty, appropriate for operational use at TSOs. With the help of conductor surface temperature measurements, weather measurements and predicted weather data, we also estimate the error of the weather forecast and the DTR itself. Following the results of the data analyses, we build an operative solution for estimating the ampacity uncertainty based on Monte Carlo random simulations and integrate it into the operational environment of ELES - the operator of the Slovenian electric power transmission network.