## 2 Materials and Methods  
The new algorithm will be showcased on the DMS for the Hydropower Plant Djerdap (HPP Djerdap), which is a medium-head concrete dam located on the Danube River approximately 943 km upstream from the river's estuary into the Black Sea. The dam is 1278 m long, 55 m high, and has a base width of 46 m. It was constructed jointly by Romania and the former Yugoslavia in 1970 and is now operated by Serbia and Romania, each with six generators, seven spillways, and a ship lift. The power output of the Hydropower Plant Djerdap depends on the amount of rainfall in the Danube River basin, with an average annual production of 6000 GWh, which accounts for approximately 20% of Serbia's electricity generation [(39; 40)].  
To model the thermal, filtration, and stress-deformation processes at the Hydropower Plant Djerdap dam (Figure 1), a three-dimensional finite element model of the dam was created (Figures 2 and 3). The model was based on the dam's three-dimensional geometric model, the engineering-geological structure of the surrounding terrain, and the exploitation conditions of the terrain, which was divided into eight geological areas. The dimensions of the model are 400 \(\times\) 442 \(\times\) 50 m. Upstream and downstream ranges are both 200 m. The FEM model includes the spillway (on the right in Figures 1 and 2) and power plant (on the left in Figures 1 and 2). To accurately capture the dam's behavior with as few elements as possible, the model used a very fine mesh for the dam and a coarser mesh for the surrounding terrain, with the mesh becoming increasingly coarse further from the dam. The finite element mesh of the model was created using tetrahedral finite elements with intermediate nodes (10 nodes per element). The structure was modeled in detail with 2,164,778 elements and 3,198,873 nodes. The finite element model of the dam was designed to be integrated into a software system for safety analysis.  
Figure 1: The HPP Djerdap.  
Figure 3: The position of the FEM model of the overflow dam and power plant of HPP Djerdap.  
Figure 2: The FEM model of the overflow dam and power plant of HPP Djerdap.  
The same finite element model was used for thermal analysis, fluid flow analysis through a porous medium, and stress-strain analysis. The spillway of the dam is divided into sections, known as lamellas. Lamela 10 is marked with the blue box in Figure 3; and will be used to showcase interpolation procedure presented in this paper. In order to include the positions of measuring devices in the FE model for all analyses, it is necessary to include the positions of the thermometers and piezometers. However, incorporating the positions of the measuring points in the FE model (by matching the position of the measuring point with a FE node) can significantly increase the number of elements and nodes in the model. Additionally, the positions of all measuring points may not be known at the time the FE model is created, or new measuring points may need to be added subsequently. Therefore, a procedure for calculating the numerical value (such as temperature, potential, displacement, etc.) when the position of the measuring point does not align with a node in the model was developed. The positions of the thermometers, manometers, and piezometers on lamella ten in the model are shown in Figure 4. Thermometers (labeled as T-x) are marked in Figure 4a, while manometers (labeled as M-x) and piezometers (labeled as P-x), which are both instruments used to measure pressure (P), are marked in Figure 4b. Lamella ten is marked in Figure 3.  
Figure 4: Measuring devices on lamella ten of HPP Djerdap: thermometers (a), manometers and piezometers (b).