In this article, a digital twin is a numerical model of a dam–foundation system with a physical basis. A dam–foundation system exhibits a complex behavior and, therefore, significant simplifications are necessary for a numerical model to be feasible, which reduces a model’s accuracy. Differences in the material characteristics of particular regions of the dam and the foundation are usually not considered. An important reason for that is the high computational cost of calibrating a model when many parameters must be optimized in such a way that calibration becomes unfeasible. A new, simple, accurate, and low time-consuming algorithm, the centroid method, is presented that allows the calibration of a dam–foundation system. The extreme efficiency of this algorithm opens the feasibility of calibrating a sectorized numerical model of an arch dam, so that a digital twin is obtained that takes into account the different characteristics of different regions or sectors of the dam and the foundation, more closely approaching the complex behavior of the dam–foundation system.

Dam safety is a relevant aspect in our society due to the importance of its functions (power generation, water supply, lamination of floods) and due to the potentially catastrophic consequences of a serious breakdown or breakage. Dam safety analyses are fundamentally based on behavior models, which are idealizations of the dam-foundation that allow us to calculate the dam's response to a certain combination of actions. The comparison of this response with the real one, measured by the auscultation or survey devices, is the main element to determine the safety status of the structure. To improve this analysis, it is necessary to increase the accuracy of the numerical models obtaining a digital twin that allows knowing, in a faithful way, how the structure is going to work in normal and extreme situations.

The generation of a topographical surface or digital elevation model for a given set of points in space is a known problem in civil engineering and topography. In this article, we propose a simple and efficient way to obtain the terrain surface by using a structural shell finite element model, giving advice on how to implement it. The proposed methodology does not need a large number of points to define the terrain, so it is especially suitable to be used with data provided by manual topographical tools. Several examples are developed to demonstrate the easiness and accuracy of the methodology. The digital terrain model of a real landscape is modeled by using different numbers of points (from 49 to 400) using a regular mesh or a randomly generated cloud of points. The results are compared, showing how the proposed methodology creates a sufficiently accurate model, even with a low number of points (compared with the thousands of points handled in a LiDAR representation). A real case application is also shown. As an appendix, the sample code to generate the examples is provided.

This paper presents a finite element methodology for generating continuous digital elevation models (DEMs) from discrete terrain data using the Poisson equation under steady-state conditions. Unlike conventional DEM interpolation techniques, the proposed methodology formulates terrain reconstruction as a constrained harmonic problem, solved directly on scattered point sets using standard finite element procedures, without requiring structured grids or intermediate interpolation stages. The approach interprets the elevation field as a harmonic scalar function whose smoothness is enforced by the variational formulation of the Poisson problem. The governing equation is solved using standard finite element procedures with Dirichlet boundary conditions applied at the measurement points, ensuring that the reconstructed surface passes exactly through the known elevations. The isotropic conductivity coefficient is set to unity and the source term to zero, which simplifies the formulation and yields a harmonic interpolation independent of any physical parameters. The resulting surfaces exhibit continuous slopes and reduced sensitivity to irregular data distributions. Numerical tests comprising two analytical examples and a real terrain case show that, compared with thin-plate FEM and RBF–NURBS reconstructions, the proposed Poisson-based approach yields smoother and more stable surfaces, with global errors of the same order of magnitude and reduced computational cost.

Urban public buildings offer large rooftop PV potential, yet cross-building comparison is often hindered by heterogeneous sizes, operating conditions, and incomplete monitoring. This study develops and applies a standardized indicator framework to benchmark rooftop PV impacts across 12 municipal food markets in Madrid, Spain, using harmonized geometric, energy, PV-system, economic, and environmental metrics. Annual PV impact is screened through changes in purchased electricity derived from pre- and post-installation bills, using 12-month windows where available, while PV generation is represented by the expected production reported in project documentation. The framework includes energy intensity (kWh/m²·year), relative electricity reduction, the reduction-to-expected-production ratio, investment cost per installed capacity, and levelized cost of energy. Descriptive statistics and an LCOE sensitivity analysis are included using discount rates of 3–7%, OPEX values of 1–2% of gross CAPEX, a 25-year system lifetime, and an optional annual degradation rate of 0.5%. The portfolio comprises approximately 735 kW of installed PV, with an aggregated billing-based electricity reduction of approximately 0.994 GWh/year compared with 1.192 GWh/year of expected PV production. The median consumption reduction is approximately 40%, and the reduction-to-expected-production ratio ranges from 0.38 to 2.42. This dispersion confirms that the ratio is a screening and data-consistency indicator rather than a PV performance ratio or a causal estimate of PV generation. The framework supports transparent portfolio screening, cross-building benchmarking, identification of anomalous cases, prioritization of detailed audits, and definition of monitoring requirements for municipal PV programs.