Simulation Methods Research Articles

Multi-objective optimization algorithms for building performance assessment – A benchmark

The increasing development in the computational field that allowed software and hardware advances enables more refined building performance analysis. Simulation-based optimization (SBO) methods allow high standards to be achieved by combining parametric modeling, simulation, and optimization methods. However, SBO methods still need development, especially regarding the correct choice of the optimization algorithm based on the specific characteristics of each problem. This study proposes a multi-objective optimization algorithms benchmark by comparing seven multi-objective optimization algorithms: RBFMOpt, NSGA2, MHACO, NSPSO, MOEA/D, HypE, and SPEA2, across nine building-related problems, including thermal, energy, and daylight simulation. The problems varied from 5 to 18 discrete, continuous, and mixed parameters. The objective functions varied between two and three. We used the hypervolume indicator, IGD+, GD+, and EPS + to compare algorithms’ performance and assess the tendency to reduce computational costs. We also performed the Kruskal-Wallis non-parametric test to analyze the impact of multiple runs on the hypervolume indicator. The results showed that RBFMOpt and HypE perform best across all problems. However, RBFMOpt tends to reduce computational costs since the algorithm requires fewer simulations to obtain the best results.

Study on Surrounding Rock Control of Withdrawal Space in Fully Mechanized Caving Mining of a 19 m Extra-Thick Coal Seam

The section span of the withdrawal space of fully mechanized top coal caving in an extra-thick coal seam is large, and with the gradual withdrawal of the hydraulic support, a series of strong dynamic pressure disasters occur in the withdrawal space, and the difficulty of surrounding rock support control increases sharply. In order to study the control mechanism of surrounding rock in the final mining withdrawal space in detail and put forward a reasonable support technology scheme, taking the large-section withdrawal space of an 8309 fully mechanized caving face in an extra-thick coal seam of a mine as the research object—through the theoretical investigation of whether the key blocks of the main roof are stably hinged under varied stopping coal caving distances and fracture locations of the main roof—the reasonable and optimal stopping coal caving distances and roadway formation time are determined. Using numerical simulation and similar simulation methods, the vertical stress and the maximum shear stress research indicators were introduced to verify the accuracy of the theoretical analysis results. The results show the following: (1) The reasonable stopping coal caving span is 1~2 times the cycle weighting interval, the best stopping coal caving distance in this geological condition is 30 m, and the best fracture position of the main roof is located above the goaf. (2) The migration of overlying strata in the withdrawal space has obvious zoning characteristics, and the zoning is as follows: a stopping coal caving area, support area of the hydraulic support, withdrawal channel area, and stopping coal pillar area. (3) According to the zoning characteristics of overlying strata movement, the asymmetric zoning support control scheme of the withdrawal space is proposed. The field monitoring results show that the maximum roof subsidence in the withdrawal space is 151 mm, the maximum internal squeezing amount of the stopping coal pillar is 82 mm, and the supporting and anchoring effect of each partition in the withdrawal space is good. The set of partition asymmetric support control schemes has been successfully applied to field practice.

Exploring complete catalytic cycle of methane oxidation to methanol on Cu2O2 stabilized within MIL-53(Al) framework: A combined DFT and microkinetic study

Although inspiration from copper-based natural enzymes has shown promise in improving catalyst design for methane-to-methanol (MTM) oxidation, high productivity, and selectivity under mild conditions remain a significant challenge. This study constructs the dinuclear copper (Cu2) species stabilized within the metal-organic framework (MOF), MIL-53(Al), containing Cu as efficient catalytic sites and explores the ability of different oxidants (O2, N2O, and H2O2) to oxidize Cu2 into the dicopper-oxo (Cu2O2) species using density functional theory (DFT) calculations. Our results indicate the kinetic and thermodynamic favorability of Cu2O2 species formation using O2 as an oxidant within the MIL-53(Al) framework. Furthermore, the thermal stability of Cu2O2/MIL-53(Al) has been verified via ab initio molecular dynamics (AIMD) calculations. The kinetics of the complete MTM oxidation cycle over Cu2O2/MIL-53(Al) have been studied using both DFT and microkinetic simulation methods. The present study predicts that the C-H activation on the Cu2O2/MIL-53(Al) has a low free energy barrier (0.77 eV) and that the high stability of CH3 and its very low free energy barrier in the C-O coupling step favors the methanol formation over the formaldehyde. More importantly, Cu2O2/MIL-53(Al) exhibits high methanol selectivity owing to the inhibition of CH3 dehydrogenation and low methanol desorption energy (0.21 eV). Microkinetic simulations confirm the methanol production under relatively mild reaction conditions (200–280 K and 1 bar). This work provides insights into the feasibility of selective MTM oxidation over this family of MOF under mild conditions.

Comparison of statistical methods for the analysis of patient-reported outcomes in randomised controlled trials: A simulation study.

Patient-reported outcomes(PROs) that aim to measure patients' subjective attitudes towards their health or health-related conditions in various fields have been increasingly used in randomised controlled trials(RCTs). PRO data is likely to be bounded, discrete, and skewed. Although various statistical methods are available for the analysis of PROs in RCT settings, there is no consensus on what statistical methods are the most appropriate for use. This study aims to use simulation methods to compare the performance (in terms of bias, empirical standard error, coverage of the confidence interval, Type I error, and power) of three different statistical methods, multiple linear regression(MLR), Tobit regression (Tobit), and median regression (Median), to estimate a range of predefined treatment effects for a PRO in a two-arm balanced RCT. We assumed there was an underlying latent continuous outcome that the PRO was measuring, but the actual scores observed were equally spaced and discrete. This study found that MLR was associated with little bias of the estimated treatment effect, small standard errors, and appropriate coverage of the confidence interval under most scenarios. Tobit performed worse than MLR for analysing PROs with a small number of levels, but it had better performance when analysing PROs with more discrete values. Median showed extremely large bias and errors, associated with low power and coverage for most scenarios especially when the number of possible discrete values was small. We recommend MLR as a simple and universal statistical method for the analysis of PROs inRCT settings.

Electronic Structure Simulations of the Platinum/Support/Ionomer Interface in Proton Exchange Membrane Fuel Cells

ABSTRACTIn this work, we present electronic structure calculations to quantify and rationalize the interactions between catalyst, support, ionomer, and active molecular species in proton exchange membrane fuel cells. Quantifying interaction energies and their scaling with size allows us to rationalize and compare the fundamental driving forces behind structure formation and material properties. Our basic approach involves simplifying the most important interactions between different components using smaller model systems, such as limited‐size platinum nanoparticles, polyaromatic hydrocarbons (graphene flakes), and fragments of various functional units of the Nafion ionomer while applying unbiased first‐principles (density functional theory) simulation methods. To guide this quantification, we propose an analysis based on the linear dependence of interaction energy on the number of interacting atom pairs in the interface. This enables us to compare and categorize interactions between catalyst, ionomer, and support with interactions like catalyst–reactant and catalyst–catalyst poison.

Artificial Intelligence in Logistics Optimization with Sustainable Criteria: A Review

In recent years, the integration of artificial intelligence (AI) into logistics optimization has gained significant attention, particularly concerning sustainability criteria. This article provides an overview of the diverse AI models and algorithms employed in logistics optimization, with a focus on sustainable practices. The discussion covers several techniques, including generative models, machine learning methods, metaheuristic algorithms, and their synergistic combinations with traditional optimization and simulation methods. By employing AI capabilities, logistics stakeholders can enhance decision-making processes, optimize resource utilization, and minimize environmental impacts. Moreover, this paper identifies and analyzes prominent challenges within sustainable logistics, such as reducing carbon emissions, minimizing waste generation, and optimizing transportation routes while considering ecological factors. Furthermore, the paper explores emerging trends in AI-driven logistics optimization, such as the integration of real-time data analytics, blockchain technology, and autonomous systems, which hold immense potential for enhancing efficiency and sustainability. Finally, the paper outlines future research directions, emphasizing the need for further exploration of hybrid AI approaches, robust optimization frameworks, and scalable solutions that accommodate dynamic and uncertain logistics environments.

Level-set lattice Boltzmann method for interface-resolved simulations of immiscible two-phase flow

Level-set lattice Boltzmann method for interface-resolved simulations of immiscible two-phase flow

Calculation acceleration for fuel cycle simulation of molten salt reactor based on multi-group cross section method

The time-consuming issue of transport calculations is prominent in the burnup calculation of nuclear reactor. Multi-Group Cross Section (MGXS) method is an acceleration technique developed based on the characteristics of Monte Carlo simulation, which can significantly reduce the computation time required to solve a single group cross section in transportation calculations. The effectiveness of the method has been verified in the test calculations of water reactor pins. However, liquid molten salt reactors (MSRs) exhibit significant differences from conventional water reactors in terms of neutron energy spectra and fuel cycle mode. The effectiveness of the MGXS method in MSR burnup simulations remains to be validated, and targeted adjustments are required during its application. In this study, OpenMC and ORIGEN2 are coupled to develop an accelerated calculation method for MSR burnup simulations based on the MGXS approach. The reasonable grouping structure of the MGXS method is explored, and the performance of different grouping structures is tested. Results show that the transport calculation can be accelerated by an average factor of 2.4 for a single burnup zone by using MGXS method and the acceleration effect is generally independent of the grouping structure adopted. The nuclide mass bias compared to the traditional direct solution can be reduced to approximately 1% when the fuel burnup is 250MWd/kg for the LEU loading scheme with the 10000 groups structure. For the TRU loading scheme, the mass bias compared to the traditional direct solution of important nuclides (such as U-233, U-235, Pu-239 and so on) can be controlled below 0.5% at a burnup of 230 MW d/kg. The results indicate that the grouping strategy proposed in this study can achieve the adaptation of MGXS to MSRs, and the 10000 groups structure adopted in the study exhibits good accuracy.

Numerical and experimental study on corrosion mechanism of the water-oil two-phase flow in the atmospheric tower top system

The atmospheric tower is the main component of the crude oil refining units and is a critical area of concern due to the risk of corrosion failure. Research on the corrosion mechanism and risk protection of atmospheric tower top systems plays a vital role in the safe operation of refineries. In this paper, the water-oil two phase process flow of the atmospheric tower top system was simulated by Aspen software. A corresponding flow corrosion simulation experiment was designed according to the main characteristic parameters of the simulated stream. The experimental results under varying temperature and impact angle conditions were analyzed by using microanalysis technology and CFD simulation methods. The process and mechanism of corrosion failure of tower top system under ammonia salt and dew point corrosion environment are revealed in physicochemical aspects. The results show that the corrosion rate was highest at the dew point temperature, but as the temperature decreases, the corrosion products adsorbed and accumulated on the surface are more difficult to remove from the surface, which slows down the corrosion rate. When the impact angle increased from 0° to 60°, the increment of the surface fluid impact force and turbulence intensity makes the corrosion products easier to be stripped off, which enhances the mass transfer efficiency between the corrosive medium and the surface to accelerate the corrosion rate. Different phase states and flow modes affected the morphology of corrosion pits on the surface. The depth and size of the pits in only water phase corrosion were larger than those in the two-phase flow corrosion, Additionally, as the impact angle increased from 0°, the morphology of pits changes from a relatively flat pattern to a more undulating shape. The research results reveal the characteristics of the main corrosion types occurring in the atmospheric tower top system of the oil refining industry, and provide a reference for corrosion risk protection methods.

A new validated TRNSYS module for phase change material-filled multi-glazed windows

Incorporating phase change materials (PCM) into multi-glazed windows (MW) has been recognized as an effective way to regulate the indoor thermal environment and reduce the energy consumption of buildings. However, the design and calculation of PCM-filled multi-glazed windows (MW + PCM) remain challenging due to the lack of general transient simulation methods and integrated tools. To address this issue, the present study developed a dynamic coupled thermal and optical model for MW + PCM based on the enthalpy-temperature and interface energy balance methods. Then, the model was implemented in C++ and integrated into the TRNSYS software as a new module (Type 2602). In parallel, a test platform comprising two test chambers was established to evaluate the effect of PCM on the thermal and optical properties of the window and to validate the newly proposed module. It was found that compared to the traditional triple-glazed window (TW), the PCM-filled triple-glazed window (TW + PCM) effectively reduces the irradiance through the window by 34.17 % and the maximum temperature of the inner surface by approximately 5.56 °C. While the increase in external surface radiation flux density from 600 to 1200 W/m2 has a diminishing effect on the heat flux variation rate during the heat dissipation process for TW + PCM, it effectively shortens the latent heat absorption time by 0.50 h and increases the temperature difference between the inner and outer surfaces by 3.02 °C. The new module demonstrates satisfactory accuracy through experimental validation and simulation comparisons, with the maximum heat flux coefficient of variance of the root mean square error (CV(RMSE)) less than 6.35 % and 11.25 % under TW and TW + PCM configurations.

Advanced Hybrid Techniques for Predicting Discharge Coefficients in Ogee-Crested Spillways: Integrating Physical, Numerical, and Machine Learning Models

Abstract The primary objective of this work was to examine the flow characteristics over an ogee spillway using both a numerical model and the Machine Learning (ML) approach. A 3D computational fluid dynamics (CFD) model was employed to simulate the flow over an ogee spillway, utilizing the Reynolds averaged Navier–Stokes equations. The simulation encompassed a wide variety of head ratios, ranging from 0.1 to 6.0, to extend the rating curve of discharge coefficient (C) and head ratio (He/H0). The formation of the negative pressure zone rapidly occurred, and the maximum velocity area developed from toe to top of the spillway surface as the head ratio increased. Then, four ML models—RF, FNN, ADB, and KNN—were utilized to estimate the discharge coefficient of the spillway. Hyperparameter tuning using the Tree-Structured Parzen Estimator (TPE) and five-fold cross-validation ensured robust model performance. The ML model's efficacy was assessed by conducting 200 random seed simulations. The RF and ADB models exhibited the highest predictive accuracy and consistency, with mean correlation coefficient (CC) values of 0.979 and 0.975, respectively. FNN and KNN also performed well but showed greater variability in their prediction. The results demonstrated reasonably good agreement between the physical, numerical, and ML models. Both numerical simulation methods and ML models, particularly RF, proved to be cost-efficient and reliable tools for designing and analyzing flow over an ogee spillway. These findings highlight the potential of integrating numerical simulations and advanced ML techniques to enhance the prediction and analysis of hydraulic structures, providing valuable insights for the design and management of spillway systems.

Effects of cooperative learning and situational simulation on nursing competence in clinical practice among nursing students: A quasi-experimental study

BackgroundAppropriate cooperative learning and situational simulation designs can enhance mental health and nursing competence in clinical practice. This approach is crucial for cultivating the clinical nursing competence of nursing students. AimTo determine the effect of combining cooperative learning and situational simulation on nursing competence in clinical practice. DesignA quasi-experimental study. Setting and participantsThis study was conducted with 142 s-year students in the nursing department of a university in Taiwan. MethodsThe experimental group received cooperative learning combined with situational simulation methods, while the control group used only cooperative learning methods. Data were collected using the Clinical Practice Stress Scale and the Fundamental Nursing Competence Scale. Percentiles and frequency distributions were used to analyze the data, and independent t-tests were conducted to compare differences between the groups. ResultsThere were no significant differences in descriptive characteristics between the groups (p > .05). Post-test measurements of nursing technical performance, total score on the fundamental nursing competence scale and six sub-dimensional scores of the students in the experimental group were significantly improved compared to the control group (p < .001). However, there were no significant differences in total clinical practice stress scale scores between the groups (p > .05). Interestingly, the knowledge score of the control group was significantly higher than that of the experimental group (p < .05). ConclusionThe combined methods of cooperative learning and situational simulation have been shown to positively impact students' academic and nursing technical performance. The results indicate improvements in nursing competence in clinical practice, with signs of a reduction in clinical practice-related stress. Nurse educators can apply these strategies in clinical nursing education to achieve better outcomes.

Study on Multi-Crack Damage Evolution and Fatigue Life of Corroded Steel Wires Inside In-Service Bridge Suspenders

The parallel steel wires used in arch bridge suspenders experience random corrosion damage on their surfaces during service. Corrosion damage, including micro-cracks, pitting, and a combination of both, leads to significant stress concentration under axial loading, which affects the performance of the steel wires. The change in the stress field caused by surface damage alters the stress intensity factor at the crack tip, and the presence of adjacent crack tips significantly amplifies the stress intensity factor, thereby accelerating crack propagation. The development of small surface damages in the steel wires is difficult to control and observe through experiments. By utilizing finite element methods for simulation, it is possible to intuitively analyze the crack propagation process, the trend of stress changes at the crack tip, and the interaction between damages. Numerical simulation results based on Paris’ law indicate that corrosion pits have a certain impact on the stress intensity factor at the crack tip. The propagation process of coplanar double cracks is highly sensitive to the initial crack size and the distance between adjacent crack tips. When the crack spacing is less than the crack depth, the stress intensity factor at the adjacent crack tips exhibits significant amplification. Based on this phenomenon, the coplanar double-crack system can be simplified to a complete single crack for analysis. By comparing the fatigue life of the double-crack system with that of the equivalent single crack, the effectiveness of the simplification rule has been validated.

Numerical Study on the Operational Ventilation Patterns of Alternative Jet Fans in Curved Tunnels

In tunnel operation ventilation systems, the arrangement of jet fans plays a decisive role in ensuring ventilation efficiency. Curved tunnels, due to their unique radius of curvature, exhibit significant differences in fan installation parameters and jet flow field distribution compared to traditional straight-line tunnels. In order to investigate the distinct characteristics, this research utilized computational fluid dynamics (CFD) simulation methods to analyze the ventilation performance of both an innovative, adjustable jet fan system and conventional jet fans within the context of curved tunnel configurations. The findings reveal that by adjusting the horizontal deflection angle of the novel jet fan, the flow field distribution can be effectively optimized, and the jet effect can be enhanced, thereby improving ventilation efficiency. Compared to traditional jet fans, the novel fan demonstrates a significantly greater capability in flow field optimization, especially when its horizontal deflection angle is adjusted, showing a trend where the jet effect initially increases and then decreases, with the longitudinal impact range being adjustable within a range of 5 m to 25 m.

Systematic Review of Quantitative Risk Quantification Methods in Construction Accidents

Construction accidents pose significant risks to workers and the public, affecting industry productivity and reputation. While several reviews have discussed risk assessment methods, recent advancements in artificial intelligence (AI), big data analytics, and real-time decision support systems have created a need for an updated synthesis of the quantitative methodologies applied in construction safety. This study systematically reviews the literature from the past decade, following the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. A thorough search identified studies utilizing statistical analysis, mathematical modeling, simulation, and artificial intelligence (AI). These methods were categorized and analyzed based on their effectiveness and limitations. Statistical approaches, such as correlation analysis, examined relationships between variables, while mathematical models, like factor analysis, quantified risk factors. Simulation methods, such as Monte Carlo simulations, explored risk dynamics and AI techniques, including machine learning, enhanced predictive modeling, and decision making in construction safety. This review highlighted the strengths of handling large datasets and improving accuracy, but also noted challenges like data quality and methodological limitations. Future research directions are suggested to address these gaps. This study contributes to construction safety management by offering an overview of best practices and opportunities for advancing quantitative risk assessment methodologies.

Pharmacophore‐Based Modeling, Synthesis, and Biological Evaluation of Novel Quinazoline/Quinoline Derivatives: Discovery of EGFR Inhibitors with Low Nanomolar Activity

AbstractThe main aim of this study is to obtain novel molecules that are more selective on cancer cells compared to healthy cells. For this purpose, four hit molecules are identified using 11 new pharmacophore hypotheses followed by scanning the in‐house database. Then, based on those hit molecules, the synthesis and analysis of four different series (three quinazolines and one quinoline series) are carried out, and their anticancer activity is investigated. Finally, by using molecular docking and dynamics simulation methods, binding mode and structure–activity relationship are examined. Among the quinazolin‐4(3H)‐one derivatives, those containing halogen atom are found to be potentially effective, while the best epidermal growth factor receptor (EGFR) inhibition and apoptosis induction are displayed by compounds containing 4‐amino‐1,2,4‐triazole moiety. Notably, four compounds (4h, 8d, 8l, and 8m) show EGFR inhibition activity at 5.298 ± 0.164, 5.46 ± 0.221, 2.670 ± 0.124, and 2.191 ± 0.908 × 10−9 m, their inhibitory activity is similar to or stronger than gefitinib (IC50: 4.169 ± 0.156 × 10−9 m). In addition, EGFR inhibitor concentration of 4g, 8e, and 8o is determined as 27588 ± 6.945, 52.41 ± 2.312, and 33657 ± 8.512 × 10−9 m. These findings indicate that generated pharmacophore hypotheses successfully determine new EGFR inhibitors. In conclusion, four novel compounds, more active than gefitinib with fewer side effects, are reached, and the structure–activity relationships are clarified.

Comparison of radiant intensity in aqueous media using experimental and numerical simulation techniques

Accurately modelling the propagation of radiant intensity in aqueous environments poses significant challenges for both academia and industry, due to complex interactions like absorption, scattering, and reflection. This study aims to improve the accuracy of optical modeling in water-based systems by comparing experimental data with numerical simulation techniques, addressing the need for more reliable simulation methods in multiple applications like treatment of water and environmental monitoring.Implementation has been done by analyzing how the method compares with the discrete ordinate method, radiometry, and actinometry. The study further quantifies the effect of the photoreactor quartz tube on measured intensity for multiple wavelengths. Losses in light intensity are estimated to be 10 ± 0.5% for FX-1 265 source. In contrast, the simulation in a water medium showed an increase of up to 64% in the light intensity delivered to the central part of the tube due to internal reflections and scattering. Model predictions from ray tracing successfully compared with the Discrete Ordinate Method (DOM) and experimental data (within ± 6%), ensuring the accurate design of complex systems for water disinfection. The data from simulations is seen to tackle challenges faced in complex radiation modeling and demonstrates that the method can be utilized as a useful tool for optimization and prediction.

Comparison between estimates of beta regression model using MSE

The multiple linear regression analysis shows the effects of explanatory variables on the dependent variable. Its function is to represent data to understand the shape and nature of the relationship between explanatory variables and the response variable. One of the main problems faced by linear regression is the nature of the data, as sometimes it does not follow a normal distribution. This has led to the emergence of different types of linear regression models such as the beta regression model, where the data of the dependent variable is less than one and confined within the period (0,1), and the data is relative and decimal. Non-traditional methods will be used to estimate beta regression parameters because some traditional methods do not provide suitable and accurate results when dealing with one of the main problems encountered in regression, which is multicollinearity. To address this issue, we used some methods include The Maximum Likelihood Estimation (MLE), ridge regression, modified Liu, and Ozkale and Kaciranlar method. Shrinking parameters are proposed for each method, and a comparison between the methods is conducted using the Mean Squared Error comparison criterion through a simulation experiment with two approaches, the simulation results showed that the ridge regression method is the best for the first and second methods of simulation. Paper type Research Paper

Effect of the water erosion on the non-equilibrium condensation in steam turbine cascade

In the final stage of steam turbines, droplets formed by non-equilibrium condensation continuously impact and erode the blades, leading to changes in surface roughness and leading edge erosion. This study investigates the effects of roughness changes and leading edge erosion, induced by water erosion, on non-equilibrium condensation in steam turbine cascades using numerical simulation methods. In a Moses-Stein nozzle, the mechanism of roughness influencing non-equilibrium condensation is analyzed. Subsequently, entropy generation theory is applied to assess the loss distribution caused by roughness variations in a Dykas cascade. Furthermore, flow field analysis and entropy generation theory are utilized to examine the loss distribution pattern resulting from leading edge erosion. Results show that increased roughness delays non-equilibrium condensation, reducing average outlet humidity (from 0.05351 to 0.04361 as roughness rises from 0 to 500 µm). The effect of roughness on thermodynamic entropy generation exhibits a non-linear relationship, balancing steam flow losses with mitigated phase-change-related losses at a roughness of 896 µm. Significant blade erosion (>3 mm) alters leading edge geometry, causing local flow separation and a substantial increase in airfoil losses.

Electromagnetic force calculation within finite volume framework

ABSTRACT In this research, the comparison of force calculation methods in magnetostatic simulations within a cell-centered finite volume framework is presented. Various procedures for postprocessing of the magnetic vector potential field are laid out to obtain the surface and volume integrals of Maxwell’s stress tensor and the Lorentz force density. Two different magnetostatic problems with multiple operating points were modeled with the AVL FIRETM M. The force results have been verified by comparing them to the Ansys Maxwell and were validated on a benchmark case from a Testing Electromagnetic Analysis Methods (TEAM) workshop. The interpolation of the magnetic flux density on a multi-material interface is presented, and it is used in conjunction with the surface integral of Maxwell’s stress tensor for an efficient global force computation. For all observed cases, the calculated results correspond well to the results found in the literature. It was found that the accuracy of the volume integral of Maxwell’s stress tensor is dependent on the mesh quality and gradient calculation scheme. Employing the semi-structured mesh with Gauss’s gradient scheme results in force discrepancies of less than 3% between the surface and volume integral of Maxwell’s stress tensor. The convergence of the iterative solver is observed to be slower in the case of the materials with permeability jump, where discontinuities between the tangential component of the magnetic flux density and the normal component of the magnetic field intensity occur.