High Computational Accuracy Research Articles

Implementation and Application of Cell-Based S-FEM Based on the Object-Oriented Programming Framework

The object-oriented programming is widely used in different fields of finite element analysis (FEA). The commonly used object-oriented codes were almost written by C++. Due to the inability to automatically manage memory and the lack of gigantic standard library and a third-party library for C++, building matrix classes are needed and a strong programming ability for program developers is also necessary. The conventional FEM method still has many disadvantages such as poor accuracy, hard stiffness matrix, mesh dependence and lack of upper bound solution. The smoothed FEM (S-FEM) method proposed by Liu et al. can efficiently overcome these disadvantages and is therefore widely used in FEA. In this work, the elastic-plastic CS-FEM method is extended and implemented using Python programming based on the framework proposed [H. Li and Y. Xiao, Implementation and numerical simulation on object-oriented elastic-plastic finite element method based on Python, J. Syst. Simul. 36(5) (2024) 1107–1117] The resulting object-oriented elastic-plastic CS-FEM framework is then applied to FEA of elastic-plastic mechanics problems. The correctness of the resulting framework and the high computational accuracy and good mesh adaptability of CS-FEM models have been verified by comparing the corresponding results with an analytical solution or ABAQUS results. The object-oriented elastic-plastic CS-FEM framework provides a more efficient and adaptable approach to FEA, and can also overcome many limitations of the conventional FEM method and C++ programming. The use of Python and the CS-FEM method offers improved computational accuracy, mesh adaptability and development efficiency, and this will make it a valuable tool for solving practical problems in mechanics and engineering.

Penalty 4-Node Quadrilateral Element Formulation for Axisymmetric Couple Stress Problems

To address the issue of size effects in axisymmetric deformation of small-scale solids, this work proposes a 4-node 12-DOF element for axisymmetric problems based on the consistent couple stress theory (CCST), following the framework of the unsymmetric finite element method. With the use of the penalty function method, an independently assumed rotational field is introduced into the virtual work principle to approximate the physical rotation, ensuring the satisfaction of the C1 continuity requirement of the CCST in a weak form. As a benefit, the enriched C0 isoparametric-based interpolation is employed to construct the test functions for displacement and rotation. Furthermore, the force-stress field that satisfies the equilibrium equations related to axisymmetric deformation is employed as the element’s force-stress trial function. In order to circumvent locking issues, reduced integration is employed in the penalty stiffness integration process. The numerical results demonstrate that the new element exhibits high computational accuracy and convergence rate in both static and modal analysis problems, effectively capturing size-dependent phenomena.

A unified Jacobi-Ritz-spectral BEM for vibro-acoustic behavior of spherical shell

In order to solve the vibration and acoustic characteristics of spherical shell in light fluid environment, based on Jacobi-Ritz-spectral BEM, a unified analysis formula for acoustic vibration of spherical shell under arbitrary boundary conditions is established. Based on the First-order shear deformation theory (FSDT) and domain decomposition method (DDM), the theoretical model of spherical shell structure is established. The improved Jacobi polynomial is innovatively used to construct the displacement tolerance function of the spherical shell. Based on the spectral Kirchhoff-Helmholtz integral formula, the theoretical model of the acoustic fluid outside the spherical shell is established. The special form of Jacobi polynomial Chebyshev polynomial is used to describe the excitation sound pressure on the spherical shell segment, so as to ensure that the generalized coordinates of the structure can be perfectly matched with the acoustic boundary element nodes. In addition, the integration along the meridian of the shell is used to control the movement of the fluid, which simplifies the surface integration. The CHIEF method is used to solve the problem of non-unique solution of acoustic variables of rotary structure. Compared with the published literature, numerical simulation results and experimental results, the proposed method has higher calculation accuracy. In addition, based on this method, the influence of boundary conditions, geometric dimensions and other factors on the acoustic and vibration characteristics of spherical shells is discussed, which accumulates data for analyzing the acoustic and vibration behavior of spherical shells.

The High Relative Accuracy of Computations with Laplacian Matrices

The High Relative Accuracy of Computations with Laplacian Matrices

Machine Learning-Assisted Hartree–Fock Approach for Energy Level Calculations in the Neutral Ytterbium Atom

Data-driven machine learning approaches with precise predictive capabilities are proposed to address the long-standing challenges in the calculation of complex many-electron atomic systems, including high computational costs and limited accuracy. In this work, we develop a general workflow for machine learning-assisted atomic structure calculations based on the Cowan code’s Hartree–Fock with relativistic corrections (HFR) theory. The workflow incorporates enhanced ElasticNet and XGBoost algorithms, refined using entropy weight methodology to optimize performance. This semi-empirical framework is applied to calculate and analyze the excited state energy levels of the 4f closed-shell Yb I atom, providing insights into the applicability of different algorithms under various conditions. The reliability and advantages of this innovative approach are demonstrated through comprehensive comparisons with ab initio calculations, experimental data, and other theoretical results.

Nonsingular Indirect Boundary Element Method and Multistrategy Particle Swarm Optimization Algorithm Applied to 3D Subsurface Cavity Inversion

ABSTRACTThe inversion of subsurface geological structures is a crucial approach for gaining insights into the internal composition of the earth. In this paper, we propose a novel inversion method combining the nonsingular indirect boundary element method (IBEM) with the multistrategy particle swarm optimization (MSPSO) algorithm, tailored for accurately inverting 3D subsurface cavities. Leveraging the semi‐analytical nature of IBEM offers advantages such as dimensionality reduction, automatic fulfillment of radiation conditions at infinity, and high computational accuracy. Furthermore, to augment global optimization and local search capabilities, an MSPSO algorithm is introduced. Employing multiple optimization strategies enhances particle diversity, accelerates algorithm convergence, and mitigates the risk of local optima. Through the consideration of subsurface cavities with varying parameters, this method quickly identifies the approximate location of the cavity within a wide search range. The final results demonstrate that the proposed method can simultaneously and accurately invert the 3D spatial position, size, and orientation of the cavity.

An Integrated Taylor Expansion and Least Squares Approach to Enhanced Acoustic Wave Staggered Grid Finite Difference Modeling

The staggered grid finite difference method has emerged as one of the most commonly used approaches in finite difference methodologies due to its high computational accuracy and stability. Inevitably, discretizing over time and space domains in finite difference methods leads to numerical artifacts. This paper introduces a novel approach that combines the widely used Taylor series expansion with the least squares method to effectively suppress numerical dispersion. We have derived the coefficients for the staggered grid finite difference method by integrating Taylor series expansions with the least squares method. To validate the effectiveness of our approach, we conducted analyses on accuracy, dispersion, and stability, alongside simple and complex numerical examples. The results indicate that our method not only inherits the capabilities of the original Taylor series and least squares methods in suppressing numerical dispersion across small and medium wavenumber ranges but also surpasses the original methods. Moreover, it demonstrates robust dispersion suppression capabilities at high wavenumber ranges.

Evaluation of Dose Calculation Algorithms Accuracy for ISOgray Treatment Planning System in Motorized Wedged Treatment Fields

Abstract Background: Different dose calculation methods vary in accuracy and speed. While most methods sacrifice precision for efficiency Monte Carlo (MC) simulation offers high accuracy but slower calculation. ISOgray treatment planning system (TPS) uses Clarkson, collapsed cone convolution (CCC), and fast Fourier transform (FFT) algorithms for dose distribution. This study’s primary goal is to evaluate the dose calculation accuracy for ISOgray TPS algorithms in the presence of a wedge. Methods: This study evaluates the dose calculation algorithms using the ISOgray TPS in the context of radiation therapy. The authors compare ISOgray TPS algorithms on an Elekta Compact LINAC through MC simulations. The study compares MC simulations for open and wedge fields with ISOgray algorithms by using gamma index analysis for validation. Results: The percentage depth dose results for all open and wedge fields showed a more than 98% pass rate for points. However, there were differences in the dose profile gamma index results. Open fields passed the gamma index analysis in the in-plane direction, but not all points passed in the cross-plane direction. Wedge fields passed in the cross-plane direction, but not all in the in-plane direction, except for the Clarkson algorithms. Conclusion: In all investigated algorithms, error increases in the penumbra areas, outside the field, and at cross-plane of open fields and in-plane direction of wedged fields. By increasing the wedge angle, the discrepancy between the TPS algorithms and MC simulations becomes more pronounced. This discrepancy is attributed to the increased presence of scattered photons and the variation in the delivered dose within the wedge field, consequently impacts the beam quality. While the CCC and FFT algorithms had better accuracy, the Clarkson algorithm, particularly at larger effective wedge angles, exhibited greater effectiveness than the two mentioned algorithms.

Kinematic matrix: One-shot human action recognition using kinematic data structure

One-shot action recognition, which refers to recognizing human-performed actions using only a single training example, holds significant promise in advancing video analysis, particularly in domains requiring rapid adaptation to new actions. However, existing algorithms for one-shot action recognition face multiple challenges, including high computational complexity, limited accuracy, and difficulties in generalization to unseen actions. To address these issues, we propose a novel kinematic-based skeleton representation that effectively reduces computational demands while enhancing recognition performance. This representation leverages skeleton locations, velocities, and accelerations to formulate the one-shot action recognition task as a metric learning problem, where a model projects kinematic data into an embedding space. In this space, actions are distinguished based on Euclidean distances, facilitating efficient nearest-neighbour searches among activity reference samples. Our approach not only reduces computational complexity but also achieves higher accuracy and better generalization compared to existing methods. Specifically, our model achieved a validation accuracy of 78.5%, outperforming state-of-the-art methods by 8.66% under comparable training conditions. These findings underscore the potential of our method for practical applications in real-time action recognition systems.

Beam Local Stress Prediction Model for Incremental Launching Construction Based on SSA-SVR Algorithm

In the multi-point incremental launching construction process, without setting temporary piers at the mid-span, it is difficult to ensure the synchronization of the launching equipment at the same pier, which can easily cause the beam to deviate from the design axis, leading to changes in the stress of the beam. Calculating the local maximum stress of the beam when lateral deviation occurs is beneficial for establishing a reasonable and reliable threshold for controlling beam deviations. To address this issue, this paper utilizes a finite element model of the bridge under typical adverse conditions, simulating the lateral deviation and asynchronous jacking of the beam to explore stress variation patterns. The results show that the beam stress increases as the lateral deviation and jacking differences increase, severely affecting the structural safety. To overcome the inefficiency of the finite element modeling method when dealing with multiple working conditions and to establish a reasonable deviation control threshold, this study proposes a beam local stress prediction model under the combined influence of lateral deviation and jacking height differences based on the SSA-SVR algorithm. The model calculates the local maximum stress of the beam for 2500 sets of parameters. An engineering case analysis shows that the prediction model has high calculation accuracy, reliable results, fast computational speed, and high efficiency. Based on the stress prediction results, it is recommended to set the jacking height difference control threshold at 20 mm. When the jacking height difference is less than 20 mm, the local maximum stress value under the combined influence of both parameters should be less than the standard limit. The corresponding lateral deviation control threshold can be dynamically adjusted according to the actual travel difference recorded by the jacking equipment, with the control precision improved to 1 mm.

Position and orientation estimation method based on 3D digital morphology contour registration

Abstract Accurately and quickly obtaining the positions and orientations of mechanical parts based on the digital morphologies of mechanical parts are the key to achieving efficient and accurate assembly of mechanical parts. However, due to poor robustness and compactness in extracting digital morphology contours of mechanical parts, the accuracy of assembly positions and orientations obtained by using digital morphology contours cannot meet the requirements of high-precision assembly. Therefore, this paper proposes a position and orientation estimation method based on 3D digital morphology contour registration. This method extracts and optimizes digital morphology contours of mechanical parts and obtains the assembly positions and orientations by using an improved iterative closest point method to register the extracted digital morphology contours with those of the mechanical parts in assembly targets with desired positions and orientations. Experiments are conducted using mechanical parts from the ABC dataset and inertial confinement fusion micro-target. From the experimental results, when using the assembly positions and orientations obtained through the method proposed in this paper to assemble mechanical parts, it can achieve translation absolute errors of 8 μm, 5 μm, and 9 μm along the X-, Y-, and Z-axes, respectively. Similarly, the angular absolute errors in rotations around the Z-, Y-, and X-axes can be less than or equal to 0.16°, 0.15°, and 0.11°, respectively. The results prove that the proposed method in this paper exhibits high computational efficiency and accuracy, providing an effective approach for digital assembly of mechanical parts.

Algorithm Analysis and Optimization of a Digital Image Correlation Method Using a Non-Probability Interval Multidimensional Parallelepiped Model

Digital image correlation (DIC), a widely used non-contact measurement technique, often requires empirical tuning of several algorithmic parameters to strike a balance between computational accuracy and efficiency. This paper introduces a novel uncertainty analysis approach aimed at optimizing the parameter intervals of a DIC algorithm. Specifically, the method leverages the inverse compositional Gauss–Newton algorithm combined with a prediction-correction scheme (IC-GN-PC), considering three critical parameters as interval variables. Uncertainty analysis is conducted using a non-probabilistic interval-based multidimensional parallelepiped model, where accuracy and efficiency serve as the reliability indexes. To achieve both high computational accuracy and efficiency, these two reliability indexes are simultaneously improved by optimizing the chosen parameter intervals. The optimized algorithm parameters are subsequently tested and validated through two case studies. The proposed method can be generalized to enhance multiple aspects of an algorithm’s performance by optimizing the relevant parameter intervals.

Non-contact Structural Displacement Measurement using UAV and DIC with Non-coplanar Fixed Region of Interest

The use of unmanned aerial vehicles (UAV) for displacement measurement using Digital Image Correlation (DIC) has been popular. A fixed region of interest (FROI) is often used to calibrate the UAV camera. Existing techniques require the FROI to be coplanar with the target plane, such that a corner of the FROI can be taken directly as the origin of the global coordinates. However, this condition does not exist when the target plane is in motion, and this has been a significant challenge in the correction of the UAV images. This paper proposed an algorithm to estimate the posture of the UAV camera for solving this issue. Numerical simulation shows that the proposed algorithm has high computation accuracy and stability, and it is robust to the amplitude of motion of the target image or camera. Field experiments confirm the feasibility of the proposed algorithm for images with non-coplanar conditions with a maximum error of less than 2.3 mm and a peak error below 5 %. In comparison to the traditional coplanar correction method, the CPS method demonstrates lower errors, making it better suited for cases where the FROI and the target plane are not coplanar.

Modeling Rayleigh wave in viscoelastic media with constant Q model using fractional time derivatives

The propagation of seismic waves within the near-surface weathering layers, characterized by their low-quality factors (Q), is often accompanied by strong attenuation and dispersion phenomena. Among these, the Rayleigh wave, with its sensitivity to dispersion, has proven to be a powerful tool for near-surface exploration. We propose a novel approach for simulating Rayleigh wave propagation in such low-Q media. Our method uses the time-domain fractional wave equation with memory effect, based on Kjartansson's constant-Q (CQ) model, for accurate characterization of the propagation process. To solve numerically the wave equation with the fractional derivatives, we employ a finite-difference method combined with the auxiliary differential equation-perfectly matched layer (ADE-PML) and the acoustic-elastic boundary approach (AEA). The algorithm's high computational accuracy is verified through comparison with the conventional integer-order wave equation based on the nearly constant-Q (NCQ) models in strong attenuation media. The research in this paper deepens our understanding of the propagation characteristics of Rayleigh waves in strongly weathering layers. This new method strongly supports those seismic imaging and inversion methods depending on seismic modeling, including the reverse time migration and the full waveform inversion of the internal structure of low-Q media.

Investigation on Wax Deposition Risk in Shale Oil Well During Production Test

Abstract During production test of the shale oil well, the low temperature environment in the wellbore is likely to cause wax precipitation of shale oil, and in turn disrupt the normal production test, increase the operating costs and risks. In view of this problem, by considering the gas-liquid flow, radial heat transfer and temperature gradient etc, a temperature and pressure field model of shale oil wellbore was established, and a prediction method of wax deposition zone in the shale oil wellbore during production test was proposed. Furthermore, by using the production data of a shale oil well with wax deposition in the South China Sea during production test, the accuracy of the model in calculating the fluid temperature and pressure of the wellbore with wax deposition was verified. The wellhead temperatures calculated by the model had a maximum error of 9.31%, and the bottom-hole pressures calculated by the model had a maximum error of 7.52%, indicating the model has high calculation accuracy. The model was used to analyze the sensitivities of wax deposition to the time and rate of production, water content and the ratio of gas to oil. It is found that the wax deposited in wellbore increases in thickness with the production time, is more strongly affected by production rate and water content, but less affected by the ratio of gas to oil. The research results can provide support for preventing wax deposition during production test of shale oil wells.

Graph-GIC: A smart and parallelized geomagnetically induced current modelling algorithm based on graph theory for space weather applications

Geomagnetically Induced Current (GIC) refers to the electromagnetic response of the Earth and its conductive modern infrastructures to space weather and would pose a significant threat to high-voltage power grids designed for the alternative current operation. To assess the impact of space weather on the power grid, one needs to calculate the GIC on a national or continental scale. In this study, we developed a smart and parallelized GIC modelling algorithm, Graph GIC. This algorithm deploys a graph representing a power grid in a single-line diagram, in which substations/transformers act as nodes and transmission lines as edges. With these denotations, a power grid and its electric parameters are mathematically represented with an adjacency matrix and an admittance matrix. We used sparse matrix and parallelisation techniques to expedite the intensive computation in cases of large-scale power grids. The Graph GIC was validated with a benchmark grid, applied to the GIC calculation of the 500 kV power grid of Guangdong, China, and conducted preliminary analysis on the grid’s susceptibility to geomagnetic storms. The Graph GIC algorithm has the advantage of an intuitive and highly scalable graph representation of a power grid at any scale. It achieves high-accuracy calculation and a speedup of about 18 times after parallelisation. This algorithm could be applied to assess the impact of space weather on a power grid up to continental scales and could be incorporated into global space weather modelling frameworks.

An improved detached eddy simulation method for cavitation multiphase flow

The evolution of cavitation flow involves intense transient characteristics and complex multi-scale motions, significantly increasing the difficulty and computational cost of solving in separation zones. This study proposes an Improved Detached Eddy Simulation (IDES) method, based on a single-equation eddy-viscosity model, aimed at enhancing the resolution of small-scale cavitation flows. By incorporating the broad-spectrum von Karman scale concept, the method effectively improves the resolution capability for small-scale flows in separated zones. The performance of the IDES model was validated through three computational cases, and the main conclusions are as follows: The results of the triangular cylinder flows show that the IDES model demonstrates a resolution capability for large-scale turbulence comparable to the Large Eddy Simulation (LES) model. The orifice flow results indicate that activating the LES method with insufficient grid resolution is highly discouraged, whereas the IDES model performs more robustly under such conditions. For hydrofoil flows, the IDES model more accurately captures the temporal evolution of cavitation, avoiding the premature cavity shedding predicted by LES under coarse grid conditions. The decomposition results of the vorticity transport equation show that both the dilatation term and viscous term are significant contributors in the vorticity transport process, with their average contributions to vorticity reaching 49.25% and 39.99%, respectively. Vortices can be considered the primary controllers of cavitation dynamics, while the dilatation term and viscous term can be regarded as the main controllers of vorticity. Overall, the energy compensation mechanism of the IDES model, based on local flow information, gives it unique advantages in handling small-scale turbulence and cavitation phenomena, providing both high computational efficiency and accuracy.

A support vector regression-based interval power flow prediction method for distribution networks with DGs integration

In distribution networks with distributed generators (DGs), power generation and load demand exhibit increased randomness and volatility, and the line parameters also suffer more frequent fluctuations, which may result in significant state shifts. Existing model-driven methods face challenges in efficiently solving uncertain power flow, especially as the size of the system increases, making it difficult to meet the demand for rapid power flow analysis. To address these issues, this paper proposes an SVR-based interval power flow (IPF) prediction method for distribution networks with DGs integration. The method utilizes intervals to describe system uncertainty and employs Support Vector Regression (SVR) for model training. The input feature vector consists of the intervals of active power generation, load demand, and line parameters, while the output feature vector represents the intervals of voltage or line transmission power. Ultimately, the SVR-based IPF prediction model is established, capturing the linear mapping relationship between input data and output IPF variables. Simulation results demonstrate that the proposed method exhibits high prediction accuracy, strong adaptability, and optimal computation efficiency, meeting the requirements for rapid and real-time power flow analysis while considering the uncertainty in distribution networks with DGs integration.

Research on hydrodynamics of the thermal agent flow for the beet pulp filtration drying

The reuse and recycling of secondary raw materials is essential to ensure sustainable development and the rational use of natural resources. One of the most important types of secondary raw materials is plant-based food waste, which is generated in large quantities at food processing plants, including sugar beet pulp, which is a valuable resource for further use. One of the main problems with using beet pulp is its high moisture content, which is ≈ 80 % wt. It is proposed to dry beet pulp by filtration drying, which is highly efficient. The calculation of industrial equipment for filtration drying should take into account the costs of overcoming the hydraulic resistance of a stationary layer of material. The aim of the article was to study the hydrodynamics of the flow of a thermal agent through a stationary layer of beet pulp of different heights and to perform computer modelling of this process. The obtained results will allow predicting the hydraulic resistance of a material layer of different heights and the required pressure drop to ensure the course of the drying process under various possible technological modes. For computer modelling of the flow of a thermal agent through a stationary layer of beet pulp, the porous media method was used in the ANSYS Fluent 2022 R2 software package. The process was simulated on the basis of the Navier-Stokes system of differential equations and the flow continuity equation with the additional use of the Darcy equation to determine the value of the hydraulic resistance of the layer ΔP. Computer simulations of the hydrodynamics of the thermal agent flow through a stationary layer of beet pulp were performed for the range of stationary layer heights H = 90÷110 mm with an interval of 5 mm. The obtained data showed a relative average deviation of 2.19 % from the experimental data, which indicates a high accuracy of calculations in this range. The study for the extended range of layer heights H = 80÷120 mm with an interval of 10 mm showed an increase in the relative average deviation to 4.09 % from the experimental data, but the results are still sufficiently accurate for practical use in the calculation of drying equipment. The obtained dependencies may be used to determine the value of the hydraulic resistance of a stationary layer of material using the filtration drying method and for practical calculations of drying equipment. Together with the results of the kinetic regularities of filtration drying, the obtained experimental data and computer modelling data on the hydrodynamics of the flow of a heat transfer agent through a material layer will allow us to calculate the optimal parameters of filtration drying for beet pulp and to assess the efficiency of filtration drying for drying beet pulp in comparison with other methods of dehydration.

A Prediction Model for Pressure and Temperature in Geothermal Drilling Based on Physics-Informed Neural Networks

With the global expansion of geothermal energy, accurate prediction of pressure and temperature during drilling has become essential for ensuring the safety and efficiency of geothermal wells. Traditional numerical methods, however, often struggle to handle complex wellbore environments due to their high data demands and limited computational accuracy. To address these challenges, this paper introduces an innovative predictive model based on Physics-Informed Neural Networks (PINNs). By integrating physical laws with deep learning, the model theoretically surpasses the limitations of conventional methods. Trained on pressure and temperature data from a geothermal well in the Xiong’an area, the model demonstrates exceptional accuracy and robustness. Additionally, the model was rigorously tested under extreme wellbore conditions, showcasing its strong generalization capabilities. The findings suggest that PINNs offer a highly advantageous solution for geothermal drilling, with significant potential for practical engineering applications.