Mesh Generation Research Articles

Automatic reorientation by deep learning to generate short-axis SPECT myocardial perfusion images

BackgroundSingle photon emission computed tomography (SPECT) myocardial perfusion images (MPI) can be displayed both in traditional short-axis (SA) cardiac planes and polar maps for interpretation and quantification. It is essential to reorient the reconstructed transaxial SPECT MPI into standard SA slices. This study is aimed to develop a deep-learning-based approach for automatic reorientation of MPI. MethodsA total of 254 patients were enrolled, including 226 stress SPECT MPIs and 247 rest SPECT MPIs. Fivefold cross-validation with 180 stress and 201 rest MPIs was used for training and internal validation; the remaining images were used for testing. The rigid transformation parameters (translation and rotation) from manual reorientation were annotated by an experienced nuclear cardiologist and used as the reference standard. A convolutional neural network (CNN) was designed to predict the transformation parameters. Then, the derived transform was applied to the grid generator and sampler in spatial transformer network (STN) to generate the reoriented image. A loss function containing mean absolute errors for translation and mean square errors for rotation was employed. A three-stage optimization strategy was adopted for model optimization: (1) optimize the translation parameters while fixing the rotation parameters; (2) optimize rotation parameters while fixing the translation parameters; (3) optimize both translation and rotation parameters together. ResultsIn the test set, the Spearman determination coefficients of the translation distances and rotation angles between the model prediction and the reference standard were 0.993 in X axis, 0.992 in Y axis, 0.994 in Z axis, 0.987 along X axis, 0.990 along Y axis and 0.996 along Z axis, respectively. For the 46 stress MPIs in the test set, the Spearman determination coefficients were 0.858 in percentage of profusion defect (PPD) and 0.858 in summed stress score (SSS); for the 46 rest MPIs in the test set, the Spearman determination coefficients were 0.9 in PPD and 0.9 in summed rest score (SRS). ConclusionsOur deep learning-based LV reorientation method is able to accurately generate the SA images. Technical validations and subsequent evaluations of measured clinical parameters show that it has great promise for clinical use.

Sonic boom near field analysis of a Mach 5 wave-rider configuration

The following paper discuss the near field sonic boom results obtained with CFD simulations regarding a Mach 5 wave rider configuration derived from the STRATOFLY heritage. Sonic boom near field have emerged as a vital tool for the mitigation and understanding of the impact of supersonic and hypersonic aircraft configurations. The work done discusses the major consideration in the CFD approach for the flow field simulations in the vicinity of the aircraft, including grid generation techniques based on the NASA sonic boom predictions workshop carried out between 2014 and 2020 and the results obtained for different flight conditions and operations. The near field simulation necessitates of accurate predictions of shock wave propagation generated by the aircraft, employing the high-fidelity numerical schemes and turbulence models. These results will be the input for our propagation tool that manage to propagate the shocks from the aircraft to the ground. This work is carried out within the MORE&LESS project, that is an EU-funded project and has the aim to investigate the environmental impact of supersonic aircraft through multi-fidelity simulations and test campaigns for creating multidisciplinary holistic framework for the evaluation of the future supersonic aircraft, trajectories, and operations.

A Robust Adaptive Mesh Generation Algorithm: A Solution for Simulating 2D Crack Growth Problems.

This paper introduces a robust algorithm that efficiently generates high-quality unstructured triangular meshes to model complex two-dimensional crack growth problems within the framework of linear elastic fracture mechanics (LEFM). The proposed Visual Fortran code aims to address key challenges in mesh generation including geometric complexity, required simulation accuracy, and computational resource constraints. The algorithm incorporates adaptive refinement and updates to the mesh structure near the crack tip, resulting in the formation of rosette elements that provide accurate approximations of stress intensity factors (SIFs). By utilizing the maximum circumferential stress theory, the algorithm predicts the new crack path based on these SIFs. Throughout the simulation of crack propagation, a node splitting approach was employed to represent the progression of the crack, while the crack growth path is determined by successive linear extensions for each crack growth increment. To compute stress intensity factors (SIFs) for each increment of crack extension, a displacement extrapolation method was used. The experimental and numerical results demonstrated the algorithm's effectiveness in accurately predicting crack growth and facilitating reliable stress analysis for complex crack growth problems in two dimensions. The obtained results for the SIF were found to be consistent with other analytical solutions for standard geometries.

A high resolution Physics-informed neural networks for high-dimensional convection–diffusion–reaction equations

In practical problems, some partial differential equations defined in high-dimensional domains or complex surfaces are difficult to calculate by traditional methods. In this paper, a novel data-driven deep learning algorithm is proposed to solve high-dimensional convection–diffusion–reaction equations. The main idea of the method is to use the neural network which combines the physical characteristics of the equation to get high accuracy numerical solution. The proposed method not only avoids the high cost of mesh generation, but also effectively reduces the numerical oscillation caused by the domination of the convection. In addition, two types of loss functions are designed to force physical properties, such as the positivity or maximum principle of the solution. Various numerical examples are performed to demonstrate the validity and accuracy of the proposed method.

Cross-Field Structured Adaptive Mesh Using Medial Axis Flow Feature Extraction

A method to generate feature-aligned anisotropic structured meshes automatically is presented for high resolution of two-dimensional complicated flow features such as normal and oblique shock waves, shock reflection, shock/shock interaction, and shock/boundary-layer interaction. The method starts from extraction of dominant flow features to be treated alongside geometric entities. This is followed by automatic generation of multiblock structured meshes of the flow domain using a cross-field based method so that the flow feature entities are embedded along with the geometries. The cross-field method allows for the automatic blocking so that anisotropic quadrilateral meshes generation and adaptation to resolve flow features can be carried out. The resulting mesh possesses high element quality for orthogonality and high resolution of the flow features, suitable for the shock capturing methods and higher-order reconstruction schemes. The method is demonstrated through a number of aerodynamic flow test cases with discussion on its efficiency, accuracy, and robustness.

DFNMesh: Finite element meshing for discrete fracture matrix models

This paper presents a novel methodology for robust Finite Element (FE) mesh generation of Discrete Fracture Matrix (DFM) models. The method can handle the complete multi-dimensional domain from the tridimensional porous rock matrix, through fracture surfaces, down to open curves for fracture–fracture intersections. The accompanying open-source code is written in modern C++ with a JSON interface and largely relies on two state-of-the-art FE libraries: NeoPZ and Gmsh. Starting from a user-defined coarse mesh, fractures are sequentially read as convex polygons and introduced without distortions to the coarse geometry. The main steps involve: intersect edges by checking for nodes on opposite sides of the fracture plane, extend intersections from edges to faces, coalesce intersections to closest existing nodes (given a tolerance), refine interface elements to conform to the fracture, identify subsets of fracture surface, mesh the surface, and locate boundaries and intersections where they arise. Finally, the space around fractures is filled with the fine-scale unstructured mesh, which is kept conformal. The robustness of the implementation is derived from the consistent background of well-defined and simple premises like convexity and side-specific element neighborhood. Results show that the proposed technique can construct adequate 3D DFM grids, while still giving users freedom to adjust between geometrical fidelity and mesh quality through more aggressive feature rejection.

Analysis of the subsurface and fluid temperature monitoring by long-term operation of borehole heat exchangers

Owing to the prevailing escalation in energy costs, escalating energy demands, depletion of conventional resources, and escalating greenhouse gas emissions, there has been an expeditious upsurge in the worldwide proliferation of alternative energy sources. Geothermal systems, in particular, are highly coveted as environmentally friendly and sustainable renewable energy reservoirs, offering efficacious cooling and heating capabilities for various structures (Xu et al., 2020; Ghasemi-Fare & Basu, 2013). The energy exchange efficiency of geothermal systems is significantly contingent upon the ground temperature, enabling the discharge of energy into the ground for cooling purposes in summer and its retrieval for heating requirements during winter. However, long-term operation of geothermal energy systems can engender an imbalance in thermal recovery through the heating and cooling processes, consequently influencing the thermomechanical behavior of the subsurface over time (Baek et al., 2017). Geothermal systems, also known as ground source heat pumps (GSHPs), are designed to operate for around 20 years, while the heat source component can be utilized for an extended duration ranging from 30 to 50 years. Understanding heat transfer characteristics and long-term performance of geothermal energy systems is crucial for optimal utilization and efficiency. However, research often lacks field investigation data, specifically for long-term monitoring and validation of fluid temperatures and subsurface temperature profiles. This research conducted comprehensive long-term measurements to assess fluid and subsurface temperature behavior in a borehole heat exchanger (BHE) system. The study examined the impact of sustained BHE performance on surface and subsurface temperature dynamics. A sophisticated three-dimensional numerical model was developed based on empirical insights from the field study and validated using monitored data. The analysis included inlet/outlet fluid temperature, spatial heterogeneity of ground temperature profiles, thermal recovery processes, and alterations caused by residual thermal energy.
 Furthermore, additional temperature sensors were deployed at various depths to monitor temperature changes at distinct levels within the subground.
 In this study, an advanced three-dimensional (3D) numerical model was developed utilizing the Finite Element Method (FEM) to effectively capture the intricate heat transfer processes occurring around BHEs. The geometry mesh was generated using a specialized triangular mesh generator, enabling spatial variation of element sizes to accurately represent the geometry and temperature distribution patterns. To address the specific requirements of U-tube heat exchanger loops, where the steepest temperature gradient is anticipated, a meticulously chosen element size of 0.7 mm, was employed. As the model extends towards the lateral boundaries, particularly in the radial direction, the element size gradually increases to ensure faithful representation of the system's characteristics. To properly account for diverse vertical temperature gradients, the number of elements and the vertical distance between slices were systematically adjusted within a range of 0.01 to 5 m. This meticulous variation facilitated accurate consideration of the distinct vertical temperature profiles. Notably, the finest discretization was applied near the bottom of the BHE (approximately z = -155 m) and at the top surface, characterized by a significant temperature gradient.
 The depicted Figure 2 showcases the model's performance in analyzing the fluid profile in comparison to the monitored data over a duration of 600 hours. This comparison reveals that the maximum relative difference between the monitored and simulated values for the inlet and outlet fluid temperature does not exceed 2.649 and 2.296 degrees Celsius, respectively. These findings offer compelling evidence of the exceptional accuracy of the proposed numerical modeling approach, thus affirming its suitability for examining the long-term sustainability of BHE systems.

Prediction-based peer-to-peer energy transaction market design for smart grids

Predicting energy costs and energy generation in traditional power grids is a complex endeavour, primarily due to the imperative of maintaining supply–demand equilibrium for upholding the stability of the power system. Predicting energy costs and generation includes the highly variable nature of energy prices and the need to analyze large amounts of data from various sources. We propose an auto-executable blockchain-based peer-to-peer(P2P) energy transaction market with a Long short-term memory (LSTM) neural network to address challenges in the energy sector. LSTM can handle non-linear relationships and can effectively model and predict the complex patterns that arise in energy markets. Our energy market enables accurate energy consumption and production prediction, facilitates decentralized and sustainable energy trading, and balances supply and demand via smart contracts. A secure and efficient blockchain-based P2P energy transaction market is designed to facilitate transactions in smart grids. The integrated system is a novel contribution that can improve energy systems’ efficiency, reliability, and sustainability. Our experiments show that our proposed energy market can reduce the electricity buying budget by 17.68% compared to the traditional market and 41.36% compared to the open loop look ahead dispatch method for 30 microgrids and the utility.

Numerical Simulation of the Conjugate Heat Transfer of a “Fluid–Solid Body” System on an Unmatched Grid Interface

Recently, when modeling transient problems of conjugate heat transfer, the independent construction of grid models for fluid and solid subdomains is increasingly being used. Such grid models, as a rule, are unmatched and require the development of special grid interfaces that match the heat fluxes at the interface. Currently, the most common sequential approach to modeling problems of conjugate heat transfer requires the iterative matching of boundary conditions, which can significantly slow down the process of the convergence of the solution in the case of modeling transient problems with fast processes. The present study is devoted to the development of a direct method for solving conjugate heat transfer problems on grid models consisting of inconsistent grid fragments on adjacent boundaries in which, in the general case, the number and location of nodes do not coincide. A conservative method for the discretization of the heat transfer equation by the direct method in the region of inconsistent interface boundaries between liquid and solid bodies is proposed. The proposed method for matching heat fluxes at mismatched boundaries is based on the principle of forming matched virtual boundaries, proposed in the GGI (General Grid Interface) method. A description of a numerical scheme is presented, which takes into account the different scales of cells and the sharply different thermophysical properties at the interface between liquid and solid media. An algorithm for constructing a conjugate matrix, the form of matrix coefficients responsible for conjugate heat transfer, and methods for calculating them are described. The operability of the presented method is demonstrated by the example of calculating conjugate heat transfer problems, the grid models of which consist of inconsistent grid fragments. The use of the direct conjugation method makes it possible to effectively solve both stationary and non-stationary problems using inconsistent meshes, without the need to modify them in the conjugation region within a single CFD solver.

Multi-compartment head modeling in EEG: Unstructured boundary-fitted tetra meshing with subcortical structures.

This paper introduces an automated approach for generating a finite element (FE) discretization of a multi-compartment human head model for electroencephalographic (EEG) source localization. We aim to provide an adaptable FE mesh generation tool for EEG studies. Our technique relies on recursive solid angle labeling of a surface segmentation coupled with smoothing, refinement, inflation, and optimization procedures to enhance the mesh quality. In this study, we performed numerical meshing experiments with the three-layer Ary sphere and a magnetic resonance imaging (MRI)-based multi-compartment head segmentation which incorporates a comprehensive set of subcortical brain structures. These experiments are motivated, on one hand, by the sensitivity of non-invasive subcortical source localization to modeling errors and, on the other hand, by the present lack of open EEG software pipelines to discretize all these structures. Our approach was found to successfully produce an unstructured and boundary-fitted tetrahedral mesh with a sub-one-millimeter fitting error, providing the desired accuracy for the three-dimensional anatomical details, EEG lead field matrix, and source localization. The mesh generator applied in this study has been implemented in the open MATLAB-based Zeffiro Interface toolbox for forward and inverse processing in EEG and it allows for graphics processing unit acceleration.

Assessing the grid impact of Electric Vehicles, Heat Pumps & PV generation in Dutch LV distribution grids

Low Carbon Technologies (LCTs), such as Photovoltaics (PVs), Electric Vehicles (EVs), and Heat Pumps (HPs), are expected to cause a huge electric load in future distribution grids. This paper investigates the grid impact in terms of over-loading and nodal voltage deviations in different distribution grids due to increasing LCT penetrations. The major objectives are the identification of the most severe LCT, grid impact issue, seasonal effect, and vulnerable distributional area, considering the physical models of the LCTs. It is concluded that Winter is the most hazardous for the future grid impact, characterized by nearly 3 times higher over-loading and 2.5 times higher voltage deviations during high HP penetrations, while suburban areas are the most vulnerable. Moreover, while HPs seem to have, in general, a greater impact compared to EVs, EVs cause more prolonged violations. While this work follows a bottom-up approach, using detailed physical models, aggregated national data has also been acquired, which is often used by top-down approaches. Different grid impact issues have been compared for the two approaches in terms of magnitude and duration. While bottom-up approaches generate more pessimistic results regarding the magnitude of the violations, results about the duration of the violations can be contradictory.

Fluid‐structure interaction with fully coupled mesh generation

AbstractThe modeling and simulation of fluid‐structure interaction (FSI) involve the two‐way coupling of a fluid flow and a deforming structure. The fluid exerts a load on the structure, the structure deforms, and, hence, the fluid flow changes, which leads to an altered loading on the structure. To accomplish this coupling, the fluid domain has to be updated after each time step, leading to a change in the fluid mesh. Various mesh update methods have been presented where an initial mesh is generated and then updated after each time step. Each method comes with different levels of complexity and has its own advantages and disadvantages. Herein, FSI simulations with fully integrated mesh generation, rather than updates, are proposed. Instead of updating the mesh at each time step, a new mesh for the fluid domain is generated based on the deformation of the solid domain. An advanced structured meshing algorithm, based on a block structure, enables this integrated mesh generation approach. An initial set of coarse‐scale conforming blocks is generated by the user, representing the topology and rough initial position of the solid and the fluid. Further information is the exact geometry at the boundary and the deformed position of the fluid‐structure interface, plus grading information to obtain a high‐quality fluid mesh. Transfinite maps are used to generate elements inside the blocks with any desired resolution and order.

FIELDimageR.Extra: Advancing user experience and computational efficiency for analysis of orthomosaic from agricultural field trials

AbstractFieldimageR.Extra is an advanced R package that enhances user experience and computational efficiency in analyzing orthomosaic images from agricultural field trials. Through the integration of modern GIS libraries like terra, stars, and sf, it surpasses traditional packages like raster and sp. The FieldimageR.Extra offers interactive visualization, vector feature creation, and spatial data editing within the R environment through the integration of mapview and mapedit packages. Notably, FieldimageR.Extra introduces new functions like fieldShape_render and fieldShape_edit, enabling flexible plot grid generation and editing capabilities. Comparative evaluations demonstrate the superior performance of FieldimageR.Extra in handling spatial data, crop and extract operations, and plot grid generation. With its comprehensive features, FieldimageR.Extra stands as a valuable addition to the FieldimageR R package, offering researchers efficient tools for unmanned aerial vehicle‐based orthomosaic image analysis in agricultural research. FIELDimageR.Extra is publicly available as a GitHub repository (https://github.com/filipematias23/FIELDimageR.Extra).

Mechanical behavior of three‐harness twill woven composite plates under tension loading

AbstractThree‐harness twill woven composite (THT‐WC) is an advanced carbon fiber reinforced composite that compromises the mechanical behaviors in both longitudinal and latitudinal directions. To explore the further practical application, the structural characteristics and static mechanical behavior of the material were investigated in this article. X‐ray computerized tomography was adopted to obtain the mesostructure details and to capture the key characteristics. With the help of mesoscale information, the 2D and 3D geometric models were established in the form of representative volume elements (RVEs). Combined with voxel mesh generation technology, a finite element model was proposed based on a 3D geometric model where macroscopic mechanical properties of materials along different yarn directions were gained. To verify the simulated geometry and predicted mechanical properties, mesoscale geometric comparison and specimen tensile tests were performed. The results show that the geometric model established in this article can reasonably reflect the periodicity fluctuation of binder warp yarns and the randomness fluctuation of weft yarns. Compared with the experimental results, the relative error of stiffness in the weft direction of the RVE is 4.25%, and that in the warp direction is 5.33%.Highlights The mechanical properties of THT‐WC were investigated experimentally. Meso‐scale reconstruction of THT‐WC was presented. A model to predict the mechanical properties of THT‐WC is established.

Structured triangular mesh generation method for free-form gridshells based on conformal mapping and virtual interaction forces

With the rapid development of computer-aided design, manufacturing, and construction techniques, free-form single-layer reticulated shells (SLRSs) are increasingly applied in modern architectures. However, generating a uniform and smooth mesh directly on a three-dimensional free-form surface is challenging. This paper proposes a fast and automatic method to generate structured triangular mesh for free-form SLRSs. The difficulty is reduced by generating the mesh on the two-dimensional (2D) parametric plane obtained by conformal mapping. The virtual interaction forces (VIFs) combined with the area map are used to automatically adjust the distribution of the 2D structured base mesh to reduce distortions. Subsequently, mesh clipping and barycentric interpolation are used to map the planar mesh back to the original surface. Finally, the VIF-based mesh smoothing is conducted to improve the mesh uniformity and smoothness. Case studies show that the proposed method successfully generates high-quality structured triangular meshes on various types of free-form SLRSs. Moreover, this method can precisely control the overall size and direction of the mesh, providing architects and engineers with more choices of mesh patterns.

New Quality Measures for Quadrilaterals and New Discrete Functionals for Grid Generation

In this paper, we review some grid quality metrics and define some new quality measures for quadrilateral elements. The curved elements are not discussed. Usually, the maximum value of a quality measure corresponds to the minimum value of the energy density over the grid. We also define new discrete functionals, which are implemented as objective functions in an optimization-based method for quadrilateral grid generation and improvement. These functionals are linearly combined with a discrete functional whose domain has an infinite barrier at the boundary of the set of unfolded grids to preserve convex grid cells in each step of the optimization process.

3D hand mesh recovery through inverse kinematics from a monocular RGB image

Recovering 3D hand mesh from a monocular RGB image has a wide range of application scenarios such as VR/AR. The parametric hand model provides a good geometric prior to the shape of hand, and is commonly used to recover the 3D hand mesh. However, the rotation parameters of hand model are not easy to learn, which influences the accuracy of model-based methods. To address this problem, we take advantage of the inverse kinematic chains of hand to derive an analytical method, which can convert hand joint locations into rotation parameters. By integrating such analytical method into the neural network, we propose an end-to-end learnable model named IKHand to recover the 3D hand mesh. IKHand comprises detection module and mesh generation module. Detection module predicts the 3D hand keypoints while mesh generation module takes these keypoints to generate the 3D hand mesh. Experimental results show that our proposed method can generate impressive and robust 3D hand meshes under several challenging conditions, and can achieve competitive results on FreiHAND dataset as well as RHD.

A PSBFEM Approach for Solving Seepage Problems Based on the Pixel Quadtree Mesh

This paper presents a PSBFEM approach that integrates the quadtree mesh generation technique based on digital images for solving seepage problems. The quantitative representation of the distribution of geometrical information and material parameters is achieved by utilizing the color intensity of each pixel, which can then be applied to seepage analysis. The presented method addresses the issue of hanging nodes by treating them as nodes of a polygonal element. We validate the proposed technique by solving three benchmark seepage problems. Results show that the image-based domain can be automatically discretized using a quadtree decomposition of the images. Furthermore, the computational efficiency and precision of the PSBFEM surpass that of the standard FEM. Therefore, the proposed technique allows for the convenient automatic discretization of the domain using pixel meshes to solve seepage problems in engineering applications.

Continuous modelling of single layer 2D carbon nanostructures based on a modified Cauchy–Born rule

AbstractGraphene is the thinnest known structure. It consists of a single layer of carbon atoms and has unique mechanical properties. The carbon atoms form bonds with neighbouring atoms that can be described by interatomic potentials. A simulation of molecular mechanical processes can be performed by applying the formalism of the finite element method to the interatomic potentials. Neglecting local effects, a continuum formulation is an efficient alternative to a discrete model. The continuum formulation requires a connection between the discrete atomic lattice and the continuum. One way of doing this is to use the Cauchy–Born rule. This paper reviews the extensions of the Cauchy–Born rule, in particular, the exponential Cauchy–Born rule, and adds an alternative approach. It is shown that all contributions dealing with the exponential Cauchy–Born rule inevitably lead to shell models with Kirchhoff–Love kinematics. The approach presented here instead uses a shell model with Reissner–Mindlin kinematics, which has the major advantage of a much simpler mesh generation and a simpler application of the boundary condition.

Numerical study of mass and heat transport within a ceramic porous tank

<p>In porous media, the thermal transfer phenomenon is widely applied in diverse energy-intensive industrial processes. This research paper aims to elucidate the simultaneous transfer of mass and heat within a ceramic porous tank. To simulate these transport phenomena, a numerical method is developed: Control Volume Finite Element Method (CVFEM), in conjunction with the utilization of a free mesh generator called Gmsh. The study showcases numerous simulation results that depict the transport phenomenon, such as the three-dimensional evolution of three parameters (temperature, saturation and pressure) during the heating of the ceramic tank. By employing this numerical model, a more comprehensive comprehension of these transport phenomena can be achieved.</p>