Sparse Mesh Research Articles

Enhancing topology optimization with colored body-fitted mesh using adaptive filter, dual re-meshing strategy, and OOP programming paradigm

This study introduces a novel topology optimization approach by employing power law-based material interpolation and adaptive filtering in the framework of the unstructured grids. As an extension of the established Solid Isotropic Material with Penalization (SIMP) method that utilizes the fixed structured mesh, the proposed Colored Body-Fitted Optimization (CBFO) method adopts the body-fitted grids to enhance efficiency, accuracy, and adaptability for diverse engineering applications. Notably, incorporating body-fitted meshes with intermediate density profiles enables improved flexibility in the numerical simulations and eliminates the need for re-meshing in each iteration. The dual re-meshing strategy drastically reduces computational costs, with only two re-meshing procedures required throughout the optimization process. This approach facilitates the generation of dense mesh regions around critical boundaries to augment solution accuracy while enabling sparse mesh configurations in the low-sensitivity regions, thereby boosting computational efficiency without compromising performance. The effectiveness, robustness, and efficiency of the CBFO method are validated through testing on multiple standard minimum compliance and compliant mechanism problems. The proposed optimization method can converge in dozens of iterations, obtain better objective function values, and save computational costs by up to 69 % compared to the previous method using the body-fitted mesh. Additionally, a concise MATLAB script implementing the proposed method using an Object-Oriented Programming (OOP) paradigm is provided in the appendix and the supplementary material, complete with annotations.

A GWO-ML-based large deformation finite element variable mapping method: An example of RITSS large deformation finite element simulation

The mapping of variables between old and new elements is a crucial aspect of large deformation finite element simulation. However, traditional mapping methods suffer from limited applicability and complex operations. In this study, a novel Gray Wolf Optimization-Machine Learning (GWO-ML) based variable mapping method for large deformation finite element analysis is proposed. This method achieves accurate mapping results without requiring explicit determination of element-to-element positional relationships. Furthermore, it effectively integrates a wider range of integration point information during the mapping process and maintains high prediction accuracy near boundaries with sparse mesh data. The remeshing and interpolation technique by small strain is employed as an illustrative example, wherein a set of automated operations is proposed to control the commercial software ABAQUS through Python scripting for conducting small strain analysis and GWO-ML mapping process. For machine learning models, Multilayer Perceptrons, Random Forest, Extreme Learning Machine, and Support Vector Regression, are compared, where the RF model has excellent computational accuracy and efficiency in terms of performance. The application of this method is investigated in scenarios with various foundation types, motion modes, loading modes, and multi-physics coupling mappings. The results confirm that the method exhibits high accuracy and robustness in simulation processes.

Image reconstruction and bladder stimulation using electrical impedance tomography

Impedance tomography (EIT) is an imaging technique that harnesses differences in electrical conductivity to visualize the interior of objects. Despite limitations such as low resolution and nonlinearity of current distribution, its potential in medicine and industry is a source of fascination. The research in this work is a step towards unlocking this potential, focusing on improving the quality of EIT image reconstruction, particularly in bladder modeling. A key element is regularization techniques, including Laplace matrices and the iterative Gauss-Newton algorithm, which balance matching accuracy and image smoothness. In the practical part, simulations were conducted on dense and sparse meshes. Modeling the urinary bladder as a rotational ellipse significantly influences the interpretation of data by algorithms, a crucial factor for the accuracy of reconstruction. Various electrode configurations were also analyzed, revealing the impact of their arrangement on electrical properties and imaging quality. Iterative testing led to identifying optimal electrode placement and grid configuration, underscoring the importance of precise modeling for obtaining high-quality images. The results underscore the critical role of appropriately selecting the regularization parameter in minimizing reconstruction errors.

A variable-node element model and its application to damage analysis of RAC using the 2D base force element method

The existing methods find it difficult to resolve the inconsistency in the nodal displacements of nodes at the interface of dense and sparse element models. Therefore, this paper proposes a new variable-node element model using the base force element method (BFEM) and successfully applies it to study the mechanical properties of recycled aggregate concrete (RAC). First, the variable-node element model with an arbitrary change of node number in the mid-edges was established, and the explicit expressions of the 2 × 2 nodal compliance matrix and nodal displacements were given. Subsequently, the triangular and quadrilateral elements of single-sides and double-sides of hanging element models were developed based on the variable-node element model. In addition, a double-notched model of RAC with different aggregate types but the same aggregate distribution position was established, and numerical simulations of uniaxial tension were performed. The results show that the compliance matrix and nodal displacement are independent of the element characteristic without Gaussian integration. The variable-node hanging element model has high numerical accuracy and applicability, and the nodes between the sparse and dense meshes do not require any construction measures. The variable-node elements ensure the coordination of the nodal displacement at the interfaces. The aggregate shape has a significant effect on the damage mode, maximum principal strain, principal stress distribution, and stress concentration, while has a negligible effect on RAC tensile strength when the aggregate distribution is the same.

Anatomy-guided multi-resolution image reconstruction in PET

Objective. In this paper, we propose positron emission tomography image reconstruction using a multi-resolution triangular mesh. The mesh can be adapted based on patient specific anatomical information that can be in the form of a computed tomography or magnetic resonance imaging image in the hybrid imaging systems. The triangular mesh can be adapted to high resolution in localized anatomical regions of interest (ROI) and made coarser in other regions, leading to an imaging model with high resolution in the ROI with clearly reduced number of degrees of freedom compared to a conventional uniformly dense imaging model. Approach. We compare maximum likelihood expectation maximization reconstructions with the multi-resolution model to reconstructions using a uniformly dense mesh, a sparse mesh and regular rectangular pixel mesh. Two simulated cases are used in the comparison, with the first one using the NEMA image quality phantom and the second the XCAT human phantom. Main results. When compared to the results with the uniform imaging models, the locally refined multi-resolution mesh retains the accuracy of the dense mesh reconstruction in the ROI while being faster to compute than the reconstructions with the uniformly dense mesh. The locally dense multi-resolution model leads also to more accurate reconstruction than the pixel-based mesh or the sparse triangular mesh. Significance. The findings suggest that triangular multi-resolution mesh, which can be made patient and application specific, is a potential alternative for pixel-based reconstruction.

A finite element simulation approach for glued-laminated timber beams using continuum-damage model and sequentially linear analysis

Glued-laminated timber (GLT) is an efficient and renewable material with potential to enhance sustainability in construction, but its potential has been partly hindered by relatively large uncertainty related to its strength. Previous research indicate that by linking information from the grading process to the GLT fabrication more reliable GLT beams could be made. To this end, this paper represents a finite element based modelling approach combining a continuum damage model with sequentially linear analysis that is suitable for simulation of the bending stiffness and strength of GLT beams. The model has been implemented in Matlab and can be easily integrated into different parametric simulation workflows. Based on validation against 36 experimentally tested GLT beams, the model can predict bending stiffness with high accuracy and provides reasonably accurate predictions for bending strength. The model is also capable of producing qualitatively realistic fracture patterns of GLT beams. The mesh-size study suggests that the best agreement for bending strength with test data is obtained with a sparse mesh, which is discussed in detail. The model is considered suitable for follow-up studies involving the optimization of GLT beam layups.

A solver for subsonic flow around airfoils based on physics-informed neural networks and mesh transformation

Physics-informed neural networks (PINNs) have recently become a new popular method for solving forward and inverse problems governed by partial differential equations. However, in the flow around airfoils, the fluid is greatly accelerated near the leading edge, resulting in a local sharper transition, which is difficult to capture by PINNs. Therefore, PINNs are still rarely used to solve the flow around airfoils. In this study, we combine physical-informed neural networks with mesh transformation, using a neural network to learn the flow in the uniform computational space instead of physical space. Mesh transformation avoids the network from capturing the local sharper transition and learning flow with internal boundary (wall boundary). We successfully solve inviscid flow and provide an open-source subsonic flow solver for arbitrary airfoils. Our results show that the solver exhibits higher-order attributes, achieving nearly an order of magnitude error reduction over second-order finite volume method (FVM) on very sparse meshes. Limited by the learning ability and optimization difficulties of the neural network, the accuracy of this solver will not improve significantly with mesh refinement. Nevertheless, it achieves comparable accuracy and efficiency to second-order FVM on fine meshes. Finally, we highlight the significant advantage of the solver in solving parametric problems, as it can efficiently obtain solutions in the continuous parameter space about the angle of attack.

Análise da influência da malha numérica na modelagem hidrodinâmica do lago Paranoá utilizando o MIKE 3

Purpose: This work aims to evaluate the effects of the different meshes constructed in MIKE 3 software on the simulation and calibration results of the model. Theoretical framework: 3D hydrodynamic models, such as MIKE 3, provide the closest representation of reality by simulating the gradients in the three spatial dimensions and solutioning the Navier-Stokes equations. In these models, meshes are used to represent complex geometries. An efficient computational mesh is required to allow convergence and stability of the solution of the equations and, furthermore, of the modelling result. Method/design/approach: Simulation of four meshes with distinct discretization, calibration, comparison, and assessment of the model performance for these four conceptual models considering: mesh’s number of elements, simulation time, mean absolute error (MAE), coefficient of determination (R2), and relative difference. Results and conclusions: For the meshes adopted for comparison, refinement only in the “throat” (region near the dam) did not show significant influences on the results that would justify its use, considering the high computational cost. Therefore, in this case, a sparse mesh and without refinement can be used in detriment of a mesh with refinement only in the “throat”. Research implication: Understand how different meshes discretization can significantly alter simulation time and highlight that optimized simulation requires an equilibrium between simulation time and mesh discretization to maintain model’s performance. Originality/value: Understanding and quantifying the influence of the discretization of the model's mesh on the simulation time and the performance of the model allows the optimization of the modeling, considering the cost-effectiveness of different discretizations leading to smaller simulation time with similar performance.

Efficient 3D Surface Patch Compression and Reconstruction using Parametric Descriptions and Transform Techniques

This paper proposes and demonstrates novel methods for compressing and reconstructing 3D surface patches typically obtained from scanners that rely on stereo vision, structured light, or time-of-flight techniques. The methods involve applying a polygon reduction to the mesh to get a set of vertices lying in structured planes of a sparse, regular grid. The data in each plane is then described parametrically, and a comparative analysis is conducted using the Discrete Fourier Transform (DFT), Discrete Cosine Transform (DCT), and Discrete Wavelet Transform (DWT). Quality factors are employed to further process the transform coefficients, resulting in substantial reductions in the amount of data saved to disk. The paper also defines file formats with the necessary parameters for a complete reconstruction of the sparse mesh. Finally, elliptic Partial Differential Equations (PDE) are used to represent the reconstructed data, and the Laplace equation is iteratively solved between adjacent planes to recover the vertex density of the original mesh. Experimental results demonstrate the effectiveness of the proposed methods, achieving compression rates of over 98% compared to the OBJ file format and over 91% compared to a list of vertices in ASCII format.

Intelligent mesh refinement based on U-NET for high-fidelity CFD simulation in numerical reactor

Thermal-hydraulic analysis of reactors is fundamental for studying many service behaviors inside the reactor core, and high-fidelity thermal-hydraulic simulation based on advanced computing techniques and supercomputing resources has attracted widespread attention. The construction of high-quality fluid domain mesh models for reactors with complex and sophisticated core structures is fundamental for high-fidelity thermal-hydraulic simulations. However, mesh models built entirely with commercial tools have limitations in terms of model quality and construction performance. An intelligent mesh refinement method based on the U-Net neural network model (Unet-IMR) is designed, which attempts to use AI technology to assist in generating high-quality mesh models. Specifically, an intelligent prediction model is constructed and used to predict the poor mesh in a given mesh model, and the designed region-sensitive refinement strategy is further applied to iteratively optimize and refine the mesh to construct a high-quality mesh model. Experimental results show that the mesh distribution and the transition between sparse and dense meshes are more reasonable in the Unet-IMR based mesh model, and meshes located at sophisticated locations have relatively high goodness-of-fit. All the meshes in the model can pass the correctness checks of the CVR-PACA software, and the simulation results are consistent with physical expectations. Furthermore, the Unet-IMR based mesh model can achieve similar simulation results with fewer meshes compared to the mesh model built with commercial tools.

Unified X-space parallelization algorithm for conserved discrete unified gas kinetic scheme

In this paper, the open source multiscale flow solver dugksFoam is optimized with a newly proposed parallelization strategy and conserved algorithm. A novel X-space parallel framework is introduced. In contrast to traditional discrete physical/velocity space decomposition parallelization methods, it can decompose each space in a hybrid manner and efficiently parallelize the computation. For better conservation of the macroscopic physical variables, flow properties in each cell are updated by moments of microscopic variable fluxes, which preserves particle multiscale information under sparse velocity space mesh. Several test cases, which include 2D lid-driven cavity flow in the transition flow regime, hypersonic rarefied flow past a 3D sphere, are carried out to verify the accuracy of the conserved discrete unified gas kinetic scheme to simulate the flows in all flow regimes. A large-scale parallel computational test case of 3D sphere with 101,600 physical mesh cells and 62,744 velocity mesh cells is conducted to measure the parallel efficiency of the conserved dugksFoam code. A significant superlinear speedup of 1631.87 has been achieved on 1120 cores.

Reconstructing the Callianthus plant–An early aquatic angiosperm from the Lower Cretaceous of China

The Lower Cretaceous Yixian Formation in northeastern China has shed unique light on the early evolution of angiosperms, including Chaoyangia, Archaefructus, Sinocarpus, Callianthus, Liaoningcarpus, Baicarpus, Nothodichocarpum and Neofructus. Among them, Callianthus was represented only by its reproductive organs, while its vegetative parts and whole plant remained unknown. This hinders our understanding of this early angiosperm in the Early Cretaceous. Herein we report new materials of Callianthus dilae Wang and Zheng 2009, emended, including a young plant, roots, articulated stems, leaves and reproductive organs from the Formation. Based on new materials and the specimens documented previously, we reconstruct Callianthus as a plant with straight, decussately branching stems, flaccid leaves with sparse meshes and an intramarginal vein, and bisexual pedicellate reproductive organs with two whorls of slightly differentiated foliar appendages. Morphological analysis indicates that Callianthus was an aquatic plant, as Archaefructus, suggesting that angiosperms might have explored aquatic habitats by the end of Barremian in the Early Cretaceous.

Day/night change in orientation of the orb weaver Azilia guatemalensis (Araneae: Tetragnathidae)

Most orb weavers orient downward on their orbs, but here we describe an unusual pattern of orientation in the tetragnathid Azilia guatemalensis. This species changes its orientation on the hub with a consistent day/night pattern. During the day, the spiders orient upward on the orb, but orient downward during the night. In addition, we found that the spiders construct a few silk lines that connect the hub with a sparse mesh near the upper edge of the orb which, in turn, is connected to the substrate. When disturbed, the spider runs using these lines and hides on the substrate, suggesting that its upward orientation during the day, and its escape behaviour, may be a response to diurnal enemies.

Interpolation Algorithm for Motion Vector Field of CTA Image and Accelerated Implementation Based on Uniform Grid and Multi-level B-spline

In order to solve the problems of slow operation speed and low registration accuracy of thin plate spline (TPS) interpolation method for motion vector field in coronary computed tomography angiography (CTA), a multi-level B-spline interpolation method (MBS) with uniform grid is proposed. On the one hand, the interpolation method used local B-spline to refine the sparse mesh layer by layer in a multiscale way to improve the accuracy of registration. On the other hand, it used the splitting matrix method to interpolate the motion vector field, greatly reducing the operation time of interpolation. The experimental results show that the proposed method can be used for CTA image registration efficiently.

Improvement of DDM Preprocessing for the Simulation of the GRAVES Radar Densified Sparse Array for Space Surveillance and Tracking

In a recent work (A. Jouade and A. Barka, “Massively parallel implementation of FETI-2LM methods for the simulation of the sparse receiving array evolution of the GRAVES radar system for space surveillance and tracking, IEEE Access , vol. 7, pp. 128968–128979, 2019), we have discussed our implementation of the finite-element tearing and interconnecting (FETI) method and the domain decomposition method (DDM) for the full-wave simulation of the large GRAVES sparse array (60 m diameter disk). Owing to the nonregular distribution of the antennas of the sparse array, such simulations in reasonable times are not accessible with existing FETI methods optimized for repetitive geometries, which do not benefit from an effective parallelization technique. A particularity of the preprocessing step of our DDM is that the complete sparse array mesh is not built upstream of the resolution of the electromagnetic problem. Each subdomain in our decomposition is equipped with its own local mesh, belonging to a limited set of unit-cell meshes, generated separately. Initially, a total of 13 692 subdomains were chosen among three types of subdomains, considering those corresponding to antennas (200), air subdomains (800), and ground plane subdomains (12 592). This simulation has required 13 692 Intel Xeon Broadwell E5-2680v4 processing cores equipped with 4 GB of memory, each handling one subdomain. A new strategy is shown, which requires only 2408 cores for the same simulation, leading to an 82.41% reduction in the required number of cores, as well as a 30% reduction in the simulation time.

Sparse metric-based mesh saliency

In this paper, we propose an accurate and robust approach to salient region detection for 3D polygonal surface meshes. The salient regions of a mesh are those that geometrically stand out from their contexts and therefore are semantically important for geometry processing and shape analysis. However, a suitable definition of region contexts for saliency detection remains elusive in the field, and the previous methods fail to produce saliency maps that agree well with human annotations. We address these issues by computing saliency in a global manner and enforcing sparsity for more accurate saliency detection. Specifically, we represent the geometry of a mesh using a metric that globally encodes the shape distances between every pair of local regions. We then propose a sparsity-enforcing rarity optimization problem, solving which allows us to obtain a compact set of salient regions globally distinct from each other. We build a perceptually motivated 3D eye fixation dataset and use a large-scale Schelling saliency dataset for extensive benchmarking of saliency detection methods. The results show that our computed saliency maps are closer to the ground-truth. To showcase the usefulness of our saliency maps for geometry processing, we apply them to feature point localization and achieve higher accuracy compared to established feature detectors.

Centrifugal stiffening analysis of gear pair with generalized component mode synthesis and semi-analytic contact technique

Cantilever beam assumption is widely used to estimate gear flexibility for analytical calculation of transmission error of gear pair. Similar to the rotating beam, it is supposed that centrifugal stiffening will also affect dynamic transmission error of gear pair. This work presents an efficient computational procedure for centrifugal stiffening analysis of gear pair. As inertia centrifugal force is distributively applied on gear body, the finite element grid model of gear pair is firstly established. Then, in order to reduce large number of degrees of freedom in finite element grid, the generalized component mode synthesis is employed to establish dynamic equation of flexible gear with constant mass matrix and co-rotated constant stiffness matrix. In order to avoid highly refined grid near contact zone, the semi-analytic contact technique which incorporates advantage of penalty method and Lagrange multiplier method is employed to calculate contact force between non-matching sparse tooth face meshes. After transforming system dynamic differential algebraic equation into ordinary differential equation, dynamic contact analysis of a helical gear pair is carried out, and dynamic transmission error at different rotational speeds are compared. Inflation deformation of gear under inertia centrifugal force is shown as explanation for influence of centrifugal stiffening on dynamic transmission error.

Calculation of Non-Homogeneous Anisotropic Rectangular Plates with Arbitrary Fixation on the Contur

The developing of the effective methodic of elastic orthotropic plates’ calculation and the research on the base of their state under different boundary conditions are of great importance nowadays. The representation of the received results in the form, convenient for practical use, is also important. For practical applications in engineering are important tables for determining deflections and internal forces of structures. Such tables for the isotropic case under various conditions of plate support on the contour are given in many works. As for the anisotropic plates, there are no such tables, with the exception of one Huber table compiled for a freely supported rectangular orthotropic plate, depending on the relationship between the stiffness values. Here is a method of calculating the non-homogeneous anisotropic rectangular plates with arbitrary fixation on the contour is set forth, which is reduced to a boundary value problem. The main idea of a calculated general methodic of linear marginal differential tasks calculation is based on underlying of the main part of a solution. Such approach is proved by means of development and some generalization of common positions of a variational method of marginal tasks of mathematical physics of self-conjugated tasks solution. To solve a system of equations in terms of displacements using finite difference method (FDM) in combination with different variations of analytical solutions. It is advisable to construct a numerical solution of the problem so that in difficult cases the support fixing and uploading solution sought, not directly, but in the form of amendments to the known solution for simple cases of reference to consolidate and uploading at finding the solutions which the analytical methods or the FDM with sparse mesh may be used. Given as examples are the results of calculation for a series of square orthotropic plates with a fixed boundary under the action of uniformly distributed load.

Photocatalytic nanofiber-coated alumina hollow fiber membranes for highly efficient oilfield produced water treatment

Cost-effective purification technology of oilfield produced water (OPW) is becoming a global challenge for future petroleum exploration and production industry. Energy-efficient operation of membrane separation is potentially promising. However, severe fouling problem of oil droplets demands new robust and fouling-resistant membranes with high permeability and rejection efficiency. Here, we propose a photocatalytic nanofiber-coated inorganic hollow fiber membrane suitable for OPW treatment. The membrane was fabricated by coating polyacrylonitrile (PAN) nanofiber incorporated with graphitic carbon nitride (GCN) photocatalyst on an alumina (Al2O3) hollow fiber membrane. While the highly porous coating made of smooth hydrophilic nanofibers facilitated water permeation, the coating effectively captured oil droplets in its opening, resulting in a better rejection efficiency of oil contaminants. Its sparse mesh morphology prevented oil contaminants to form dense fouling film on the membrane surface and maintained high permeate flux even after 180 min filtration. The best permeate flux of 640 L·m−2·h−1 and oil rejection percentage of 99% were recorded for 180 min crossflow filtration of OPW at 2 bar along with the highest pure water flux of 816 L·m−2·h−1. The photocatalytic activity of GCN enabled the coating to degrade the captured oil contaminants under UV irradiation, demonstrating permeate flux of 577 L·m−2·h−1 and oil rejection of 97% after three cycles of 180 min filtration. The excellent fouling resistance and cleaning performances of the membrane are considerably beneficial for a long-term repeated filtration operation. This work will motivate researchers to develop nanofiber-coated hollow fiber membranes for future membrane separation technology.

A parallel generator for sparse unstructured meshes to solve the eikonal equation

Mesh generation is the first step in a wide range of applications including navigation for robots or virtual agents in pedestrian simulations. To find the shortest travel time to a target, a common technique is to solve the eikonal equation on a mesh. We propose EikMesh, an extension of the DistMesh algorithm. EikMesh is a fast parallel mesh generator that reduces the number of mesh points, and thus the computation time, while maintaining precision of numerical solvers on the mesh. It automatically refines where desired, in our case, where the eikonal equation undergoes changes, e.g. near obstacles. The first crucial step is the generation of a sophisticated initial mesh which reduces the number of smoothing steps. In addition, EikMesh avoids expensive Delaunay-re-triangulations. Space filling curves manage storage space in a cache-friendly manner. EikMesh scales better than the parallelized traditional DistMesh and significantly outperforms it for a number of test cases.