Remeshing Method Research Articles

A dual-modified implicit time integration method for three-dimensional impact modelling within the framework of the SBFEM

This paper presents a dual-modified implicit time integration method (DMITIM) for three-dimensional impact modelling within the framework of the scaled boundary finite element method (SBFEM). Controlled by a single parameter, this method effectively dissipates high-frequency responses in impact problems without affecting low-frequency responses, ensuring time integration stability. To address the issue of false oscillations during impacts, additional Lagrange multipliers are introduced to supplement the velocity and acceleration corrections at each time integration step. For nonmatching meshes, by leveraging the mesh flexibility of the SBFEM, a rapid and straightforward remeshing method is utilized to establish a node-to-node contact scheme. The numerical results demonstrate that the DMITIM significantly reduces false oscillations in the velocity and contact force during impact events. It also showcases the flexibility of the SBFEM in handling nonmatching meshes. The combination of the SBFEM with the DMITIM provides enhanced simulation accuracy and stability for impact problems compared to the results from ABAQUS using the HHT-α time integration algorithm.

Isotopological remeshing and statistical shape analysis: Enhancing premolar tooth wear classification and simulation with machine learning

ObjectiveThe aim of this study was to evaluate the accuracy of a combined approach based on an isotopological remeshing and statistical shape analysis (SSA) to capture key anatomical features of altered and intact premolars. Additionally, the study compares the capabilities of four Machine Learning (ML) algorithms in identifying or simulating tooth alterations. Methods113 premolar surfaces from a multicenter database were analyzed. These surfaces were processed using an isotopological remeshing method, followed by a SSA. Mean Euclidean distances between the initial and remeshed STL files were calculated to assess deviation in anatomical landmark positioning. Seven anatomical features were extracted from each tooth, and their correlations with shape modes and morphological characteristics were explored. Four ML algorithms, validated through three-fold cross-validation, were assessed for their ability to classify tooth types and alterations. Additionally, twenty intact teeth were altered and then reconstructed to verify the method's accuracy. ResultsThe first five modes encapsulated 76.1% of the total shape variability, with a mean landmark positioning deviation of 10.4 µm (±6.4). Significant correlations were found between shape modes and specific morphological features. The optimal ML algorithms demonstrated high accuracy (>83%) and precision (>86%). Simulations on intact teeth showed discrepancies in anatomical features below 3%. ConclusionThe combination of an isotopological remeshing with SSA showed good reliability in capturing key anatomical features of the tooth. Clinical significanceThe encouraging performance of ML algorithms suggests a promising direction for supporting practitioners in diagnosing and planning treatments for patients with altered teeth, ultimately improving preventive care.

Calcium carbonate crystallization process analysis on a heat transfer surface

This paper explores the growth process of calcium carbonate crystallization fouling on a heat surface using finite element methods to solve physical equations such as momentum, energy, and concentration diffusion, incorporating the impact of bulk crystallization on the concentration of scaling ions. The simulation uses deformation geometry, moving grids, and automatic re-meshing methods to study the dynamic growth of fouling layers and the spatiotemporal changes in fluid velocity, temperature, and concentration field-related parameters caused by it. Results indicate that the deposition interface temperature increases along the flow direction under constant heat flux conditions, leading to an increase in deposition rate. When the interface temperature exceeds 340 K, the fouling deposition rate becomes highly sensitive to temperature changes. The fouling thickness also increases along the flow direction, causing the heat transfer surface near the outlet to face a more severe heat transfer deterioration caused by scaling. Under constant temperature conditions, the deposition rate increases rapidly near the inlet and varies less along the flow direction. When the wall temperature remains constant, scaling is more likely to occur at the fluid inlet as the fluid temperature increases. This model also examines the effects of changes in the porosity of the fouling layer and ion interactions in composite salt solutions on the growth characteristics of the fouling layer.

Adaptively Isotropic Remeshing Based on Curvature Smoothed Field.

With the development of 3D digital geometry technology, 3D triangular meshes are becoming more useful and valuable in industrial manufacturing and digital entertainment. A high quality triangular mesh can be used to represent a real world object with geometric and physical characteristics. While anisotropic meshes have advantages of representing shapes with sharp features (such as trimmed surfaces) more efficiently and accurately, isotropic meshes allow more numerically stable computations. When there is no anisotropic mesh requirement, isotropic triangles are always a good choice. In this paper, we propose a remeshing method to convert an input mesh into an adaptively isotropic one based on a curvature smoothed field (CSF). With the help of the CSF, adaptively isotropic remeshing can retain the curvature sensitivity, which enables more geometric features to be kept, and avoid the occurrence of obtuse triangles in the remeshed model as much as possible. The remeshed triangles with locally isotropic property benefit various geometric processes such as neighbor-based feature extraction and analysis. The experimental results show that our method achieves better balance between geometric feature preservation and mesh quality improvement compared to peers. We provide the implementation codes of our resampling method at github.com/vvvwo/Adaptively-Isotropic-Remeshing.

Surface remeshing with preservation of sharp features through iterative identification and optimization of sample points

High-quality triangular meshes with sharp features are necessary for geometric processing applications, e.g., CAD models. Existing approaches either directly utilize the original sharp features as outputs, or predetermine feature sample points and reconstruct feature edges after an optimization process. However, these may result in poor-quality triangular facets close to feature edges or even feature preservation failure. With this regard, we present a feature-preservation surface remeshing method to generate high-quality triangular meshes with sharp feature preservation from raw manifold meshes. Unlike existing predetermination strategy, we introduce a heuristic strategy to dynamically determine feature sample points in each iteration. Based on the projection distance, each feature sample point is identified and projected onto the original feature edges, achieving the preservation of feature sample points. Besides, to eliminate the large gaps between two adjacent feature sample points and edge-close sample points, a feature edge continuity preservation strategy is proposed. Some additional sample points are further projected onto the large gaps and the edge-close sample points are deviated from the feature edges, achieving the preservation of reconstructed feature edges. Experimental results on several models demonstrate the effectiveness and efficiency of our method in generating high-quality triangular meshes with sharp feature preservation.

A FEM/DEM adaptive remeshing strategy for brittle elastic failure initiation and propagation

AbstractThis article presents an adaptive remeshing strategy between the finite element method (FEM) and the discrete element method (DEM). To achieve this strategy, an edge‐to‐edge coupling method based on Lagrange multipliers has been set‐up to ensure the continuity of velocities at the interface. To switch from a computation initially purely FEM to a FEM‐DEM one, a field transfer method was required. In particular, a displacement field transfer method has been set‐up. The switching from a FEM subdomain to a DEM one is activated by a transition criterion. Each time a FEM subdomain is substituted by a DEM one, the DEM subdomain microscopic properties are set‐up with respect to the subdomain geometry and desired particle refinement. This is performed thanks to the linking to the so‐called “Cooker,” a tool distributed along with the GranOO Workbench. Two subdomain remeshing cases were dealt with: that of an initially FEM subdomain that is converted to DEM, and that of DEM subdomains which coalesce. A numerical test case shows that the dynamic remeshing method behaves as expected: FEM subdomains are substituted by DEM ones when the transition criterion is met, and DEM subdomains coalesce when required. The final numerical test case shows a good agreement with a crack propagation experiment of the literature, while a speedup of about 20 was observed when compared to pure DEM computation.

Numerical optimisation of the active lift turbines using OpenFoam's overset method

This work presents a preliminary study of the numerical optimization of "active lift turbine" using computational fluid dynamics (CFD). This active lift turbine is designed to improve efficiency of vertical axis energy recovery turbines (wind and tidal turbines). It uses a crank rod system to convert normal forces into momentum in order to improve the yield.
 After a validation work of CFD model in two dimensions, the numerical optimization of the tidal turbine system is carried out. In fact, due to the specific characteristics of the active lift turbine, the blades do not follow a circular trajectory (Fig. \ref{fig:combined}). The OpenFoam overset module is therefore chosen because it allows to control the motion of the blades easily \cite{Chalmers}. The Overset method allows a good performance evaluation and limits the risk of numerical divergence that could be caused by mesh deformation methods; Moreover it limits the computation time compared to remeshing methods. However, it is more expensive than a more traditional Arbitrary Mesh Interface method \cite{Openfoam}, which is not suitable for the active lift turbine simulations.
 The impact of several parameters on the performances is studied. The simulations are performed for a range of operating conditions including different inflow velocities, angles of attack and active flow turbine settings (like the amplitude of the radius variation, see Fig \ref{fig:combined}). The results are evaluated in terms of the turbine power output and efficiency.
 The results show the importance of numerical simulation for the development of new types of energy recovery systems. It allows a better understanding of the interactions between the turbine and the fluid, and of the operation of such systems.
 Further studies are required for the active lift turbine: conventional attempts at optimisation are not perfectly suited to this system. Improving the lift/drag ratio makes less sense when the normal forces should also be taken into account to improves the performances. Furthermore, other aspects of operation should be analysed: variation of the turbulence rate, implementation of boundary layer re-attachment systems...

In-Timestep Remeshing for Contacting Elastodynamics

We propose In-Timestep Remeshing, a fully coupled, adaptive meshing algorithm for contacting elastodynamics where remeshing steps are tightly integrated, implicitly, within the timestep solve. Our algorithm refines and coarsens the domain automatically by measuring physical energy changes within each ongoing timestep solve. This provides consistent, degree-of-freedom-efficient, productive remeshing that, by construction, is physics-aware and so avoids the errors, over-refinements, artifacts, per-example hand-tuning, and instabilities commonly encountered when remeshing with timestepping methods. Our in-timestep computation then ensures that each simulation step's output is both a converged stable solution on the updated mesh and a temporally consistent trajectory with respect to the model and solution of the last timestep. At the same time, the output is guaranteed safe (intersection- and inversion-free) across all operations. We demonstrate applications across a wide range of extreme stress tests with challenging contacts, sharp geometries, extreme compressions, large timesteps, and wide material stiffness ranges - all scenarios well-appreciated to challenge existing remeshing methods.

Development of multiphase subchannel code with new numerical method in COSINE code package

A new subchannel code of COSINE code package with three-phase and eleven-equation was developed in the present study. The governing equations were spatially discretized with the staggered mesh and a semi-implicit time discrete scheme was adopted. The Newton downhill method was implemented to accelerate the convergence, and the hydraulic cell re-meshing method was used to mitigate non-physical water packing phenomena. The flow blockage test and the Pryor pressure test were used to assess the new numerical method, and some benchmarking tests, including cross flow, droplet entertainment, post-CHF and reflooding heat transfer, were used for the preliminary validation. The results show that the convergence method can significantly accelerate the convergence and the re-meshing method can eliminate the artificial pressure spike. It is also shown that the various thermal-hydraulics phenomena predicted by the present code are in good agreement with the reference results.

Accelerating surface remeshing through GPU-based computation of the restricted tangent face

High-quality mesh surfaces are crucial for geometric processing in a variety of applications. To generate these meshes, polyhedral remeshing techniques truncate Voronoi cells of the original surface and yield precise intersections, but the calculation is complicated. Some methods apply auxiliary points to construct Voronoi diagrams to simplify these techniques, thereby extracting co-planar facets to approximate the original surface. However, extracting these approximate facets from the constructed Voronoi diagram makes it inefficient and non-parallelizable. To this end, we propose an efficient GPU method for manifold surface remeshing, where the restricted tangent face (RTF) is utilized to approximate the original surface. By intersecting the pre-clipped Voronoi cell with the tangent plane, this method directly calculates the RTF of each point without any auxiliary points or traversing Voronoi cells. Moreover, to restrict the movement of points, we introduce a projection method based on the KNN strategy, where each point is projected onto the triangular facet in the original surface. Owing to the independence and non-interference of the RTF computation and projection of each point, our method is implemented in parallel on the GPU. Experimental results on various mesh surfaces demonstrate the superior performance of our method in the viability, effectiveness, and efficiency.

A Quasi-Optimal Shape Design Method for Electromagnetic Scatterers Based on NURBS Surfaces and Filter-Enhanced GWO

This paper presents a quasi-optimal and efficient method for designing the shape of electromagnetic (EM) scatterers. Optimizing the EM scatterer shape to achieve satisfactory scattering properties is a crucial, yet challenging problem due to the complex geometry involved and the high non-linearity in the optimization. In this paper, the geometric complexity is to be handled by modeling EM scatterer shapes as non-uniform rational basis spline (NURBS) surfaces, which enables an easy and intuitive shape control. Using the surfaces’ control points as optimization variables, the shape optimization problem is to be solved with the heuristic optimization strategy, which can effectively handle non-linearity and the associated local optima. Specifically, the recently developed grey wolf optimizer (GWO) is employed. Although GWO can effectively avoid local optima and achieve quasi-optimal results, it requires repeated calls to time-consuming EM simulations. To solve this efficiency issue, a filter-enhanced version of GWO is proposed to reduce the times of calling EM simulations, and an efficient, adaptive remeshing method is proposed to accelerate the numerical analysis process within each EM simulation call. Altogether, they lead to a quasi-optimal and efficient method for optimizing EM scatterers. Its effectiveness has also been validated by several examples.

Continuum modeling of non-conservative fluid membrane for simulating long-term cell dynamics.

Living cells actively deform and move by their force generations in three-dimensional (3D) space. These 3D cell dynamics occur over a long-term time scale, ranging from tens of minutes to days. On such a time scale, turnover of cell membrane constituents due to endocytosis and exocytosis cannot be ignored, i.e., the surface membrane dynamically deforms without mass conservation. Although membrane turnover is essential for large deformation of cells, there is no computational framework yet to simulate long-term cell dynamics with a non-conservative fluidic membrane. In this paper, we proposed a computational framework for simulating the long-term dynamics of a cell membrane in 3D space. For this purpose, in the proposed framework, the cell surface membrane is treated as a viscous fluid membrane without mass conservation. Cell shape is discretized by a triangular mesh, and its dynamics are expressed by effective energy and dissipation function. The mesh structure, distorted by membrane motion, is dynamically optimized by introducing a modified dynamic remeshing method. To validate the proposed framework, numerical simulations were performed, showing that the membrane flow is reproduced in a physically consistent manner and that the artificial effects of the remeshing method were negligible. To further demonstrate the applicability of the proposed framework, numerical simulations of cell migration induced by a mechanism similar to the Marangoni effect, i.e., the polarized surface tension actively generated by the cell, were performed. The observed cell behaviors agreed with existing analytical solutions, indicating that the proposed computational framework can quantitatively reproduce long-term active cell dynamics with membrane turnover. Based on the simple description of cell membrane dynamics, this framework provides a useful basis for analyzing various cell shaping and movement.

Continuous remeshing for inverse rendering

AbstractWe present a novel method for joint optimization and remeshing and apply it to inverse rendering. Rapid advances in differentiable rendering during the last years paved the way for fast inverse rendering of complex scenes. But serious problems with gradient‐based optimization of triangle meshes remain. Applying gradient steps to the vertices can lead to mesh defects, such as flipped triangles, crumpled regions, and self‐intersections. Choosing a good vertex count is crucial for the optimization quality and performance but is usually done by hand. Moreover, meshes with fixed triangulation struggle to adapt to complex geometry. Our novel method tackles all these problems by applying an adaptive remeshing step in each single iteration of the optimization loop. By immediately collapsing suspicious triangles, we avoid and heal mesh defects. We use a closed‐loop‐controlled location‐dependent edge length. We compare our solution to state‐of‐the‐art methods and find that it is faster and more accurate. It produces finer meshes with fewer defects, requires less parameter tuning and can reconstruct more complex objects.

An elastic‐inelastic model and embedded bounce‐back control for layered printing with cementitious materials

AbstractThis paper presents a finite‐deformation model for extrusion‐based layered printing with cementitious materials. The evolution of mechanical properties as the printed material cures and stiffens results in nonphysical reduction in the magnitude of elastic strains when standard constitutive models are employed. This elastic recovery of the printing induced deformation contradicts the experimentally observed behavior of the printed cementitious materials that harden at a nearly‐frozen deformed state. A thermodynamically motivated constraint on the evolution of elastic strains is imposed on the constitutive model to remedy the nonphysical bounce‐back effect. An algorithm that is based on a strain‐projection technique for the elastic part of deformation is developed that complements the inelastic response given by the Drucker–Prager model. It is then embedded in a finite strain finite element framework for the modeling and simulation of cure hardening and inelastic response of the early age cementitious materials. A ghost mesh method is proposed for continuous layer‐wise printing of the material without the need for intermittent mesh generation technique or adaptive remeshing methods. The model is validated via comparison with experimental data and representative test cases are presented that investigate the mathematical and computational attributes of the proposed model.

A geometrically and locally adaptive remeshing method for finite difference modeling of mining-induced surface subsidence

Surface subsidence induced by underground mining is a typical serious geohazard. Numerical approaches such as the discrete element method (DEM) and finite difference method (FDM) have been widely used to model and analyze mining-induced surface subsidence. However, the DEM is typically computationally expensive, and is not capable of analyzing large-scale problems, while the mesh distortion may occur in the FDM modeling of largely deformed surface subsidence. To address the above problems, this paper presents a geometrically and locally adaptive remeshing method for the FDM modeling of largely deformed surface subsidence induced by underground mining. The essential ideas behind the proposed method are as follows: (i) Geometrical features of elements (i.e. the mesh quality), rather than the calculation errors, are employed as the indicator for determining whether to conduct the remeshing; and (ii) Distorted meshes with multiple attributes, rather than those with only a single attribute, are locally regenerated. In the proposed method, the distorted meshes are first adaptively determined based on the mesh quality, and then removed from the original mesh model. The tetrahedral mesh in the distorted area is first regenerated, and then the physical field variables of old mesh are transferred to the new mesh. The numerical calculation process recovers when finishing the regeneration and transformation. To verify the effectiveness of the proposed method, the surface deformation of the Yanqianshan iron mine, Liaoning Province, China, is numerically investigated by utilizing the proposed method, and compared with the numerical results of the DEM modeling. Moreover, the proposed method is applied to predicting the surface subsidence in Anjialing No. 1 Underground Mine, Shanxi Province, China.

Analysis of the effects of dynamic mesh update method on simulating indoor airflow induced by moving objects

Local interference flow induced by the movement of human bodies or objects indoors can directly affect breathing air quality. However, very few studies have been carried out on the flow induced by moving objects due to high experimental costs. As an alternative, computational fluid dynamic (CFD) method has been employed in predicting the flow induced by moving objects indoors. During the numerical computations, the mesh needs to be updated continuously for the moving objects behave as part of the boundary. Although the dynamic mesh update (DMU) methods have been used in the CFD method, the performances of these DMU methods vary widely, and it is still lack of analysis on the selection of the DMU methods. In this study, the DMU methods provided by ANSYS FLUENT are used for comparing the numerical performances between computational and experimental results. Five aspects of numerical performance, accuracy, mesh quality, mesh generation complexity, continuity, and computational efficiency, are discussed integrally. The results show the dynamic layering (DL) method is preferred for the case of linear movement due to the high computational efficiency and accuracy though it is difficult and time-consuming in mesh generation. Spring-based smoothing & remeshing (SS&R) method can be used when the complicated-shaped or nonlinearly moving objects are part of the boundary. Both computational efficiency and accuracy of overset mesh (OM) method are low when the moving objects are clinging to the boundary, so this method is not recommended for simulating the flow fields.

Modeling and fabrication with specified discrete equivalence classes

We propose a novel method to model and fabricate shapes using a small set of specified discrete equivalence classes of triangles. The core of our modeling technique is a fabrication-error-driven remeshing algorithm. Given a triangle and a template triangle, which are coplanar and have one-to-one corresponding vertices, we define their similarity error from a manufacturing point of view as follows: the minimizer of the maximum of the three distances between the corresponding pair of vertices concerning a rigid transformation. To compute the similarity error, we convert it into an easy-to-compute form. Then, a greedy remeshing method is developed to optimize the topology and geometry of the input mesh to minimize the fabrication error defined as the maximum similarity error of all triangles. Besides, constraints are enforced to ensure the similarity between input and output shapes and the smoothness of the resulting shapes. Since the fabrication error has been considered during the modeling process, the fabrication process is easy to proceed. To assist users in performing fabrication using common materials and tools manually, we present a straightforward manufacturing solution. The feasibility and practicability of our method are demonstrated over various examples, including seven physical manufacturing models with only nine template triangles.

Adaptive surface mesh remeshing based on a sphere packing method and a node insertion/deletion method

Triangular mesh has been a prevalent form of 3D model representation in various areas ranging from modeling to finite element analysis due to their simplicity and flexibility. In the paper, we present a triangular mesh remeshing method based on a sphere packing method and a node insertion/deletion method for surface meshes. First, a new set of nodes are generated on the surface mesh via a sphere packing method and added to the original surface mesh. Then, original nodes are deleted through some basic operations. Finally, the mesh is optimized by edge flipping. To regenerate an adaptive mesh, we consider some geometric features to calculate a size field and record and smooth it with an octree background grid. The proposed method remeshes the surface mesh without projection of local areas, the intersection of fronts, Lloyd relaxation, and other complicated calculations, and the proposed method can generate a high-quality mesh without dependence on the quality of the original mesh, which make the method efficient and effective.

Robustness versus Performance – Nested Inherence of Objectives in Optimization with Polymorphic Uncertain Parameters

Fuzzy probability based randomness is utilized for polymorphic uncertain design and a priori parameters in design optimization tasks. Methods for the algorithmic interface between optimization and polymorphic uncertainty analysis are introduced. Uncertain design vectors are incorporated by affine transformation from deterministic design vectors. Multiple uncertainty reducing measures are discussed, which are required for the evaluation and comparability of fitness in optimization.Nested uncertainty reducing measures are mandatory for polymorphic uncertain objectives. The inherence of multiple nested objectives is pointed out, which leads to inherence of multi-objective optimization in single-objective optimization problems with polymorphic uncertain parameters.In this contribution, a framework is presented considering polymorphic uncertain a priori and design parameters in a multi-objective optimization. A parameter based geometric design optimization of a steel hook is investigated. Several uncertainty reducing measures are evaluated for optimization of performance and robustness.Fuzzy design parameters are considered with respect to geometry and, therefore, an automated geometry regeneration and remeshing method is propagated. Material characteristics are modeled with stochastic a priori parameters. The load conditions are assumed to be a priori polymorphic uncertain. Pareto optimality is evaluated depending on the surrogate formulation of uncertainty reducing measures.

Controllable curl-correction of 3D frame fields

Hexahedral meshes represent an attractive discretization strategy in finite element analyses owing to their good numerical performance. Frame field-based remeshing is an important technique for controllable hexahedral meshing. Existing frame-field generation methods cannot be directly used for purely hexahedral meshing due to possible topological conflicts. These problems are less severe in the case of hexahedral-dominant meshing. However, the quality of these hexahedral-dominant meshes is largely affected by the curl of the input frame fields. With the aim of overcoming this issue, we propose a direction-preserving and length-controllable curl-correction method of 3D frame fields. We analyze and construct the discretized curl energy of the 3D vector field on tetrahedral meshes and extend it to frame fields, i.e., the composition of three vector fields. In order to preserve the input directions as much as possible, three scalar fields were introduced to denote the stretch length of the three vectors of the frame fields and represent the new fields as a combination of the original frame fields and scalar fields. Through global-optimization of the curl energy combined with a smooth term, the final curl-corrected frame fields are obtained, which are further used for hexahedral-dominant remeshing. The results indicate that the proposed method can reduce the curl of the frame fields efficiently while keeping their directions as well as controlling the extent of their length. By applying such frame fields to existing hexahedral-dominant remeshing methods, direction- and size-controllable hexahedral-dominant meshes can be obtained. Besides, the proposed method deduces to a convex quadratic programming problem with simple box constraints, which is easy-to-solve.