Unstructured and semi-structured hexahedral mesh generation methods

Discretization techniques such as the finite element method, the finite volume method or the discontinuous Galerkin method are the most used simulation techniques in ap- plied sciences and technology. These methods rely on a spatial discretization adapted to the geometry and to the prescribed distribution of element size. Several fast and robust algorithms have been developed to generate triangular and tetrahedral meshes. In these methods local connectivity modifications are a crucial step. Nevertheless, in hexahedral meshes the connectivity modifications propagate through the mesh. In this sense, hexahedral meshes are more constrained and therefore, more difficult to gener- ate. However, in many applications such as boundary layers in computational fluid dy- namics or composite material in structural analysis hexahedral meshes are preferred. In this work we present a survey of developed methods for generating structured and unstructured hexahedral meshes.Peer ReviewedPostprint (published version

A case study in hexahedral mesh generation: Simulation of the human mandible

We provide a case study for the generation of pure hexahedral meshes for the numerical simulation of physiological stress scenarios of the human mandible. Due to its complex and very detailed free-form geometry, the mandible model is very demanding. This test case is used as a running example to demonstrate the applicability of a combinatorial approach for the generation of hexahedral meshes by means of successive dual cycle eliminations, which has been proposed by the second author in previous work. We report on the progress and recent advances of the cycle elimination scheme. The given input data, a surface triangulation obtained from computed tomography data, requires a substantial mesh reduction and a suitable conversion into a quadrilateral surface mesh as a first step, for which we use mesh clustering and b-matching techniques. Several strategies for improved cycle elimination orders are proposed. They lead to a significant reduction in the mesh size and a better structural quality. Based on the resulting combinatorial meshes, gradient-based optimized smoothing with the condition number of the Jacobian matrix as objective together with mesh untangling techniques yielded embeddings of a satisfactory quality. To test our hexahedral meshes for the mandible model within an FEM simulation we used the scenario of a bite on a ‘hard nut.’ Our simulation results are in good agreement with observations from biomechanical experiments

Estimation of Travel Times for Minor Roads in Urban Areas Using Sparse Travel Time Data

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link

A novel application of entropy analysis for assessing changes in movement variability during cumulative tackles in young elite rugby league players.

The aim of this study was to identify between-position (forwards vs. backs) differences in movement variability in cumulative tackle events training during both attacking and defensive roles. Eleven elite adolescent male rugby league players volunteered to participate in this study (mean ± SD, age; 18.5 ± 0.5 years, height; 179.5 ± 5.0 cm, body mass; 88.3 ± 13.0 kg). Participants performed a drill encompassing four blocks of six tackling (i.e. tackling an opponent) and six tackled (i.e. being tackled by an opponent while carrying a ball) events (i.e. 48 total tackles) while wearing a micro-technological inertial measurement unit (WIMU, Realtrack Systems, Spain). The acceleration data were used to calculate sample entropy (SampEn) to analyse the movement variability during tackles performance. In tackling actions SampEn showed significant between-position differences in block 1 (p = 0.0001) and block 2 (p = 0.0003). Significant between-block differences were observed in backs (block 1 vs 3, p = 0,0021; and block 1 vs 4, p = 0,0001) but not in forwards. When being tackled, SampEn showed significant between-position differences in block 1 (p = 0.0007) and block 3 (p = 0.0118). Significant between-block differences were only observed for backs in block 1 vs 4 (p = 0,0025). Movement variability shows a progressive reduction with cumulative tackle events, especially in backs and when in the defensive role (tackling). Forwards present lower movement variability values in all blocks, particularly in the first block, both in the attacking and defensive role. Entropy measures can be used by practitioners as an alternative tool to analyse the temporal structure of variability of tackle actions and quantify the load of these actions according to playing position

7th International Meshing Roundtable '98

The goal of the 7th International Meshing Roundtable is to bring together researchers and developers from industry, academia, and government labs in a stimulating, open environment for the exchange of technical information related to the meshing process. In the past, the Roundtable has enjoyed significant participation from each of these groups from a wide variety of countries

The receding front method applied to hexahedral mesh generation of exterior domains

Two of the most successful methods to generate unstructured hexahedral meshes are the grid-based methods and the advancing front methods. On the one hand, the grid-based methods generate high-quality hexahedra in the inner part of the domain using an inside–outside approach. On the other hand, advancing front methods generate high-quality hexahedra near the boundary using an outside–inside approach. To combine the advantages of both methodologies, we extend the receding front method: an inside–outside mesh generation approach by means of a reversed advancing front. We apply this approach to generate unstructured hexahedral meshes of exterior domains. To reproduce the shape of the boundaries, we first pre-compute the mesh fronts by combining two solutions of the Eikonal equation on a tetrahedral reference mesh. Then, to generate high-quality elements, we expand the quadrilateral surface mesh of the inner body towards the unmeshed external boundary using the pre-computed fronts as a guide.Two of the most successful methods to generate unstructured hexahedral meshes are the grid-based methods and the advancing front methods. On the one hand, the grid-based methods generate high-quality hexahedra in the inner part of the domain using an inside–outside approach. On the other hand, advancing front methods generate high-quality hexahedra near the boundary using an outside–inside approach. To combine the advantages of both methodologies, we extend the receding front method: an inside–outside mesh generation approach by means of a reversed advancing front. We apply this approach to generate unstructured hexahedral meshes of exterior domains. To reproduce the shape of the boundaries, we first pre-compute the mesh fronts by combining two solutions of the Eikonal equation on a tetrahedral reference mesh. Then, to generate high-quality elements, we expand the quadrilateral surface mesh of the inner body towards the unmeshed external boundary using the pre-computed fronts as a guide.Peer ReviewedPostprint (author's final draft

Achieving Finite Element Mesh Quality via Optimization of the Jacobian Matrix Norm and Associated Quantities, Part II - A Framework for Volume Mesh Optimization and the Condition Number of the Jacobian Matrix

Three-dimensional unstructured tetrahedral and hexahedral finite element mesh optimization is studied from a theoretical perspective and by computer experiments to determine what objective functions are most effective in attaining valid, high quality meshes. The approach uses matrices and matrix norms to extend the work in Part I to build suitable 3D objective functions. Because certain matrix norm identities which hold for 2 x 2 matrices do not hold for 3 x 3 matrices. significant differences arise between surface and volume mesh optimization objective functions. It is shown, for example, that the equivalence in two-dimensions of the Smoothness and Condition Number of the Jacobian matrix objective functions does not extend to three dimensions and further. that the equivalence of the Oddy and Condition Number of the Metric Tensor objective functions in two-dimensions also fails to extend to three-dimensions. Matrix norm identities are used to systematically construct dimensionally homogeneous groups of objective functions. The concept of an ideal minimizing matrix is introduced for both hexahedral and tetrahedral elements. Non-dimensional objective functions having barriers are emphasized as the most logical choice for mesh optimization. The performance of a number of objective functions in improving mesh quality was assessed on a suite of realistic test problems, focusing particularly on all-hexahedral ''whisker-weaved'' meshes. Performance is investigated on both structured and unstructured meshes and on both hexahedral and tetrahedral meshes. Although several objective functions are competitive, the condition number objective function is particularly attractive. The objective functions are closely related to mesh quality measures. To illustrate, it is shown that the condition number metric can be viewed as a new tetrahedral element quality measure

Estimation of Travel Time using Temporal and Spatial Relationships in Sparse Data

Travel time is a basic measure upon which e.g. traveller information systems, traffic management systems, public transportation planning and other intelligent transport systems are developed. Collecting travel time information in a large and dynamic road network is essential to managing the transportation systems strategically and efficiently. This is a challenging and expensive task that requires costly travel time measurements. Estimation techniques are employed to utilise data collected for the major roads and traffic network structure to approximate travel times for minor links. Although many methodologies have been proposed, they have not yet adequately solved many challenges associated with travel time, in particular, travel time estimation for all links in a large and dynamic urban traffic network. Typically focus is placed on major roads such as motorways and main city arteries but there is an increasing need to know accurate travel times for minor urban roads. Such information is crucial for tackling air quality problems, accommodate a growing number of cars and provide accurate information for routing, e.g. self-driving vehicles. This study aims to address the aforementioned challenges by introducing a methodology able to estimate travel times in near-real-time by using historical sparse travel time data. To this end, an investigation of temporal and spatial dependencies between travel time of traffic links in the datasets is carefully conducted. Two novel methodologies are proposed, Neighbouring Link Inference method (NLIM) and Similar Model Searching method (SMS). The NLIM learns the temporal and spatial relationship between the travel time of adjacent links and uses the relation to estimate travel time of the targeted link. For this purpose, several machine learning techniques including support vector machine regression, neural network and multi-linear regression are employed. Meanwhile, SMS looks for similar NLIM models from which to utilise data in order to improve the performance of a selected NLIM model. NLIM and SMS incorporates an additional novel application for travel time outlier detection and removal. By adapting a multivariate Gaussian mixture model, an improvement in travel time estimation is achieved. Both introduced methods are evaluated on four distinct datasets and compared against benchmark techniques adopted from literature. They efficiently perform the task of travel time estimation in near-real-time of a target link using models learnt from adjacent traffic links. The training data from similar NLIM models provide more information for NLIM to learn the temporal and spatial relationship between the travel time of links to support the high variability of urban travel time and high data sparsity.Ministry of Education and Training of Vietna