Advancing Front Algorithm Research Articles

On the Efficiency of the Advancing-Front Surface Mesh Generation Algorithm

An efficient advancing front algorithm is presented to create high-quality surface elements on CAD models. Various novel schemes are developed to improve the efficiency of the algorithm while not sacrificing its robustness and the resulting mesh quality. New features include a fast projection scheme that can perform robustly in case of badly defined surfaces, a procedure that computes the ideal point by an approach that can preserve the advantageous features of both the mapping and direct methods, and an octree data structure that can speed up the local search of all existing front nodes about the ideal point. To our knowledge, the proposed algorithm is one of the fastest algorithms for surface mesh generation. On an AMD Ryzen 5 3600 machine, the sequential version of the proposed algorithm can create a quality mesh at a speed of up to 100,000 elements per second. This speed is more than 3 times higher than a state-of-the-art code can achieve. Another advantage of the proposed algorithm is its ability to maintain its high efficiency when millions or more elements are created on one single surface. In this circumstance, the efficiency of some state-of-the-arts codes slows down by one or two orders. After parallelized based on the taskflow approach, the proposed algorithm can create more than 1.6 million elements on real-world configurations in 7 s by using 6 computer cores. This speed is higher than a state-of-the-art commercial code can achieve by one order. • An efficient surface mesh generator for large-scale triangular mesh generation of industrial CAD models, which is far faster than existing schemes. • The nonlinear calculation such as orthogonal projection and ideal point calculation is comprehensively improved. • Traditional surface mesh generation methods such as direct method and mapping method are combined. • The design of spatial index data structure (octree and AD tree) makes the algorithm have strong scalability.

Enhancement on parallel unstructured overset grid method for complex aerospace engineering applications

In the present study, an efficient overset grid method by means of parallel implicit hole-cutting is proposed for the sake of simulating unsteady flows in aerospace engineering involving multiple bodies in relative movement. In view of the degraded computational efficiency and robustness for conventional overset grid assembly, several innovative techniques are developed within the overset grid assembly process, viz., a bookkeeping alternative digital tree method to speed up the donor-cell searching, a fast parallel advancing front algorithm to accelerate the wall-distance calculation and a message-passing strategy with efficient information communication and lower storage expenditure within distributed computational architecture. The contribution of the developed techniques is evidenced by comparison with the existing alternative ways in terms of computing efficiency. Subsequently, the overset grid method is embedded into an in-house programed URANS solver to examine its capability in predicting the flow field of complex applications such as helicopter, store separation and component deploying. Results show that the developed overset grid methodology is, in practice, able to resolve the aerodynamic characteristics of complex aerospace engineering with a high-fidelity flow topology and accuracy.

SAFT: Shotgun advancing front technique for massively parallel mesh generation on graphics processing unit

AbstractLarge‐scale numerical simulations need efficient parallel mesh generation schemes. Several parallel advancing front algorithms were proposed in the past decades, most of which require domain decomposition. In this article, we present a shotgun algorithm for parallel advancing front mesh generation. Our algorithm is front‐based, therefore does not require domain decomposition. We've implemented the algorithm on GPU, which has thousands of CUDA cores. Different from traditional volume‐based parallelization, each CUDA thread handles one face at a time. We deal with conflicts by discarding illegal new elements which intersect with each other. We name this proposed method “SAFT”, which stands for “shotgun advancing front technique”. Its performance, as well as scalability, has been evaluated on a laptop equipped with one NVIDIA Geforce RTX2060 graphics card. We have been able to generate high‐quality 2D meshes efficiently (233k elements per second).

A geometric algorithm based on the advancing front approach for sequential sphere packing

The arrangement of calculation samples with a high initial solid fraction and lower computation times are the primary concern of discrete element simulations. When generating thousands of particles, the advancing front algorithm, as one of the effective constructive packing methods, provides a time-saving and non-overlapping packing methodology compared to dynamic approaches, which are extremely time consuming in these situations. This paper proposes a sequential packing algorithm based on the advancing front approach. New particles with random sizes are sequentially inserted into a predefined void space to make contact with at least three existing neighboring particles by analytically solving the trilateration equations. The algorithm allows for an arrangement of particles with random sizes to obtain a low-porosity particle assembly. To increase the algorithm efficiency, a feasible measure of the spatial gridding is proposed to simplify the detection of the advancing fronts. The generated packings can be isotropic, and the number of contacts per particle is sufficiently high to reach a stable state. When the generated packing structures are filled with particles, the physical properties, including the average coordination number, solid fraction, second-order fabric tensor, contact orientation and particle size distribution, are analyzed with different size ratios. Examples of practical geometric models for real industrial applications to railway ballast and a gear are presented.

Contributions to the generalization of advancing front particle packing algorithms

SummaryThe generation of a set of particles with high initial volume fraction is a major problem in the context of discrete element simulations. Advancing front algorithms provide an effective means to generate dense packings when spherical particles are assumed. The objective of this paper is to extend an advancing front algorithm to a wider class of particles with generic size and shape. In order to get a dense packing, each new particle is placed in contact with other two (or three in 3D) particles of the advancing front. The contact problem is solved analytically using wrapping intersection technique. The results presented herein will be useful in the application of these algorithms to a wide variety of practical problems. Examples of geometric models for applications to biomechanics and cutting tools are presented. Copyright © 2015 John Wiley & Sons, Ltd.

A staggered approach to structural shape and topology optimization

AbstractThis contribution is concerned with the design and evaluation of a staggered approach to computational shape and topology optimization. The main idea is to interrelate a classical boundary variation scheme based on the results from shape sensitivity analysis and an evolutionary‐type element removal procedure that relies on the topological sensitivity as a rejection criterion. The key ingredient in this perspective is to consider an advancing front algorithm that is gradually removing, from the evolving boundary of the domain, a number of finite elements based on the evaluation of the topological sensitivity.This process is repeated until the minimum topological sensitivity is no longer encountered at the boundary but in the interior of the domain, such that a topological change is to be considered for the current design layout. However, we first aim to establish a more accurate approximation of the true optimal shape of the newly established (zig‐zag representation) of the design boundary. This is achieved by the evaluation of the shape sensitivity and the accompanying boundary variations obtained by a basic descent algorithm. Only then, we create a hole in the interior of the domain by removing all cells that are adjacent to the nodal point that exhibits the minimum topological sensitivity and resume the advancing front algorithm to alter the newly established design boundary. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Modified algorithm for generating high volume fraction sphere packings

Advancing front packing algorithms have proven to be very efficient in 2D for obtaining high density sets of particles, especially disks. However, the extension of these algorithms to 3D is not a trivial task. In the present paper, an advancing front algorithm for obtaining highly dense sphere packings is presented. It is simpler than other advancing front packing methods in 3D and can also be used with other types of particles. Comparison with respect to other packing methods have been carried out and a significant improvement in the volume fraction (VF) has been observed. Moreover, the quality of packings was evaluated with indicators other than VF. As additional advantage, the number of generated particles with the algorithm is linear with respect to time.

A staggered approach to shape and topology optimization using the traction method and an evolutionary-type advancing front algorithm

Abstract We investigate a novel approach for structural shape optimization on the basis of complementary shape and topological sensitivity analysis. As in early approaches to shape optimization, the domain variation is specified by modification of boundary nodal points, hence leading to an updated Lagrangian description for the course of optimization. To overcome the formation of oscillating boundaries in the optimal design trials, we employ the traction method to establish smooth descent directions for shape variation. Therein, an auxiliary elastic problem is solved in which the shape sensitivity constitutes the external loading and the deformation of the auxiliary elastic body is used as a descent direction for shape variation rather than the shape sensitivity itself. We complement this method through an evolutionary-type element removal procedure that is based on the topological sensitivity such that an advancing front algorithm is gradually removing elements from the design boundary of the domain. Once the minimum topological sensitivity is no longer encountered at the design boundary, we create a hole in the domain, again using the topological sensitivity to specify its exact location, and resume the element removal procedure for the newly established design boundary. Since this approach yields only a vague estimate of the true optimal shape of newly established holes, the traction method is again used for shape variation of the extended design boundary.

Region segmentation for STL triangular mesh of CAD object

Region segmentation involves in breaking a polygonal mesh into 'meaningful' patches with characteristic geometrical property respectively. Considering the characteristics of nonuniformity, sparseness and known facet normal for STL model from CAD system, an efficient approach for region segmentation is put forward. The algorithm contains two steps: extracting region boundaries and segmenting regional meshes. Region boundaries are classified into sharp feature edge and non-sharp feature edge. The former is detected based on dihedral edge angle angle between facets, while the latter is identified by analysing intrinsic region properties of triangular facets distribution without curvature estimation. By means of unidirectional increment of feature edges, continuous region boundaries are generated. Finally, we withdraw meaningful patches from STL model based on advancing front algorithm depending on the boundaries. Examples are given to show the feature edges detection, boundaries generation and region segmentation based on the boundaries.

Advancing front circle packing to approximate conformal strips

A circle packing is a set of tangent and disjoint discs. Maps between circle packings with the same tangency are discrete analogues of conformal mappings, which have application for example in mechanical, fluid, and thermal engineering. We describe an advancing front algorithm to compute the circle packing of a strip around a closed planar curve. Conformal mappings preserve local angles and shapes; our algorithm uses these properties to obtain via the fast Fourier transform the centers and radii for the circle packing of successive trigonometric Lagrange curves in a strip. To check the algorithm, different results are compared with well-known conformal mappings. Real time deformations of circle packings are possible by changing the shape of the initial closed curve.

An indirect approach for automatic generation of quadrilateral meshes with arbitrary line constraints

AbstractA new approach to the automatic generation of a quadrilateral mesh with arbitrary line constraints is proposed in this paper. It is an indirect all‐quad mesh generation and presented in the following steps: (1) discretizing the constrained lines within the domain; (2) converting the above domain to a triangular mesh together with the line constraints; (3) transforming the generated triangular mesh with line constraints to an all‐quad mesh through performing an advancing front algorithm from the line constraints, which enables the construction of quadrilaterals layer by layer, and roughly keeps the feature of the initial triangular mesh; (4) optimizing the topology of the quadrilateral mesh to reduce the number of irregular nodes; (5) smoothing the generated mesh toward high‐quality all‐quad mesh generation. Finally, a few application examples are given to demonstrate the reliability and usefulness of the proposed algorithm. Copyright © 2011 John Wiley & Sons, Ltd.

Adaptive spacetime meshing for discontinuous Galerkin methods

Spacetime-discontinuous Galerkin (SDG) finite element methods are used to solve hyperbolic spacetime partial differential equations (PDEs) to accurately model wave propagation phenomena arising in important applications in science and engineering. Tent Pitcher is a specialized algorithm, invented by Üngör and Sheffer (2000) and extended by Erickson et al. (2005) to construct an unstructured simplicial ( d + 1 ) -dimensional spacetime mesh over an arbitrary d-dimensional space domain. Tent Pitcher is an advancing front algorithm that incrementally adds groups of elements to the evolving spacetime mesh. It supports an accurate, local, and parallelizable solution strategy by interleaving mesh generation with an SDG solver. When solving nonlinear PDEs, previous versions of Tent Pitcher must make conservative worst-case assumptions about the physical parameters which limit the duration of spacetime elements. Thus, these algorithms create a mesh with many more elements than necessary. In this paper, we extend Tent Pitcher to give the first spacetime meshing algorithm suitable for efficient simulation of nonlinear phenomena using SDG methods. We adapt the duration of spacetime elements to changing physical parameters due to nonlinear response. Given a triangulated 2-dimensional Euclidean space domain M corresponding to time t = 0 and initial and boundary conditions of the underlying hyperbolic spacetime PDE, we construct an unstructured tetrahedral mesh in the spacetime domain E 2 × R . For every target time T ⩾ 0 , our algorithm meshes the spacetime volume M × [ 0 , T ] with a bounded number of non-degenerate tetrahedra. A recent extension of Tent Pitcher due to Abedi et al. (2004) adapts the spatial size of spacetime elements in 2D × time to a posteriori estimates of numerical error. Our extension of Tent Pitcher retains the ability to perform adaptive refinement and coarsening of the mesh. We thus obtain the first adaptive nonlinear Tent Pitcher algorithm to build spacetime meshes in 2D × time.

Anisotropic quadrilateral mesh generation: An indirect approach

In this paper a new indirect approach is presented for anisotropic quadrilateral mesh generation based on discrete surfaces. The ability to generate grids automatically had a pervasive influence on many application areas in particularly in the field of Computational Fluid Dynamics. In spite of considerable advances in automatic grid generation there is still potential for better performance and higher element quality. The aim is to generate meshes with less elements which fit some anisotropy criterion to satisfy numerical accuracy while reducing processing times remarkably. The generation of high quality volume meshes using an advancing front algorithm relies heavily on a well designed surface mesh. For this reason this paper presents a new technique for the generation of high quality surface meshes containing a significantly reduced number of elements. This is achieved by creating quadrilateral meshes that include anisotropic elements along a source of anisotropy.

An algorithm for tetrahedral mesh generation based on conforming constrained Delaunay tetrahedralization

An unstructured tetrahedral mesh generation algorithm for 3D model with constraints is presented. To automatically generate a tetrahedral mesh for model with constraints, an advancing front algorithm is presented based on conforming constrained Delaunay tetrahedralization (CCDT). To reduce the number of visibility tests between vertices with respect to model faces as well as the computation of constrained Delaunay tetrahedra, a sufficient condition for DT (constrained Delaunay tetrahedralization whose simplexes are all Delaunay) existence is presented and utilized coupled to uniform grid and advancing front techniques in our algorithm. The mesh generator is robust and exhibits a linear time complexity for mechanical models with uniform density distribution.

Automatic metric 3D surface mesh generation using subdivision surface geometrical model. Part 2: Mesh generation algorithm and examples

AbstractIn this paper, a new metric advancing front surface mesh generation scheme is suggested. This new surface mesh generator is based on a new geometrical model employing the interpolating subdivision surface concept. The target surfaces to be meshed are represented implicitly by interpolating subdivision surfaces which allow the presence of various sharp and discontinuous features in the underlying geometrical model. While the main generation steps of the new generator are based on a robust metric surface triangulation kernel developed previously, a number of specially designed algorithms are developed in order to combine the existing metric advancing front algorithm with the new geometrical model. As a result, the application areas of the new mesh generator are largely extended and can be used to handle problems involving extensive changes in domain geometry. Numerical experience indicates that, by using the proposed mesh generation scheme, high quality surface meshes with rapid varying element size and anisotropic characteristics can be generated in a short time by using a low‐end PC. Finally, by using the pseudo‐curvature element‐size controlling metric to impose the curvature element‐size requirement in an implicit manner, the new mesh generation procedure can also generate finite element meshes with high fidelity to approximate the target surfaces accurately. Copyright © 2003 John Wiley & Sons, Ltd.

Automatic generation of tetrahedral meshes from medical images

A new tetrahedral meshing algorithm from the series of medical images is proposed. Sectional contours are extracted from medical images, and by the use of correspondence, tiling, and branching process, the side surfaces between sections are triangulated in addition to the triangulation on each section. As for the mesh generation for an object between two sections, an advancing front algorithm is employed to generate tetrahedral elements by using basic operators. Sample meshes are constructed from medical images for finite element analysis of biomechanical models.

Medial Axis Construction in Three Dimensions and its Application to Mesh Generation

An algorithm for the construction of the medial axis of a three-dimensional body given by a triangulation of its bounding surface is described. The indirect construction is based on the Delaunay-triangulation of a set of sample points on the bounding surface. The point set is refined automatically so as to capture the correct topology of the medial axis. The computed medial axis (or better medial surface) is then used for hex-dominant mesh generation. Quad-dominant meshes are generated on the medial subfaces first and extruded to the boundary of the body at both sides. The resulting single cell layer is subdivided in direction normal to the boundary, yielding columns of hexahedral and three-sided prismatic cells. The resulting volume mesh is orthogonal at the boundary and ‘semi-structured’ between boundary and medial surface. Mixed cell types (tets, pyramids, degenerate hexahedra) may result along the medial surface. An advancing front algorithm (paving) is used for meshing the subfaces of the medial surface. Development of the mesh generator has not been fully completed with respect to degenerate parts of the medial axis. First medium-complexity bodies have been meshed, however, showing moderate meshing times.

Reliable Whisker Weaving via Curve Contraction

Whisker Weaving is an advancing front algorithm for all-hexahedral mesh generation. It uses global information derived from grouping the mesh dual into surfaces, the STC, to construct the connectivity of the mesh, then positions the nodes afterwards. Currently, we are able to reliably generate hexahedral meshes for complicated geometries and surface meshes. However, the surface mesh must be modified locally. Also, in large, highly-unstructured meshes, there are usually isolated regions where hex quality is poor. Reliability has been achieved by using new, provable curvecontraction algorithms to sequence the advancing front process. We have also demonstrated that sheet moving can remove certain types of invalid connectivity.

Volume triangulation from planar cross sections

In a CAD system, a series of sectional contours can be easily obtained from solid models of 3D objects. A new tetrahedral meshing algorithm from these series of planar cross sections is proposed. In this scheme, the planar sections of three-dimensional objects and the side surfaces between two planar sections are triangulated first, and then an advancing front algorithm is employed to construct tetrahedral elements by using basic operators. Sample meshes are constructed from a series of planar cross section and analysed using ADINA.

Q-Morph: an indirect approach to advancing front quad meshing

Q-Morph is a new algorithm for generating all-quadrilateral meshes on bounded three-dimensional surfaces. After first triangulating the surface, the triangles are systematically transformed to create an all-quadrilateral mesh. An advancing front algorithm determines the sequence of triangle transformations. Quadrilaterals are formed by using existing edges in the triangulation, by inserting additional nodes, or by performing local transformations to the triangles. A method typically used for recovering the boundary of a Delaunay mesh is used on interior triangles to recover quadrilateral edges. Any number of triangles may be merged to form a single quadrilateral. Topological clean-up and smoothing are used to improve final element quality. Q-Morph generates well-aligned rows of quadrilaterals parallel to the boundary of the domain while maintaining a limited number of irregular internal nodes. The proposed method also offers the advantage of avoiding expensive intersection calculations commonly associated with advancing front procedures. A series of examples of Q-Morph meshes are also presented to demonstrate the versatility of the proposed method. Copyright © 1999 John Wiley & Sons, Ltd.