Advancing Front Technique Research Articles

Surface reconstruction for mid-slice generation on variable lamination manufacturing

A new rapid prototyping process, variable lamination manufacturing (VLM), has been developed to reduce building time and to improve the surface finish of parts by using a 4-axis-controlled hotwire cutter and expandable polystyrene foam sheet as a laminating material of the part (VLM-S). The objective of this study is to reconstruct the surface of the original 3D computer-aided design (CAD) model in order to generate mid-slice data using the advancing front technique (AFT). The generation of 3D layers by a 4-axis-controlled hotwire cutter requires a completely different procedure to generate toolpath data unlike the conventional RP CAD systems. The cutting path data for VLM-S are created by VLM-Slicer, which is a special CAD/CAM software with automatic generation of 3D toolpath. For the conventional sheet type system like LOM, the STL file would be sliced into 2D data only. However, due to the use of thick layers and a sloping edge with the first-order approximation between the top and bottom layers, VLM-Slicer requires surface reconstruction, mid-slice, and toolpath data generation as well as 2D slicing. Surface reconstruction demands that the connection between the two neighboring cross-sectional contours use the triangular facets. VLM-S employs thick layers with finite thickness, so that surface reconstruction is necessary to obtain a sloping angle of a side surface and the point data at a half of the sheet thickness. In the process of the toolpath data generation the surface reconstruction algorithm is expected to minimize the error between the ruled surface and the original parts.

A parallel advancing front grid generation scheme

AbstractA parallel advancing front scheme has been developed. The domain to be gridded is first subdivided spatially using a relatively coarse octree. Boxes are then identified and gridded in parallel. A scheme that resembles closely the advancing front technique on scalar machines is recovered by only considering the boxes of the active front that generate small elements. The procedure has been implemented on the SGI origin class of machines using the shared memory paradigm. Timings for a variety of cases show speedups similar to those obtained for flow codes. The procedure has been used to generate grids with tens of millions of elements. Copyright © 2001 John Wiley & Sons, Ltd.

A quadrilateral mesh generator for adaptive procedures in bulk forming processes

The simulation of real industry metal forming processes often requires the presence of adaptive procedures. With that purpose a quadrilateral mesh generator was developed. The algorithm is based on the simple fact that it is always possible to subdivide a region into quadrilaterals whenever the polygonal line that forms its boundary has an even number of sides and that, by joining two contiguous triangles, a quadrilateral may be formed. Rather than using an advancing front technique a cloud of nodal points is initially formed based on error estimators and criteria to define an optimal element size. With this procedure, using an adaptive process, the refinement is created where it will be needed.

GENERATION OF THE UNSTRUCTURED FE-GRIDS FOR COMPLEX 2D OBJECTS/NESTRUKTŪRINIŲ BE TINKLŲ GENERAVIMAS SUDĖTINGIEMS DVIMAČIAMS OBJEKTAMS

GENERATION OF THE UNSTRUCTURED FE-GRIDS FOR COMPLEX 2D OBJECTS/NESTRUKTŪRINIŲ BE TINKLŲ GENERAVIMAS SUDĖTINGIEMS DVIMAČIAMS OBJEKTAMS

GENERATION OF THE UNSTRUCTURED FE-GRIDS FOR COMPLEX 2D OBJECTS

Summary For the numerical simulation of engineering problems, the finite element method (FEM) is among the most popular approaches. One of the main concerns in a finite element analysis is the adequacy of the finite element grid. The accuracy of the FEM depends on the size, shape and placement of the elements. On the other hand, the total computational cost is determined by the total number of elements in FE model. An increased accuracy can be obtained by the global reduction of the element size, but this can be characterised by drastically increased computational cost. Thus, in many engineering applications it is desirable to generate not regular FE mesh with finer grid in the regions where accuracy of numerical simulation is of most importance and with more coarse grid in the other regions. In this paper we present a new approach to the grid generation of the multimaterial or multidomain engineering systems by the advancing front technique. This technique has proved successful in generating unstructured...

H-Morph: an indirect approach to advancing front hex meshing

H-Morph is a new automatic algorithm for the generation of a hexahedral-dominant finite element mesh for arbitrary volumes. The H-Morph method starts with an initial tetrahedral mesh and systematically transforms and combines tetrahedral into hexahedra. It uses an advancing front technique where the initial front consists of a set of prescribed quadrilateral surface facets. Fronts are individually processed by recovering each of the six quadrilateral faces of a hexahedron from the tetrahedral mesh. Recovery techniques similar to those used in boundary constrained Delaunay mesh generation are used. Tetrahedral internal to the six hexahedral faces are then removed and a hexahedron is formed. At any time during the H-Morph procedure a valid mixed hexahedral-tetrahedral mesh is in existence within the volume. The procedure continues until no tetrahedral remain within the volume, or tetrahedral remain which cannot be transformed or combined into valid hexahedral elements. Any remaining tetrahedral are typically towards the interior of the volume, generally a less critical region for analysis. Transition from tetrahedral to hexahedra in the final mesh is accomplished through pyramid shaped elements. Advantages of the proposed method include its ability to conform to an existing quadrilateral surface mesh, its ability to mesh without the need to decompose or recognize special classes of geometry, and its characteristic well-aligned layers of elements parallel to the boundary. Example test cases are presented on a variety of models.

Development of a Fully Systemized Chimera Methodology for Steady/Unsteady Problems

A new systemized procedure for chimera-domain decomposition is presented. This procedure consists of a new cut-paste algorithm for optimal mesh interface and a two-step search method for donor cell identification. It is fully automated and requires minimal user input. The cut-paste algorithm is based on the advancing front technique in which the fronts are iteratively determined from the initial fronts, which are a collection of fringe points obtained from conventional Chimera hole cutting. The final fronts are determined iteratively in such a way that the overlapping region is minimized. With this method, interpolation points are located away from solid walls where flow gradient is high. We also can reduce the error that may arise from interpolation in stiff gradient regions. Two- and three-dimensional examples are chosen to demonstrate the effectiveness of this new procedure

Tetrahedral meshes from planar cross-sections

In biomedicine, many three-dimensional (3D) objects are sampled in terms of slices such as computed tomography (CT), magnetic resonance imaging (MRI), and ultrasound imaging. It is often necessary to construct surface meshes from the cross sections for visualization, and thereafter construct tetrahedra for the solid bounded by the surface meshes for the purpose of finite element analysis. In Ref. [1] (C. Bajaj, E. Coyle and K. Lin, Graphical Models and Image Processing 58 (6) (1996) 524–543), we provided a solution to the construction of a surface triangular mesh from planar -section contours. Here we provide an approach to tetrahedralize the solid region bounded by planar contours and the surface mesh. It is a difficult task because the solid can be of high genus (several through holes) as well as have complicated branching regions. We develop an algorithm to effectively reduce the solid into prismatoids, and provide an approach to tetrahedralize the prismatoids. Our tetrahedralization approach is similar to the advancing front technique (AFT) for its flexible control of mesh quality. The main criticism of AFT is that the remaining interior may be badly shaped or even untetrahedralizable. The emphasis of our prismatoid tetrahedralization approach is on the characterization and prevention of untetrahedralizable parts. Ruppert and Seidel (J. Ruppert, R. Seidel, On the difficulty of tetrahedralizing three-dimensional non-convex polyhedra, in: Proceedings 5th Annual ACM Symposium Comput. Geom., 1989, p. 380–392) have shown that the problem of deciding whether a polyhedron is tetrahedralizable without adding Steiner points is NP-complete. We characterize this problem under certain constraints, and design one rule to reduce the chance of generating untetrahedralizable shapes. The characterization also leads to the classification of two common untetrahedralizable categories which can be better processed if they do occur.

Automatic adaptive finite element mesh generation over arbitrary two-dimensional domain using advancing front technique

The basic principles for the generation of adaptive finite element meshes over arbitrary two-dimensional domains using the advancing front technique are described. Methods to generate triangular and quadrilateral meshes are also presented. In addition to the description of the mesh generation algorithms, implementation details concerning both the speed and memory requirement are given. Mesh generation examples demonstrate that the proposed mesh generator is capable of discretizing the problem domain into a well-graded, high quality adaptive finite element mesh with element sizes compatible with the user specification. The whole automatic mesh generation program can be run on an IBM PC compatible machine and meshes with up to 9000 elements can be generated within a practical time limit.

A Scheme for Generating Unstructured Grids on Spheres with Application to Parallel Computation

Numerical solution of differential equations on the surface of the sphere requires grid generation. Examples include numerical simulations of mantle convection, weather, and climate. Because of their ability to offer local resolution at modest computational cost, unstructured grids are attractive in this context. However, unstructured grids suffer from drawbacks such as high computational overhead and inefficient generation schemes. Here we present a scheme for generating unstructured grids on the surface of the sphere that overcomes these limitations. We also show how the scheme can be easily used to allow efficient domain decomposition for parallel computations. The surface of the sphere is covered with a spherical spiral, which is used to provide an underlying structure for the grid. The spiral is populated by nodes, which are then connected using an advancing front technique to generate near-equilateral spherical triangular elements. Methods for producing local grid refinement by adjusting the pitch of the spherical spiral are discussed, as is the extension of the method to the case of coupled pressure–velocity solvers. The same general idea of a spherical spiral also serves as the starting point for an algorithm to subdivide the grid into subdomains for parallel computation. The resulting unstructured grids are generally of very high quality: in uniform grids, 99.4% of the elements have areas between 90 and 107% of the mean element area, and 99.8% of the edges have lengths between 84 and 132% of the mean edge length. The quality of the grids increases with mesh density. Partitioning of the nodes and elements produces well-balanced and compact subdomains, with a maximum load imbalance that is small and rises gradually with number of subdomains. The proposed scheme produces grids that combine the benefits of an unstructured mesh with the structure conferred by the underlying spherical spiral. For example, this underlying structure greatly facilitates tasks such as element searching. This scheme is an attractive alternative for generating unstructured triangular grids on the sphere.

An advancing front point generation technique

An algorithm to construct boundary-conforming, isotropic clouds of points with variable density in space is described. The input required consists of a specified mean point distance and an initial triangulation of the surface. Borrowing a key concept from advancing front grid generators, one point at a time is removed and, if possible, surrounded by admissible new points. This operation is repeated until no active points are left. Timings show that the scheme is about an order of magnitude faster than volume grid generators based on the advancing front technique, making it possible to generate large (>106) yet optimal clouds of points in a matter of minutes on a workstation. Several examples are included that demonstrate the capabilities of the technique. Copyright © 1998 John Wiley & Sons, Ltd.

Regularized Vortex Sheet Evolution in Three Dimensions

A computational method is presented to track the evolution of regularized three-dimensional vortex sheets through an otherwise irrotational, inviscid, constant-density fluid. The sheet surface is represented by a triangulated mesh with interpolating functions locally defined inside each triangle.C1continuity is maintained between triangles via combinations of cubic Bézier triangular interpolants. The self-induced sheet motion generally results in a highly deformed surface which is adaptively refined as needed to capture regions of increasing curvature and to avoid severe Lagrangian deformation. Automatic mesh refinement is implemented with an advancing front technique. Sheet motion is regularized by adding a length scale cutoff to the Biot–Savart kernel. Toroidal and periodic-cylinder vortex sheets are simulated, modeling vortex rings and vortex/jet combinations, respectively. Comparisons with previous 2D results are favorable and 3D results are presented.

Improved adaptive quadrilateral mesh generation using fission elements

An improved technique for quadrilateral mesh generation using an approach based on fission elements is presented. Considerable work has been carried out by Zhu et al. [1][Zhu, J. Z., Zienkiewicz, O. C., Hinton, E. & Wu, J., A new approach to the development of automatic quadrilateral mesh generation. Int. J. Numer. Meth. Engng, 1991, 32, 849–866] in applying the advancing front technique to quadrilateral mesh generation. In this paper more details of the specific characters of quadrilateral elements and an improved mesh generation technique in which the final quadrilateral elements are accurately generated according to element size parameters, are presented. A new kind of transition element called fission elements are used in this quadrilateral element generation technique. These elements are used when two subfronts which both have an odd number. Active sides are formed after two triangles have been generated and combined to form a quadrilateral. This avoids having to add an extra constraint during the mesh generation and guarantees that the quadrilateral mesh generation is as easy as triangular mesh generation. Some new techniques for quadrilateral element mesh enhancement are proposed. All of these are demonstrated by a variety of examples.

Parallel adaptive tetrahedral mesh generation by the advancing front technique

A parallel adaptive tetrahedral mesh generation program using the advancing front method is described. The problem domain is initially defined by a course background mesh of tetrahedral elements which forms the input for finite element analysis and from which adaptive parameters are calculated. Parallel adaptive mesh generation is then carried out by dividing the background mesh into subdomains and refining each subdomain concurrently using the nodal parameters previously calculated and undertaken by the advancing front method.

Generation and optimization of tetrahedral meshes by advancing front technique

An algorithm for tetrahedron mesh generation and optimization with respect to a shape and a size criterion is presented. A well distributed set of nodes is first generated by an octree method, and the set is then triangulated. The advancing front technique is used to mesh the whole volume. Emphasis has been placed on management of the front. The method involves priority construction of enhanced quality tetrahedra. Each face is assigned to a front corresponding to the quality of the best tetrahedron which can be constructed. Elements are destroyed in the case of non-convergence. Optimization procedures make local use of the algorithm used to mesh the complete model. Industrial examples of relatively complex volumes are given, demonstrating that a high quality and optimized mesh can be obtained by the proposed method. © 1998 John Wiley & Sons, Ltd.

Triangulation of 3D surfaces

A simple generator of graded triangular meshes on spatial surfaces is introduced in this paper. The algorithm is based on the approximation of the surface by tensor product polynomial patches which are uniquely mappable on a planar parametric space. Each of the patches is triangulated separately in its parametric space, using modified advancing front technique allowing for generation of pre-stretched elements, and the obtained triangulation is mapped back onto the original surface. Large effort has been devoted to the treatment of singularities arising on surfaces approximated by degenerated patches.

Two-dimensional implicit flux split steady and unsteady Euler calculations using unstructured moving grids

AbstractTwo-dimensional Euler equations are solved on unstructured triangular meshes using commonly available minicomputers. The driving algorithm is an upwind biased implicit cell-centred finite volume scheme. The spatial discretisation involves a naturally dissipative flux-split approach that sharply captures Shockwaves. The grid generation method uses a type of advancing front technique which triangulates a given set of points. To demonstrate the application, the steady flow results are presented for single and two component aerofoils. The unsteady results are obtained using a dynamic mesh algorithm for an aerofoil pitching harmonically about the quarter chord. The paper presents a description of the grid generation and movement algorithm and of the Euler solver, along with results and comparison that assess their capabilities.

3D mesh adaptation. Optimization of tetrahedral meshes by advancing front technique

The objective of the paper is to present an automatic mesh generator which builds a mesh which respects the element densities prescribed as a result of an error sensitivity analysis. The desired new mesh is fully characterized by the distribution of the refinement levels on the initial mesh. Therefore, the most important criterion in the choice of a mesh generator comes from the ability to produce a mesh with imposed density while meeting ‘acceptable’ shape quality requirements. In this spirit, a new method for tetrahedron mesh generation and optimization with respect to both a shape and a size criterion is presented. The advancing front technique is used to mesh the whole volume. Then, optimization procedures make astute local use of the algorithm used to mesh the complete model. The process is iterative. The corresponding method involves extracting sub-volumes or shells from the tetrahedron mesh volume, which are then remeshed by an advancing front technique to improve their quality. The sub-volumes are constructed by determining the set of tetrahedra which touch the same node, edge or face. Local transformations are extended to non-convex sub-regions which gives a higher quality mesh. Industrial examples of relatively complex volumes are given, demonstrating that a high quality and optimized mesh can be obtained by the proposed method.

AN AUTOMATIC TETRAHEDRAL MESH GENERATION SCHEME BY THE ADVANCING FRONT METHOD

SUMMARY The paper deals with the discretization of any given multi-connected volume into a set of tetrahedral elements. A simple but robust tetrahedrization scheme based on a two-stage advancing front technique is presented. The method evolves from the triangulated domain bounding surfaces for which geometry representations are derived from triangular Bezier patches. Tetrahedral elements are then generated which fill the domain volume based on the set of distributed interior nodes. A new and eAcient procedure is introduced for the distribution of the mesh interior nodes which uses an inverse-power interpolation technique. The proposed scheme is robust in that it is capable of tetrahedrizing a given arbitrary domain of any degree of irregularity, and allows the distribution of its interior nodes to be specified by the user. Results are presented typical of those which might be encountered in hydrodynamics modelling involving flows with a free surface.

Progress in grid generation via the advancing front technique

We describe recent extensions and improvements to the advancing front grid generation technique. These improvements target a range of applicability, speed and user friendliness. The range of applicability is enlarged by the ability to produce volumetric grids around thin surfaces (such as shells, membranes, fabrics or surfaces with cusps), the generation of high aspect ratio grids for Navier-Stokes applications, the generation of higher order triangular and tetrahedral elements, and the generation of quadrilateral and hexahedral elements. Speed improvements are the result of reduced search overheads, as well as vectorization and parallelization. User friendliness is enhanced by the ability to grid directly discrete data and simpler ways of specifying the desired element size and shape in space. Numerous examples are included that demonstrate the versatility and maturity that advancing front grid generators have achieved.