Fully automatic mesh generator for 3D domains of any shape

Computer Methods in Applied Mechanics and Engineering, 2010

This paper describes an automatic and efficient approach to construct unstructured tetrahedral and hexahedral meshes for a composite domain made up of heterogeneous materials. The boundaries of these material regions form non-manifold surfaces. In earlier papers, we developed an octree-based isocontouring method to construct unstructured 3D meshes for a single-material (homogeneous) domain with manifold boundary. In this paper, we introduce the notion of a material change edge and use it to identify the interface between two or several different materials. A novel method to calculate the minimizer point for a cell shared by more than two materials is provided, which forms a non-manifold node on the boundary. We then mesh all the material regions simultaneously and automatically while conforming to their boundaries directly from volumetric data. Both material change edges and interior edges are analyzed to construct tetrahedral meshes, and interior grid points are analyzed for proper hexahedral mesh construction. Finally, edge-contraction and smoothing methods are used to improve the quality of tetrahedral meshes, and a combination of pillowing, geometric flow and optimization techniques is used for hexahedral mesh quality improvement. The shrink set of pillowing schemes is defined automatically as the boundary of each material region. Several application results of our multi-material mesh generation method are also provided.

1994

The research reported in this dissertation was undertaken to investigate efficient computational methods of automatically generating three dimensional unstructured tetrahedral meshes. The work on two dimensional triangular unstructured grid generation by Lewis and Robinson [LeR76] is first examined, in which a recursive bisection technique of computational order nlog(n) was implemented. This technique is then extended to incorporate new methods of geometry input and the automatic handling of multiconnected regions. The method of two dimensional recursive mesh bisection is then further modified to incorporate an improved strategy for the selection of bisections. This enables an automatic nodal placement technique to be implemented in conjunction with the grid generator. The dissertation then investigates methods of generating triangular grids over parametric surfaces. This includes a new definition of surface Delaunay triangulation with the extension of grid improvement techniques to...

International Journal for Numerical Methods in Engineering, 2000

An algorithm is presented for the triangulation of arbitrary non-convex polyhedral regions starting with a prescribed boundary triangulation matching existing mesh entities in the remainder of the domain. The algorithm is designed to circumvent the termination problems of volume meshing algorithms which manifest themselves in the inability to successfully create tetrahedra within small subdomains to be referred to herein as cavities. To address this need, a robust Delaunay algorithm with an e cient and termination guaranteed face recovery method is the most appropriate approach. The algorithm begins with Delaunay vertex insertion followed by a face recovery method that conserves the boundary of the cavity by utilizing local mesh modi cation operations such as edge split, collapse and swap and a new set of tools which we call complex splits. The local mesh modi cations are performed in such a manner that each original surface triangulation is represented either as was, or as a concatenation of triangles. When done in this manner, it is always possible to split the matching mesh entities, ensuring that a compatible mesh is created. The algorithm is robust and has been tested against complex manifold and non-manifold cavities resulting in a valid mesh of the entire domain.

Handbook of Computational Geometry, 2000

2007

Abstract: This paper describes an approach to construct unstructured tetrahedral and hexa-hedral meshes for a domain with multiple materials. We have developed an octree-based iso-contouring method to construct unstructured 3D meshes for a single material domain. Based on it, we analyze each material change edge instead of sign change edge to figure out in-terfaces between two materials, and mesh each material region with conforming boundaries. Two kinds of surfaces, the boundary surface and the interface between two different material regions, are meshed and distinguished. Both material change edges and interior edges are an-alyzed to construct tetrahedral meshes, and interior grid points are analyzed for hexahedral mesh construction. Finally the edge-contraction and smoothing method is used to improve the quality of tetrahedral meshes, and a combination of pillowing, geometric flow and optimiza-tion techniques are used for hexahedral mesh quality improvement. The shrink set is def...

We present a preliminary method to generate polyhedral meshes of general non-manifold domains. The method is based on computing the dual of a general tetrahedral mesh. The resulting mesh respects the topology of the domain to the same extent as the input mesh. If the input tetrahedral mesh is Delaunay and well-centered, the resulting mesh is a Voronoi mesh with planar faces. For general tetrahedral meshes, the resulting mesh is a polyhedral mesh with straight edges but possibly curved faces. The initial mesh generation phase is followed by a mesh untangling and quality improvement technique. We demonstrate the technique on some simple to moderately complex domains.

Proceedings of the 16th International Meshing Roundtable, 2008

This paper describes an approach to construct unstructured tetrahedral and hexahedral meshes for a domain with multiple materials. In earlier works, we developed an octreebased isocontouring method to construct unstructured 3D meshes for a single-material domain. Based on this methodology, we introduce the notion of material change edge and use it to identify the interface between two or several materials. We then mesh each material region with conforming boundaries. Two kinds of surfaces, the boundary surface and the interface between two different material regions, are distinguished and meshed. Both material change edges and interior edges are analyzed to construct tetrahedral meshes, and interior grid points are analyzed for hexahedral mesh construction. Finally the edge-contraction and smoothing method is used to improve the quality of tetrahedral meshes, and a combination of pillowing, geometric flow and optimization techniques is used for hexahedral mesh quality improvement. The shrink set is defined automatically as the boundary of each material region. Several application results in different research fields are shown.

International Journal for Numerical Methods in Engineering, 1997

This paper aims to outline the di erent phases necessary to implement a Delaunay-type automatic mesh generator. First, it summarizes this method and then describes a variant which is numerically robust by mentioning at the same time the problems to solve and the di erent solutions possible. The Delaunay insertion process by itself, the boundary integrity problem, the way to create the ÿeld points as well as the optimization procedures are discussed. The two-dimensional situation is described fully and possible extensions to the three-dimensional case are brie y indicated. ? 1997 by John Wiley & Sons, Ltd.

CGALmesh is the mesh generation software package of the Computational Geometry Algorithm Library (CGAL). It generates isotropic simplicial meshes-surface triangular meshes or volume tetrahedral meshes-from input surfaces, 3D domains as well as 3D multi-domains, with or without sharp features. The underlying meshing algorithm relies on restricted Delaunay triangulations to approximate domains and surfaces, and on Delaunay refinement to ensure both approximation accuracy and mesh quality. CGALmesh provides guarantees on approximation quality as well as on the size and shape of the mesh elements. It provides four optional mesh optimization algorithms to further improve the mesh quality. A distinctive property of CGALmesh is its high flexibility with respect to the input domain representation. Such a flexibility is achieved through a careful software design, gathering into a single abstract concept, denoted by the oracle, all required interface features between the meshing engine and the input domain. We already provide oracles for domains defined by polyhedral and implicit surfaces.

International Journal for Numerical Methods in Engineering, 1990

Fully automatic three-dimensional mesh generation is a fundamental requirement for automating the numerical solution of partial differential equations. Two techniques in particular-the octree and Delaunay approaches-have been used towards this end. A method that combines both approaches to fully automatic mesh generation is presented here. The resulting algorithm provides the linear growth rate and divide-andconquer approach of the octree method with the simplicity and optimal properties of the Delaunay triangulation.

International Journal for Numerical Methods in Engineering, 2002

Guaranteed-quality unstructured meshing algorithms facilitate the development of automatic meshing tools. However, these algorithms require domains discretized using a set of linear segments, leading to numerical errors in domains with curved boundaries. We introduce an extension of Ruppert's Delaunay refinement algorithm to twodimensional domains with curved boundaries and prove that the same quality bounds apply with curved boundaries as with straight boundaries. We provide implementation details for two-dimensional boundary patches such as lines, circular arcs, cubic parametric curves, and interpolated splines. We present guaranteed-quality triangular meshes generated with curved boundaries, and propose solutions to some problems associated with the use of curved boundaries.

International Journal of Machine Learning and Computing

Objective of this paper is to propose a new semi-automatic, adaptive and optimized triangular mesh generation technique for any domain (including free formed curves). This new technique is found by merging the generalised equations which were proposed in previous works with Delaunay triangulation method. The new technique is demonstrated for several domains with various boundaries. Initial meshes are generated for these domains, which are later optimized manually by addition, removal or replacement of sampling points. Finalized meshes consist of triangular elements with aspect ratio of less than 2 and minimum skewness of more than 45 degrees.

International Journal for Numerical Methods in Engineering, 2021

This paper presents a methodology aiming at easing considerably the generation of high-quality meshes for complex 3D domains. We show that the whole mesh generation process can be controlled with only five parameters to generate in one stroke quality meshes for arbitrary geometries. The main idea is to build a meshsize field h(x) taking local features of the geometry, such as curvatures, into account. Meshsize information is then propagated from the surfaces into the volume, ensuring that the magnitude of |∇h| is always controlled so as to obtain a smoothly graded mesh. As the meshsize field is stored in an independent octree data structure, the function h can be computed separately, and then plugged in into any mesh generator able to respect a prescribed meshsize field. The whole procedure is automatic, in the sense that minimal interaction with the user is required. Applications examples based on models taken from the very large ABC dataset, are then presented, all treated with the same generic set of parameter values, to demonstrate the efficiency and the universality of the technique.

Computers & Mathematics with Applications, 1979

A method for automatic generation of triangnlar finite element meshes for starshaped domains is introduced. The mesh is simply obtained by inputting, besides the data defining the boundary of the domain, a positive integer parameter p for specification of the wished degree of refinement. It is proved that, for a very wide class of starshaped two dimensional domains, the following necessary condition for convergence of the finite element method is satisfied: There exists a strictly positive constant c, independent of p. such that: minm>c T m(T) vp, p=l,Z,... p(T) and h(T) being respectively the dieter of the inscribed circle and the largest edge of a generated triangle T.

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