Efficient unstructured quadrilateral mesh generation

2014

This paper describes a scheme for finite element mesh generation of a convex, non-convex polygon and multiply connected linear polygon. We first decompose the arbitrary linear polygon into simple sub regions in the shape of polygons.These subregions may be simple convex polygons or cracked polygons.We can divide a nonconvex polygon into convex polygons and cracked polygons We then decompose these polygons into simple sub regions in the shape of triangles. These simple regions are then triangulated to generate a fine mesh of triangular elements. We propose then an automatic triangular to quadrilateral conversion scheme. Each isolated triangle is split into three quadrilaterals according to the usual scheme, adding three vertices in the middle of the edges and a vertex at the barrycentre of the element. To preserve the mesh conformity a similar procedure is also applied to every triangle o f the domain to fully discretize the given convex polygonal domain into all quadrilaterals, thus...

International Journal for Numerical …, 1996

We propose a new optimization strategy for unstructured meshes that, when coupled with existing automatic generators, produces meshes of high quality for arbitrary domains in 3D. Our optimizer is based upon a non-differentiable definition of the quality of the mesh which is natural for finite element or finite volume users: The quality of the worst element in the mesh. The dimension of the optimization space is made tractable by restricting, at each iteration, to a suitable neighborhood of the worst element. Both geometrical (node repositioning) and topological (reconnection) operations are performed. It turns out that the repositioning method is advantageous with respect to both the usual node-by-node techniques and the more recent differentiable optimization methods. Several examples are included that illustrate the efficiency of the optimizer.

2012

This lecture reviews the state of the art in quadrilateral and hexahedral mesh generation. Three lines of development – block decomposition, superposition and the dual method – are described. The refinement problem is discussed, and methods for octree-based meshing are presented. 1

Citeseer

2017

abstrakt. Polygonal meshes represent important geometric structures with a large number of applications. The study of polygonal meshes is motivated by many processing tasks in automotive/aerospace industry, egineering, architecture, engineering, construction industry, and industrial design. Much of literature on polygonal representations focuses on quadrilateral meshes which are composed of quadrilaterals as they possess several advantages compared to triangle meshes. In this short contribution we present a comparative study of known methods for constuctions of quadrangulations of various classes and for different purposes. We suggest a new method for computing all unique quadrilateral meshes of a certain class based on sequential construction.

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.

Computers & Structures, 1988

Some recent efforts on the development of methods to ensun the robustness of automatic thracdimensional mesh generation techniques arc discuss& The topic arcas considered arc mesh entity classification, finite octrcc cell triangulation, and coarse mesh generation by element removal.

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...

1998

This paper proposes a computational method for fully automated quadrilateral meshing. Unlike previous methods, this new scheme can create a quadrilateral mesh whose directionality is precisely controlled. Given as input: (1) a 2D geometric domain, (2) a desired node spacing distribution as a scalar function de ned over the domain, and (3) a desired mesh directionality as a vector eld de ned over the domain, the proposed method rst packs square cells closely in the domain. The centers of the squares are then connected by Delaunay triangulation, yielding a triangular mesh topology. The triangular mesh is further converted into a quad-dominant mesh or an all-quad mesh that satis es the given mesh directionality. Since the closely packed square cells mimic a pattern of Voroni polygons corresponding to a well-shaped graded quadrilateral mesh, the proposed method generates a high quality mesh whose element sizes and mesh directionality conform well to the given input.

Terrestrial, Atmospheric and Oceanic Sciences, 2016

This research developed an automatic two-dimensional finite element meshing system to resolve practical engineering problems in the fields of geology, hydrology, and water resources. This system first used the Delaunay triangulation method to create reasonable-density triangular mesh and then converted it into quadrilateral mesh by combining proper pairs of adjacent triangles. A series of combination patterns aiming at three cases were established. The effect of the number of boundary edges on the subsequent meshing procedures were studied and summarized. For the geometry with multiple domains an adjustment method is proposed to completely eliminate the residual triangles during quadrilateral meshing through adjusting the number of boundary edges in each loop to be even. A special boundary loop identification method is proposed for priority treatment. Corresponding treatment methods aimed at three different situations are established for common boundary loops. For a certain boundary loop with an odd number of boundary edges, the appropriate edge for new point insertion is determined by the position properties and relative density errors. Practical applications confirm that the method proposed in this paper could successfully implement the full conversion from the triangular mesh to the quadrilateral mesh.

Volume 1: 21st Computers and Information in Engineering Conference, 2001

A computer code for the generation of unstructured two-dimensional triangular meshes around arbitrary complex geometries has been developed. The code is based on Delaunay triangulation with an automatic point insertion scheme and a smoothing technique. The geometrical definition of the domain to be meshed is prescribed by means of B-spline curves obtained from two approaches of interest in Computer-Aided Geometric Design named inverse design and interpolation problems. The presented scheme is based on an interpolation procedure along a B-spline curve proposed by the author in a recent paper. This technique prevents that the resulting grid may overlap convex portions of the boundaries. The main goal is to study the possibility of extend the methodology of unstructured grid generation beginning with boundaries described by polylines to other in which they are prescribed by piecewise polynomials curves capable to drive more realistic problems. Several figures and examples from Computat...

Journal of Computational Physics

We describe a high order technique to generate quadrilateral decompositions and meshes for complex two dimensional domains using spectral elements in a field guided procedure. Inspired by cross field methods, we never actually compute crosses. Instead, we compute a high order accurate guiding field using a continuous Galerkin (CG) or discontinuous Galerkin (DG) spectral element method to solve a Laplace equation for each of the field variables using the open source code Nektar++. The spectral method provides spectral convergence and sub-element resolution of the fields. The DG approximation allows meshing of corners that are not multiples of π/2 in a discretization consistent manner, when needed. The high order field can then be exploited to accurately find irregular nodes, and can be accurately integrated using a high order separatrix integration method to avoid features like limit cycles. The result is a mesh with naturally curved quadrilateral elements that do not need to be curved a posteriori to eliminate invalid elements. The mesh generation procedure is implemented in the open source mesh generation program NekMesh.

Engineering with Computers, 2011

In this article the authors present PolyFront, a new triangulation algorithm for two dimensional domains with holes. PolyFront is based on a normal offsetting technique, where a domain is triangulated starting from a discretization of its boundary and constructing the mesh layer by layer going toward the interior of the domain. The authors propose some numerical experiments to compare this algorithm with other four mesh generators. This comparison shows that the algorithm gives good quality meshes with reduced computational time.

Handbook of Computational Geometry, 2000

IEEE Transactions on Magnetics, 1990

Devoted to the mesh generation of 3DD-domains, this paper briefly describes difleerent approaches actually in progress. A new method is introduced which can be seen as a variant of the Delaunay-Vomnoi's tessellation coupled with a control of the given boundary used to defined the domain to be meshed.