2D and 3D finite element meshing and remeshing

Mackerle, Jaroslav

doi:10.1108/eum0000000006495

Cited by 12 publications

(7 citation statements)

References 829 publications

(7 reference statements)

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“…This fact is confirmed by the large number of references quoted in the bibliographies and special issues related to adaptive analysis and meshing [1][2][3][4][5] published recently. In fact, many effective adaptive refinement procedures had been implemented in many research programs [6] and even in commercial packages [7].…”

Section: Introductionsupporting

confidence: 72%

An automatic adaptive refinement procedure for the reproducing kernel particle method. Part II: Adaptive refinement

Lee

Shuai

2006

Comput Mech

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In Part II of this study, an automatic adaptive refinement procedure using the reproducing kernel particle method (RKPM) for the solution of 2D linear boundary value problems is suggested. Based in the theoretical development and the numerical experiments done in Part I of this study, the Zienkiewicz and Zhu (Z-Z) error estimation scheme is combined with a new stress recovery procedure for the a posteriori error estimation of the adaptive refinement procedure. By considering the a priori convergence rate of the RKPM and the estimated error norm, an adaptive refinement strategy for the determination of optimal point distribution is proposed. In the suggested adaptive refinement scheme, the local refinement indicators used are computed by considering the partition of unity property of the RKPM shape functions. In addition, a simple but effective variable support size definition scheme is suggested to ensure the robustness of the adaptive RKPM procedure. The performance of the suggested adaptive procedure is tested by using it to solve several benchmark problems. Numerical results indicated that the suggested refinement scheme can lead to the generation of nearly optimal meshes for both smooth and singular problems. The optimal convergence rate of the RKPM is restored and thus the effectivity indices of the Z-Z

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Section: Introductionsupporting

confidence: 72%

An automatic adaptive refinement procedure for the reproducing kernel particle method. Part II: Adaptive refinement

Lee

Shuai

2006

Comput Mech

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“…There are many papers dealing with general or specific issues of mesh generation algorithms. A list of more than 1700 references is presented by Mackerle [6].…”

Section: Mesh Modelingmentioning

confidence: 99%

Object-oriented programming in FEM and BEM: a bibliography (1990–2003)

Mackerle

2004

Advances in Engineering Software

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“…This fact is reflected by the number of special issues and bibliography published in international journals in the last decade [1][2][3][4][5][6][7][8]. Since mesh generation could be defined as the process of breaking up a physical domain into small subdomains (elements) in order to facilitate numerical solution, a natural way to classify different mesh generation schemes is according to the dimensions of the domain to be discretized.…”

Section: Introductionmentioning

confidence: 99%

A new automatic adaptive 3D solid mesh generation scheme for thin-walled structures

Lee¹,

Xu²

2005

Int. J. Numer. Meth. Engng

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SUMMARYA new algorithm to generate three-dimensional (3D) mesh for thin-walled structures is proposed. In the proposed algorithm, the mesh generation procedure is divided into two distinct phases. In the first phase, a surface mesh generator is employed to generate a surface mesh for the mid-surface of the thin-walled structure. The surface mesh generator used will control the element size properties of the final mesh along the surface direction. In the second phase, specially designed algorithms are used to convert the surface mesh to a 3D solid mesh by extrusion in the surface normal direction of the surface. The extrusion procedure will control the refinement levels of the final mesh along the surface normal direction. If the input surface mesh is a pure quadrilateral mesh and refinement level in the surface normal direction is uniform along the whole surface, all hex-meshes will be produced. Otherwise, the final 3D meshes generated will eventually consist of four types of solid elements, namely, tetrahedron, prism, pyramid and hexahedron. The presented algorithm is highly flexible in the sense that, in the first phase, any existing surface mesh generator can be employed while in the second phase, the extrusion procedure can accept either a triangular or a quadrilateral or even a mixed mesh as input and there is virtually no constraint on the grading of the input mesh. In addition, the extrusion procedure development is able to handle structural joints formed by the intersections of different surfaces. Numerical experiments indicate that the present algorithm is applicable to most practical situations and well-shaped elements are generated.

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2D and 3D finite element meshing and remeshing

Cited by 12 publications

References 829 publications

An automatic adaptive refinement procedure for the reproducing kernel particle method. Part II: Adaptive refinement

An automatic adaptive refinement procedure for the reproducing kernel particle method. Part II: Adaptive refinement

Object-oriented programming in FEM and BEM: a bibliography (1990–2003)

A new automatic adaptive 3D solid mesh generation scheme for thin-walled structures

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