The finite difference method at arbitrary irregular grids and its application in applied mechanics

This paper describes a new algorithm to generate interior nodes within any arbitrary multi-connected regions. The boundary nodes and the interior nodes are then linked up to form the best possible triangular elements by a completely revised technique in an efficient and stable manner. Owing to the generality of the central generation program, the global domain is allowed to be divided into as many irregular subdomains as desired, in order to model closely the actual physical situation. Moreover, the boundaries of the sub-domains are updated from time to time when necessary to include the possibilities of progressive refinement around a sharp corner, generating radiating mesh from a prescribed node, generating mesh between two circular arcs, etc. Despite its flexibility and capabilities, data for triangulation have been kept to a minimum by a logical input module; no connectivity information between subregions is needed, and common boundaries are defined once only. All these features have contributed to a powerful method to generate 3-node or 6-node triangular element meshes of great variety within the most irregular heterogeneous regions.

A new mesh generation scheme for arbitrary planar domains

An attempt is made to provide a clear overall picture of the finite element mesh generation field. A scheme for classifying mesh generation methods is proposed, whereby seven major mesh generation approaches are identified. The basis for classification is the temporal order in which nodes and elements are created. The published mesh generation methods are reviewed. Only four approaches are found to have fully automatic mesh generation methods. These approaches are compared on the criteria of element types and shapes, mesh density control, and time efficiency.

Finite element mesh generation methods: a review and classification

By allowing the use of quadrants with cut corners, this modeling technique overcomes some of the drawbacks of standard quadtree encoding for finite element mesh generation.

A Modified Quadtree Approach To Finite Element Mesh Generation

We present an algorithm for the generation of coarse and fine finite element (FE) meshes on multiply connected surfaces, based on the medial axis transform (MAT). The MAT is employed to automatically decompose a complex shape into topologically simple subdomains, and to extract important shape characteristics and their length scales. Using this technique, we can create a coarse subdivision of a complex surface and select local element size to generate fine triangular meshes within those subregions in an automated manner. Therefore, this approach can lead to integration of fully automatic FE mesh generation functionality into FE preprocessing systems.

/pdf/an-automatic-coarse-and-fine-surface-mesh-generation-scheme-27c0z3i3m9.pdf

An automatic coarse and fine surface mesh generation scheme based on medial axis transform: Part i algorithms

Automatic generation of triangular grid: I—subdivision of a general polygon into convex subregions. II—triangulation of convex polygons

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Automatic generation of triangular grid: I—subdivision of a general polygon into convex subregions. II—triangulation of convex polygons