A new mesh generation scheme for arbitrary planar domains

TLDR

The paper introduces an algorithm that generates interior nodes for any arbitrary multi‑connected planar region. It links boundary and interior nodes to create optimal triangular elements, permitting arbitrary subdivision into irregular subdomains, progressive refinement around sharp corners, radiating meshes from prescribed nodes, and mesh between circular arcs, all while requiring only minimal input data and no inter‑subregion connectivity. The resulting method produces versatile 3‑node or 6‑node triangular meshes for highly irregular heterogeneous regions.

Abstract

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.