A C# Algorithm for Creating Triangular Meshes of Highly-Irregular 2D Domains Using the Advancing Front Technique

Abstract

This paper describes a C# algorithm for creating efficient triangular meshes of highly-irregular 2D domains. The algorithm, which is based on the advancing front technique, requires boundary nodes as the only input. Basic shapes such as lines, curves, rectangles, polygons, circles, and/or ellipses are used to construct the domain. Shapes are interactively added to the domain in a sequential order. Whenever a shape is added, however, it is directly exploded to a set of nodes appended to the end of the domain. Nodes must be continuous and must not cross one another. Inside openings of the domain are implemented via connector lines; which have a two-way trip; one from the boundary to the starting point of the opening and the other from the ending point of the opening back to the boundary. Nodes are interactively moved or deleted; which allows a variable node density to be created easily and which optimizes the final shape of the domain. The algorithm produces well-conditioned (close-to- equilateral) triangular elements. An additional smoothing procedure, however, is performed by shifting each interior node to the center of the surrounding polygon. Numbering of nodes has a definite influence on the band width of the coefficient matrix associated with the mesh. The smaller the band width, the less storage and amount of computation required. The Cuthill-McKee algorithm for renumbering mesh nodes is applied. The implementation of the algorithm using the C# object-oriented language allows flexibility in programming and increases the efficiency in the construction of complex highly- irregular two-dimensional domains. Examples of created domains along with their generated meshes in both simply and multiply connected domains are presented.