A scheme for the automatic generation of triangular finite elements

Abstract

SUMMARYThis paper describes a method for the automatic triangulation of arbitrary multilateral plane domains. In addition, the method can be used in connection with that suggested by Zienkiewicz and Phillips' for the subdivision of curved-boundary domains. The method can be described as general fully automatic and computer oriented. A Fortran computer program has been prepared by the author. Output can be of interactive, graphical or alphanumerical form. The program has been applied to a number of cases. The resulting triangulations are always satisfactory, even when vigorous changes of mesh sizes are encountered.

A knowledge‐based A‐priori approach to mesh generation in thermal problems

“…The case of a primitive with one prescribed temperature and one convection boundary condition is considered later. The approximate heat flow rate in each primitive and for conduction and convection problems is calculated according to Qh = h,A,(T, -G) (10) When the analytical solution for a primitive does not exist, the primitive is divided into several sub-primitives for which analytical solutions can be found. In this example, the primitive is The resulting heat flux approximation at the critical point D is q + qd, as shown in Figures 13(b) and 13(c).…”

Unstructured Mesh Generation

“…The simple but crucial next insight-arguably, the "true" advancing front technique-was to interleave vertex creation with element creation, so the front can guide the placement of vertices. Alan George [51] took this step in 1971, but it was forgotten and reinvented in 1980 by Sadek [96] and again in 1987 by Peraire, Vahdati, Morgan, and Zienkiewicz [90], who also introduced support for anisotropic triangles. Immediately thereafter, methods of this design appeared for tetrahedral meshing [75,88].…”

“…Courtesy of David Marcum. who specializes in meshes for aerodynamics, prefers to lay down a whole row of elements before starting another, so that the elements near the boundary are as structured as possible. Sadek [96] prioritizes elements within a row by noting corners in the front where the angle is not close to 180…”

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

“…We can also classify existing FE mesh generators depending on their underlying algorithmic approaches: 9 topology decomposition [21][22][23][24][25][26]; 9 spatial decomposition [27][28][29]; and 9 recursive subdivision of a region to element level [30,311 Mesh generation schemes based on the geometry interrogation approach include mapping mesh generation and spatial decomposition. Meshing schemes using the geometry interrogation and modification approach include the techniques of topology decomposition, recursive subdivision, and some forms of point insertion followed by area/volume triangulation.…”