No abstract

A scheme is presented for the automatic generation of triangular meshes over general analytical curved surfaces with explicit control on the discretization error over the interior of the domain. The element size on the curved surface is estimated based on the given allowable discretization error and the surface curvature. The mesh generation starts with the subdivision of the curved boundary of the domain into straight line segments in compliance with the given discretization error constraint. Elements are generated directly over the surface in such a way that the discretization error is kept within the required geometrical tolerance. Those elements violating the given constraint are noted and post‐processed by either element subdivision or node repositioning. Various schemes as to how improvement should be made are proposed, which reduce the discretization error by different strategies depending on the position of the point where the maximum discretization error occurs.

An algorithm is proposed for the generation of 'hybrid' finite element meshes composed of quadrilateral and triangular elements over any arbitrary planar domain. Although more complicated hybrid meshes are to be generated, the new meshing strategy does not require more input data than a correct representation of the domain boundary. Mesh generation is started by constructing as many square elements as possible in the interior part of the domain, leaving a relatively small region around the boundary which is to be tliscretized into triangular elements by standard triangulation procedures. As a result, only the qualit-v of the triangular elements near the boundary will be affected by the irregularity of the domain. The extraction of the interior part and forming of square elements of an irregular domain will be discussed in detail. Examples of meshes generated over simply connected and multiconnected domains are given.