An efficient automatic mesh generator for quadrilateral elements implemented using C++

Abstract

This paper presents an efficient mesh generation algorithm for creating unstructured quadrilateral meshes for finite element computations. The algorithm is developed by improving upon an existing recursive mesh generation scheme and implemented using the C++ object-oriented language. Exhaustive cases of misshaped elements for which a general remedy is not possible are identified through extensive numerical testing and treated case by case. These improvements make it possible to generate quadrilateral elements for any case without any need for final mesh resolution by human interference. The implementation of the algorithm using object-oriented methods allows flexibility in programming and increases the computational efficiency of mesh generation. The use of object data structures, such as line segments and elements, expedites the algorithm implementation. Numerical experience shows that not only is programming simplified when objects are used, but computational speed is also increased. When comparing two nodes for best splitting lines, line segments do not compare nodes on the same segment. This immediately eliminates all nodes on the segment the starting point of the potential splitting line is on. By automatically doing this, a great saving in computing time is achieved. Examples of automatic mesh generation in both simply and multiply connected domains are given and their computational efficiencies are also assessed.