The numerical algorithms became quite complex and require dynamic data structures. As such, an advanced front (AF) algorithm which is a well-known and efficient algorithm of the non-structural mesh generation is given. An accelerated version of this algorithm is presented as an example to demonstrate, that a simplified relational database model is an efficient tool for handling dynamic data structures arising from numerical problems. The main advantage of this technique is the simple and uniform data structure and the application of the balanced trees for searching and modification.