Domain decomposition for hexahedral mesh generation using singularity lines

It has been observed that, some critical lines of the decomposition where other than four blocks join (called singularity lines) are of high importance. This has motivated many researchers to develop methods that first identify these lines and then, based on them, generate the decomposition of the domain. However, even for simple models these methods often fail to identify all the necessary singularity lines and, as a result, a block decomposition cannot be created.

In this thesis, a novel approach of generating singularity lines and using them to generate block decompositions of 3퐷 domains is presented. As opposed to existing algorithms that rely on a tetrahedral mesh that discretizes the domain, here the medial object (or medial axis) of the domain is used. The key contributions of the work can be summarised into the following three.<br><br>1) A method that utilises the structure of the medial object and the directional information of its touching vectors to generate a novel direction field that consists of frames on medial vertices and medial edges and cross-fields on medial surfaces is presented.<br><br>2) A method that utilises this direction field to construct singularity lines on the interior of the domain (as far as possible from the boundary) and a set of streamlines emanating from them (that represent partition surfaces) is presented.<br><br>3) A method that utilises the proximity information that is encapsulated by the medial object to extend singularity lines, streamlines and concave features of the domain into a set of partition surfaces that divide the domain into block regions is presented.<br><br>Furthermore, the proximity information that is encapsulated by the medial object provides additional information that proves useful to understand the reason the singularity lines appear on the interior of the domain.

Based on that, limitations are presented and suggestions are proposed on possible paths of research to tackle them. By making the connection between the medial object of the domain and singularity lines, a new step is performed in the way to generating a method that can automatically create a hexahedral mesh for an arbitrary model. At the current stage, the method is presented for models of simple or moderate complexity that are useful to experiment and provide a framework to investigate and extend the capabilities of the method.

In order for the method to be able to analyse industrial models of high complexity further development and research is required.