Quadtree and Octree Implicit Boundary Methods

Core Team Members: Jack S. Hale, Team Legato, University of Luxembourg.

« Supported by the Fonds National de la Recherche, Luxembourg (#6693582) »

In this project we are developing methods that alleviate complex mesh generation procedures almost entirely. Mesh preparation and generation is a time consuming and expensive process, and by eliminating it we believe that practical clinical analysis using mathematical models will become more widespread.

By importing geometry either through a levelset function description, image data or surface geometry tesselations, we can construct a finite element simulation without directly constructing a mesh for the analysis. To do this we use a nested octree approach, where discretisation fields (where the solution of the PDE lives) and geometry fields (where the description of the domain of the PDE lives) are stored in interlinked octree hierarchies. Then, on octree cells of the discretisation where the geometric boundary of the domain intersects the discretisation cell, we perform a sub-tesselation of the interior and exterior and surface of the domain. This process is shown in 2D and 3D in the videos below.

More technical details can be found in the following presentation:

Parallel simulations of soft-tissue using an adaptive quadtree/octree implicit boundary finite element method, WCCM 2014 Barcelona.