IMR PROCEEDINGS

23rd International Meshing Roundtable
London, UK
October 1215,2014
Department of Computer Science, FCFM, University of Chile, Blanco Encalada 2120, Santiago, Chile
Email: nancy@dcc.uchile.cl
Summary
A polyhedral mesh fulfills the Delaunay condition if the vertices of each polyhedron are cospherical and each polyhedron circumsphere
is pointfree. If Delaunay tessellations are used together with the finite volume method, it is not necessary to partition each
polyhedron into tetrahedra; cospherical elements can be used as final elements. This paper presents a mixedelement mesh generator
based on the modified octree approach that has been adapted to generate polyhedral Delaunay meshes. The main dierence
with its predecessor is to include a new algorithm to compute Delaunay tessellations for each 1irregular cuboids (cuboids with at
most one Steiner point on their edges) that minimize the number of mesh elements. In particular, we show that when Steiner points
are located at edge midpoints, 24 dierent cospherical elements can appear while tessellating 1irregular cubes. By inserting
internal faces and edges to these new elements, this number can be reduced to 13. When 1irregular cuboids with aspect ratio equal
to sqrt(2) are tessellated, 10 cospherical elements are required. If 1irregular cuboids have aspect ratio between 1 and
sqrt(2), all the tessellations are adequate for the finite volume method. The proposed algorithm can be applied to any point set to compute the
Delaunay tessellation inside the convex hull of the point set. Simple polyhedral Delaunay meshes generated by using the adapted
mesh generator are shown.
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