In this work, we propose using edge valence as a quality predictor when used as a driver for adapting all hexahedral meshes. Edge valence, for hexahedra, is defined as the number of faces attached to an edge. It has shown to be a more reliable quality predictor than node valence for hexahedral meshes. An edge valence of 3, 4, or 5 within the volume of a hexahedral mesh has provided at least a positive scaled Jacobian for all observed meshes, without the presence of over constraining geometry. It is often desirable to adapt an existing mesh through sheet operations such as column collapse, sheet insertion, or sheet extraction. Examples of hexahedral mesh adaptation include refining and coarsening. This work presents a general algorithm for a priori prediction of edge valence when used with column collapse and sheet extraction operations. Using the predicted edge valence we present a method for guiding the mesh adaptation procedure which will result in an overall higher quality mesh than when driven by mesh quality alone. Other quality metrics such as the Jacobian are unfit for predictive algorithms because of their heavy dependence on node positioning instead of hex topology. Results have been derived from application of the algorithm towards the localized coarsening process.



College and Department

Ira A. Fulton College of Engineering and Technology; Civil and Environmental Engineering



Date Submitted


Document Type





hexahedral, adaptation, valence