Pillowing doublets: refining a mesh to ensure that faces share at most one edge

Occasionally one may be confronted by a hexahedral or quadrilateral mesh containing doublets, two faces sharing two edges. In this case, no amount of smoothing will produce a mesh with agreeable element quality: In the planar case, one of these two faces will always have an angle of at least 180 degrees between the two edges. We describe a robust scheme for refining a hexahedral or quadrilateral mesh to separate such faces, so that any two faces share at most one edge. Note that this also ensures that two hexahedra share at most one face in the three dimensional case. We have implemented this algorithm and incorporated it into the CUBIT mesh generation environment developed at Sandia National Laboratories.