Conformal Refinement of All-Quadrilateral and All-Hexahedral Meshes According to an Anisotropic Metric

Conformal refinement using a shrink and connect strategy known as pillowing or buffer insertion contracts contiguous elements of an all-quadrilateral or an all-hexahedral mesh and reconnects them to locally increase vertex density. Using layers as shrink sets, the present method anisotropically refines an initial mesh to match a prescribed size map expressed as a metric field. An anisotropic smoother further enhances vertex clustering to capture the features of the metric. Both two and three-dimensional test cases confirm the feasibility of such an approach. The present refinement method is not yet complete, however, because it lacks local vertex removal and reconnection capabilities. It is, nevertheless, a step towards an automated tool for conformal adaptation of all-quadrilateral and all-hexahedral meshes.