THE WHISKER WEAVING ALGORITHM: A CONNECTIVITY-BASED METHOD FOR CONSTRUCTING ALL-HEXAHEDRAL FINITE ELEMENT MESHES

Abstract

This paper introduces a new algorithm called whisker weaving for constructing unstructured, all-hexahedral finite element meshes. Whisker weaving is based on the Spatial Twist Continuum (STC), a global interpretation of the geometric dual of an all-hexahedral mesh. Whisker weaving begins with a closed, all-quadrilateral surface mesh bounding a solid geometry, then constructs hexahedral element connectivity advancing into the solid. The result of the whisker weaving algorithm is a complete representation of hex mesh connectivity only: Actual mesh node locations are determined afterwards. The basic step of whisker weaving is to form a hexahedral element by crossing or intersecting dual entities. This operation, combined with seaming or joining operations in dual space, is sufficient to mesh simple block problems. When meshing more complex geometries, certain other dual entities appear such as blind chords, merged sheets, and self-intersecting chords. Occasionally specific types of invalid connectivity arise. These are detected by a general method based on repeated STC edges. This leads into a strategy for resolving some cases of invalidities immediately. The whisker weaving implementation has so far been successful at generating meshes for simple block-type geometries and for some non-block geometries. Mesh sizes are currently limited to a few hundred elements. While the size and complexity of meshes generated by whisker weaving are currently limited, the algorithm shows promise for extension to much more general problems.