Finite element mesh generation via switching function representation

Abstract

K-dimensional trees (quadtress, octress, etc.) are useful data structures and provide efficient techniques for adaptively generating and refining a required mesh. A drawback of these techniques is that they necessitate the subdivision of an element into 2 K congruent subelements every time a subdivision is required, even if, as hapenns in many cases, the required subdivision is only in one direction. In this article, an alternative data structure, based upon switching function representation, which overcomes this problem proposed. The proposed data structure shares many similar properties with quadtrees and octrees, but has the advantage of being capable of subdividing an element into 2 J ( J < K) subelements. As a result, only subelements which are really desired are virtually generated. A comparison of the proposed approach with the one based on the quadtree encoding is made to demonstrate the computational efficiency of the approach.