A three-step renumbering procedure for high-order finite element analysis

An e¦cient renumbering method for high-order Þnite element models is presented. The method can be used to reduce the proÞle and wavefront of a coe¦cient matrix arising in high-order Þnite element computation. The method indirectly performs node renumbering and involves three main steps. In the Þrst step, nodes at corners of the elements are numbered using an existing renumbering algorithm. In the second step, elements are numbered in an ascending order of their least new corner node numbers. Finally, based on the new element numbers, both corner and non-corner nodes are renumbered using an algorithm that simulates the node elimination procedure in a frontal solution method. The method is compared to the algorithms that directly perform node renumbering. The numerical results indicate that the three-step algorithm presented here is an order of magnitude faster and the resulting renumbering produces excellent proÞle and wavefront characteristics of the coe¦cient matrix