Journal of the Serbian Society for Computational Mechanics / Vol. 12 / No. 1, 2018 / pp 126-143 (DOI: 10.24874/jsscm.2018.12.01.09) An Improved Nodal Ordering for Reducing the Bandwidth in FEM A. Mohseni 1 , H. Moslemi 1* , M.R. Seddighian 1 1 Department of Civil Engineering, Shahed University, Tehran, Iran e-mail: h.moslemi@shahed.ac.ir * corresponding author Abstract In finite element method, reducing the bandwidth of sparse symmetric matrices plays a key role to have an efficient solution. This problem can be simulated as a vertex numbering problem on a graph, where each edge represents two connected nodes in finite element mesh. In this paper, a new algorithm is proposed for a nodal ordering of the standard and randomly structured graphs to reduce the bandwidth of sparse symmetric matrices. A fast search algorithm for the location of pseudo-peripheral nodes is presented. This algorithm results in a bandwidth smaller than or equal to some existing algorithms such as the Cuthill–Mckee (CM) and the modified Gibbs–Poole– Stockmeyer (MGPS). With this approach, the bandwidth is reduced in more than 50% of instances of benchmark tests compared with the outcomes of the existing algorithms. Keywords: Bandwidth reduction, finite element method, sparse symmetric matrix, pseudo- peripheral nodes. 1. Introduction Application of the finite element analysis (FEA) in many problems in structural engineering involves the solution of sparse systems of simultaneous equations with the form (1): Ax b  (1) where ‘A’ is a n×n sparse zeros patterned symmetric matrix, called stiffness matrix, ‘x’ is the unknown variable vector and ‘b’ is the right-hand side vector. ‘n’ denotes the number of degrees of freedom. To improve the accuracy of the solution in FEA many degrees of freedom are usually needed which leads to very high computational and memory cost in the analysis process. But if the nodes are reordered properly, the bandwidth of the sparse matrix will be reduced, and a great deal of the computational effort and memory will be conserved. For the stiffness sparse symmetric matrix A with entries aij, the ith bandwidth of A is defined as the difference between the first and last non-zero element of the ith row of the matrix. This parameter is correspondent to the maximum difference in the node numbers within element i. The bandwidth of matrix A is defined as the maximum bandwidth of all rows.   max | 0 i j a ij     (2)