Reducing the bandwidth of sparse symmetric matrices

TLDR

Finite‑element analysis requires solving large sparse symmetric systems, where the stiffness matrix structure reflects the element layout, a problem addressed by Rosen. The study aims to develop an automatic renumbering scheme that narrows the bandwidth of the stiffness matrix for efficient solution. A direct renumbering algorithm is proposed and compared with existing methods.

Abstract

The finite element displacement method of analyzing structures involves the solution of large systems of linear algebraic equations with sparse, structured, symmetric coefficient matrices. There is a direct correspondence between the structure of the coefficient matrix, called the stiffness matrix in this case, and the structure of the spatial network delineating the element layout. For the efficient solution of these systems of equations, it is desirable to have an automatic nodal numbering (or renumbering) scheme to ensure that the corresponding coefficient matrix will have a narrow bandwidth. This is the problem considered by R. Rosen1. A direct method of obtaining such a numbering scheme is presented. In addition several methods are reviewed and compared.