Reducing the bandwidth of sparse symmetric matrices

A direct method of obtaining an automatic nodal numbering scheme to ensure that the corresponding coefficient matrix will have a narrow bandwidth is presented.

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.