# NASA Technical Reports Server (NTRS) 19760009755: An interactive graphics package for the automatic node renumbering of finite element matrices

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NASA Technical Reports Server (NTRS) 19760009755: An interactive graphics package for the automatic node renumbering of finite element matrices**

An interactive graphics software package which allows users to display the non-zero structure of large sparse symmetric materials was described and methods used to implement it as a portable FORTRAN callable subroutine were summarized. In particular, the system permits the display of the resulting matrix after reordering the rows and columns, with

Autor: **NASA Technical Reports Server (NTRS)**

Fuente: https://archive.org/

## Introducción

AN INTERACTIVE GRAPHICS PACKAGE FOR THE
AUTOMATIC NODE RENUMBERING OF FINITE ELEMENT MATRICES*
Ronald F.

Boisvert and William G.

Poole, Jr.
College of William and Mary
and
Institute for Computer Applications in Science and Engineering (ICASE)
SUMMARY
An interactive graphics software package vhich allows users to display
the non-zero structure of large sparse symmetric matrices is described and
methods used to implement it as a portable FORTRAN callable subroutine are
summarized.

In particular, the system permits the display of the resulting
matrix after reordering the rows and columns, with the reordering scheme
either defined by the user or automatically generated by the program with the
aim of reducing matrix bandwidth and profile.

Although the primary application of the package has been to the finite element analysis of structures, it
is equally well suited to the many other areas of engineering and science
which use sparse matrices.
INTRODUCTION
Frequently, in many areas of application, we must solve the linear algebraic system of equations represented by
Ax = b
(1)
where A is a non-singular n x n symmetric matrix and x and b are nvectors.

Here we assume that n is moderately large (from about one hundred
to several thousand) and that the matrix A is sparse; that is, the number of
non-zero elements in the matrix is small compared to n^.
In order to describe the non-zero structure of sparse matrices the concepts of bandwidth and profile are helpful.

The bandwidth of a matrix A is
defined as b = max, |i-j|, which is simply the radius of the smallest band
a
iy
about the diagonal which includes all non-zero components of the matrix.

The
This paper is a result of work performed, in part, under NASA Grant NCR
U7-102-001 while in residence at ICASE, NASA Langley Research Center.

The
work of the second author also was partially supported by the Office of
Naval Research Contract N0001^-73-A-037U-0001, NR OUU-1*59.

The first
author is currently at the Computer Science ...