MESH_BANDWIDTH
Geometric Bandwidth of a Mesh

MESH_BANDWIDTH is a MATLAB program which computes the geometric bandwidth of a mesh.

The user specifies an element file, containing the indices of the nodes that make up each element. Examples of such a file include the order 3 and order 6 triangulation files, but any order of element may be used.

Not only may any element type be used, but the geometric region may be of any spatial dimension.

The program reads the element information and computes the geometric bandwidth M as

M = ML + 1 + MU
where ML is the lower bandwidth, namely, the maximum value over all nodes I of the difference (I-J), taken over all nodes J that share an element with node I. The upper bandwidth is the maximum value of (J-I) under the same conditions.

The geometric bandwidth M is the linear algebraic bandwidth of the adjacency matrix of the mesh, where I and J are considered to be adjacent if there is some element that includes both nodes.

The geometric bandwidth is of interest since it is the bandwidth of the finite element matrix associated with the mesh, when a scalar quantity is being approximated and there is a single unknown for every node, and the unknowns have the same numbering as the nodes.

Usage:

mesh_bandwidth ( 'element_file' )
where The program reads the element file and prints out the geometric mesh bandwidth.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

MESH_BANDWIDTH is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

TRIANGLE, a C program which computes a triangulation of a geometric region.

TRIANGULATION_DISPLAY_OPENGL, a C++ program which reads files defining a triangulation and displays an image using Open GL.

TRIANGULATION_ORDER3, a directory which contains a description and examples of order 3 triangulations.

TRIANGULATION_ORDER6, a directory which contains a description and examples of order 6 triangulations.

TRIANGULATION_PLOT, a MATLAB program which reads data defining a triangulation and creates a PostScript image of the nodes and triangles.

Reference:

  1. Alan George, Joseph Liu,
    Computer Solution of Large Sparse Positive Definite Matrices,
    Prentice Hall, 1981,
    QA 188.G46
  2. Norman Gibbs, William Poole, Paul Stockmeyer,
    An Algorithm for Reducing the Bandwidth and Profile of a Sparse Matrix,
    SIAM Journal on Numerical Analysis,
    Volume 13, pages 236-250, 1976.
  3. Norman Gibbs,
    Algorithm 509: A Hybrid Profile Reduction Algorithm,
    ACM Transactions on Mathematical Software,
    Volume 2, Issue 4, pages 378-387, 1976.
  4. Joseph ORourke,
    Computational Geometry,
    Cambridge University Press,
    Second Edition, 1998.

Source Code:

Examples and Tests:

Some sample mesh files include:

You can go up one level to the MATLAB source codes.

Last revised on 06 August 2009.