tet_mesh_rcm


tet_mesh_rcm, a MATLAB code which computes the reverse Cuthill-McKee (RCM) reordering for nodes in a tetrahedral mesh ("tet mesh").

The user supplies a node file and a tetrahedron file, containing the coordinates of the nodes, and the indices of the nodes that make up each tetrahedron. Either 4-node or 10-node tetrahedrons may be used.

The program reads the data, computes the adjacency information, carries out the RCM algorithm to get the permutation, applies the permutation to the nodes and tetrahedrons, and writes out new node and tetrahedron files that correspond to the RCM permutation.

Note that the node file would normally contain exactly 3 values on each line, namely the X, Y and Z coordinates of the nodes. However, this is not necessary. Extra information can be included on each line, for instance, a "W" coordinate. Each line should include the same number of items, but all will be permuted correctly together. The program does not actually need to know the coordinates of the nodes, so in fact, ANY data (as long as it is real numeric data) associated with the nodes can be listed in the node file, and will be correctly permuted.

Usage:

tet_mesh_rcm 'prefix'
where 'prefix' is the common file prefix:

Licensing:

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

Languages:

tet_mesh_rcm is available in a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

mesh_bandwidth, a MATLAB code which returns the geometric bandwidth associated with a mesh of elements of any order and in a space of arbitrary dimension.

quad_mesh_rcm, a MATLAB code which computes the reverse cuthill-mckee (rcm) reordering for nodes in a mesh of 4-node quadrilaterals.

rcm, a MATLAB code which carries out reverse cuthill-mckee computations.

tet_mesh, a MATLAB code which works with tet meshes.

tet_mesh_boundary, a MATLAB code which returns the nodes and faces of the boundary of a tetrahedral mesh, which themselves form a 3d triangular mesh or "tri_surface".

tet_mesh_display, a MATLAB code which can read in the node and tetra files defining a tet mesh and display a wireframe image.

tet_mesh_l2q, a MATLAB code which converts a linear to quadratic tet mesh.

tet_mesh_order4, a directory which contains a description and examples of a tet mesh using order 4 elements.

tet_mesh_order10, a directory which contains a description and examples of a tet mesh using order 10 elements.

tet_mesh_q2l, a MATLAB code which converts a quadratic (10-node) to linear (4-node) tetrahedral mesh.

tet_mesh_quality, a MATLAB code which computes the quality of a tetrahedral mesh.

tet_mesh_refine, a MATLAB code which can refine a tet mesh.

tet_mesh_rcm_test

tet_mesh_tet_neighbors, a MATLAB code which computes the tetrahedron-to-tetrahedron adjacency information.

tet_mesh_volumes, a MATLAB code which computes the volume of each tetrahedron in a tet mesh;

triangulation_rcm, a MATLAB code which applies the reverse cuthill-mckee reordering to a triangulation of 2d data.

Reference:

  1. HL Crane, Norman Gibbs, William Poole, Paul Stockmeyer,
    Algorithm 508: Matrix Bandwidth and Profile Reduction,
    ACM Transactions on Mathematical Software,
    Volume 2, Number 4, December 1976, pages 375-377.
  2. Herbert Edelsbrunner,
    Geometry and Topology for Mesh Generation,
    Cambridge, 2001,
    ISBN: 0-521-79309-2,
    LC: QA377.E36.
  3. Alan George, Joseph Liu,
    Computer Solution of Large Sparse Positive Definite Matrices,
    Prentice Hall, 1981,
    ISBN: 0131652745,
    LC: QA188.G46
  4. Norman Gibbs,
    Algorithm 509: A Hybrid Profile Reduction Algorithm,
    ACM Transactions on Mathematical Software,
    Volume 2, Number 4, December 1976, pages 378-387.
  5. 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, Number 2, April 1976, pages 236-250.
  6. Barry Joe,
    GEOMPACK - a software package for the generation of meshes using geometric algorithms,
    Advances in Engineering Software,
    Volume 13, 1991, pages 325-331.
  7. Per-Olof Persson, Gilbert Strang,
    A Simple Mesh Generator in MATLAB,
    SIAM Review,
    Volume 46, Number 2, June 2004, pages 329-345.

Source Code:


Last revised on 02 April 2019.