TET_MESH_RCM
Reverse Cuthill-McKee Node Reordering

TET_MESH_RCM is a FORTRAN90 program which computes the reverse Cuthill-McKee 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

• prefix_nodes.txt, the node coordinates;
• prefix_elements.txt, the element definitions.
• prefix_rcm_nodes.txt, the reordered node coordinates;
• prefix_rcm_elements.txt, the reordered element definitions.

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:

CVT_TET_MESH, is a FORTRAN90 program which uses CVT techniques to compute a tet mesh in a region.

MESH_BANDWIDTH, is a FORTRAN90 program 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 FORTRAN90 program which computes the reverse Cuthill-McKee (RCM) reordering for nodes in a mesh of 4-node quadrilaterals.

RCM, a FORTRAN90 library which carries out reverse Cuthill-McKee computations.

TABLE_TET_MESH, a FORTRAN90 program which computes the tet mesh for a given set of points.

TEST_TET_MESH, a FORTRAN90 library which defines regions for which a tet mesh is desired.

TET_MESH, a FORTRAN90 library which works with tet meshes.

TET_MESH_DISPLAY, a MATLAB program which reads in the node and tetra files defining a tet mesh and displays a wireframe image.

TET_MESH_DISPLAY_OPENGL, a C++ program which reads a tet mesh and displays the nodes and edges using OpenGL.

TET_MESH_L2Q, a FORTRAN90 program which converts a linear (4-node) to quadratic (10-node) tetrahedral 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 FORTRAN90 program which converts a quadratic (10-node) to linear (4-node) tetrahedral mesh.

TET_MESH_QUALITY, a FORTRAN90 program which computes the quality of a tetrahedral mesh.

TET_MESH_REFINE, a FORTRAN90 program which can refine a tet mesh.

TET_MESH_TET_NEIGHBORS, a FORTRAN90 program which computes the tetrahedral adjacency information.

TET_MESH_VOLUMES, a FORTRAN90 program which computes the volume of each tetrahedron in a tet mesh;

TRIANGULATION_RCM, a FORTRAN90 program 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:

• tet_mesh_rcm.f90, the source code.

Examples and Tests:

CUBE4 is an order 4 tet mesh of a cube:

• cube4_output.txt, the printed output from the command
  "tet_mesh_rcm cube4_nodes.txt cube4_tetras.txt"
• cube4_nodes.txt, the node file.
• cube4_elements.txt, the element file.
• cube4_rcm_nodes.txt, the RCM reordered node file.
• cube4_rcm_elements.txt, the RCM reordered element file.

P03_00224.

• p03_00224_output.txt, the printed output from the command
  "tet_mesh_rcm p03_00224_nodes.txt p03_00224_tetras.txt"
• p03_00224_nodes.txt, the node file.
• p03_00224_elements.txt, the element file.
• p03_00224_rcm_nodes.txt, the RCM reordered node file.
• p03_00224_rcm_elements.txt, the RCM reordered element file.

List of Routines:

• MAIN is the main program for TET_MESH_RCM.
• ADJ_BANDWIDTH computes the bandwidth of an adjacency matrix.
• ADJ_PERM_BANDWIDTH computes the bandwidth of a permuted adjacency matrix.
• ADJ_PRINT prints adjacency information.
• ADJ_PRINT_SOME prints some adjacency information.
• CH_CAP capitalizes a single character.
• CH_EQI is a case insensitive comparison of two characters for equality.
• CH_TO_DIGIT returns the integer value of a base 10 digit.
• DEGREE computes the degrees of the nodes in the connected component.
• FILE_COLUMN_COUNT counts the number of columns in the first line of a file.
• FILE_ROW_COUNT counts the number of row records in a file.
• GENRCM finds the reverse Cuthill-Mckee ordering for a general graph.
• GET_UNIT returns a free FORTRAN unit number.
• I4_SWAP swaps two integer values.
• I4COL_COMPARE compares columns I and J of an I4COL.
• I4COL_SORT_A ascending sorts an I4COL.
• I4COL_SORT2_A ascending sorts the elements of each column of an I4COL.
• I4COL_SORTED_UNIQUE_COUNT counts unique elements in an I4COL.
• I4COL_SWAP swaps columns J1 and J2 of an I4COL.
• I4MAT_DATA_READ reads data from an I4MAT file.
• I4MAT_HEADER_READ reads the header from an I4MAT.
• I4MAT_TRANSPOSE_PRINT_SOME prints some of the transpose of an I4MAT.
• I4MAT_WRITE writes an I4MAT file.
• I4ROW_COMPARE compares two rows of an I4ROW.
• I4ROW_SORT_A ascending sorts the rows of an I4ROW.
• I4ROW_SWAP swaps two rows of an I4ROW.
• I4VEC_PRINT prints an I4VEC.
• I4VEC_REVERSE reverses the elements of an I4VEC.
• LEVEL_SET generates the connected level structure rooted at a given node.
• MESH_BASE_ONE ensures that the element definition is one-based.
• PERM_CHECK checks that a vector represents a permutation.
• PERM_INVERSE3 produces the inverse of a given permutation.
• R8COL_PERMUTE permutes an R8COL in place.
• R8MAT_DATA_READ reads data from an R8MAT file.
• R8MAT_HEADER_READ reads the header from an R8MAT file.
• R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT, transposed.
• R8MAT_WRITE writes an R8MAT file.
• RCM renumbers a connected component by the reverse Cuthill McKee algorithm.
• ROOT_FIND finds a pseudo-peripheral node.
• S_TO_I4 reads an I4 from a string.
• S_TO_I4VEC reads an I4VEC from a string.
• S_TO_R8 reads an R8 from a string.
• S_TO_R8VEC reads an R8VEC from a string.
• S_WORD_COUNT counts the number of "words" in a string.
• SORT_HEAP_EXTERNAL externally sorts a list of items into ascending order.
• TET_MESH_ORDER4_ADJ_COUNT counts the number of nodal adjacencies.
• TET_MESH_ORDER4_ADJ_SET sets the nodal adjacency matrix.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN90 source codes.