RCM Numberer

This command is used to construct a reverse Cuthill-McKee (RCM) degree-of-freedom numbering algorithm to provide the mapping between the degrees-of-freedom at the nodes and the equation numbers. An RCM numberer uses the reverse Cuthill-McKee scheme to order the matrix equations.

The command to construct an RCM numberer is a follows:

numberer RCM

C++ Implementation

#include <graph/numberer/RCM.h>

class RCM: public GraphNumberer;

RCM is a subclass of GraphNumberer which performs the numbering using the reverse Cuthill-McKee numbering algorithm.

Constructor

The integer classTag is passed to the MovableObject classes constructor. The flag GPS is used to mark whether the Gibbs-Poole-Stodlmyer algorithm is used to determine a starting vertex when no starting vertex is given.


Invokes the destructor on any ID object created when number() is invoked.

Public Methods

If the present ID used for the result is not of size equal to the number of Vertices in theGraph, it deletes the old and constructs a new ID. Starts by iterating through the Vertices of the graph setting the tmp variable of each to \(-1\). The Vertices are then numbered using a depth first sort of the Graph, with each unmarked Vertex in the Graph at a distance \(d\) from starting Vertex being placed in the d’th level set. As this is RCM, the Vertices in level set \(n\) are assigned a higher number than those in level set \(n+1\) with the tmp variable of the starting Vertex being assigned numVertices \(-1\). The tags of the Vertices are placed into the ID at location given by their tmp variable. These are replaced with the ref variable of each Vertex, which is returned on successful completion.

The Vertex chosen as the starting Vertex is the one whose tag is given by lastVertex. If this is \(-1\) or the Vertex corresponding to lastVertex does not exist then another Vertex is chosen. If the GPS flag in constructor is false the first Vertex from the Graphs VertexIter is used; if true a RCM numbering using the first Vertex from the VertexIter is performed and the Vertices in the last level set are then used to create an ID lastVertices with which number(theGraph, lastVertices) can be invoked to determine the numbering.

This method is invoked to determine the best starting Vertex for a RCM using a Vertex whose tag is in lastVertices. To do a RCM numbering is performed using each of the Vertices in startVertices as the Vertex in level set \(0\). The Vertex which results in the numbering with the smallest profile is chosen as the starting Vertex. The RCM algorithm outlined above is then called with this starting Vertex.

int sendSelf(Channel &theChannel, FEM_ObjectBroker &theBroker);

Returns \(0\).

int recvSelf(Channel &theChannel, FEM_ObjectBroker &theBroker);

Returns \(0\).

References

Code Developed by: fmk