Difference between revisions of "Resequence Command"
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where | where | ||
* (<tt>x</tt>, <tt>y</tt>) define the coordinates (in | * (<tt>x</tt>, <tt>y</tt>) define the coordinates (in [[ConsistentUnits Command#Legacy and Consistent Units|length units]]) for a point (or <tt>(R,Z)</tt> coordinates if axisymmetric). The resequencing will start at the one node nearest to that point. | ||
* <tt>(id)</tt> is a previously defined [[Keypoint Command|keypoint]]. The resequencing will start at the node at that keypoint. | * <tt>(id)</tt> is a previously defined [[Keypoint Command|keypoint]]. The resequencing will start at the node at that keypoint. | ||
== XML Input Files == | == XML Input Files == | ||
In <tt>XML<tt> files, the two options | In <tt>XML</tt> files, the two options are: | ||
<Resequence x='(x)' y='(y)'/> | <Resequence x='(x)' y='(y)'/> | ||
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<Resequence keypt='(id)'/> | <Resequence keypt='(id)'/> | ||
where <tt>(x)</tt>, <tt>( | where <tt>(x)</tt>, <tt>(y)</tt>, and <tt>(id)</tt> are the same as defined [[#Scripted Input Files|above]]. Whichever method is used, it must be the ''last'' command in the single [[FEA Boundary Conditions#XML Input Files|<tt><GridBCs></tt> block]] in the file. | ||
== Notes == | == Notes == | ||
The resequencing is done using the "GPS Algorithm, named after Gibbs, Poole, and Stockmeyer (1976).<ref name='RS'>N. E. Gibbs, W. G. Poole, and P. K. Stockmeyer, "An Algorithm for Reducing the Bandwidth and Profile of a Sparse Matrix," <i>SIAM Journal of Numerical Analysis</i>, <b>13</b>, 236-250 (1976).</ref> Another bandwidth minimization method is the RCM method or the Reverse Cuthill-McKee method.<ref name="RCM">E. Cuthill and J. McKee. "Reducing the bandwidth of sparse symmetric matrices," In Proc. 24th Nat. Conf. ACM, 157–172 (1969).</ref> No method gets the absolute minimum. In testing, GPS and RCM get similar results but GPS is faster. | |||
# It is best to start the resequencing at a node on the boundary of the object and probably on a corner. The final bandwidth may depend on the node selected for resequencing. The bandwidth is reported in FEA output results. You can vary the resequencing node to find the minimum value. | # It is best to start the resequencing at a node on the boundary of the object and probably on a corner. The final bandwidth may depend on the node selected for resequencing. The bandwidth is reported in FEA output results. You can vary the resequencing node to find the minimum value. | ||
# Another use of this command is to verify mesh connectivity. Since disconnected sections of a static FEA mesh will cause a singular stiffness matrix, the calculations will fail. | # Another use of this command is to verify mesh connectivity. Since disconnected sections of a static FEA mesh will cause a singular stiffness matrix, the calculations will fail. If you use a <tt>Resequence</tt> command on a disconnected mesh, it will detect the problem and abort the calculations. | ||
== References == | == References == | ||
<references/> | <references/> | ||
Latest revision as of 12:55, 4 February 2022
The Resequence command is used to renumber the numbers in an attempt to minimize the bandwidth of the problem. The smaller the bandwidth, the faster will be the FEA calculations.
Scripted Input Files
The two options in scripted input files are
Resequence (x),(y)
or
Resequence (id)
where
- (x, y) define the coordinates (in length units) for a point (or (R,Z) coordinates if axisymmetric). The resequencing will start at the one node nearest to that point.
- (id) is a previously defined keypoint. The resequencing will start at the node at that keypoint.
XML Input Files
In XML files, the two options are:
<Resequence x='(x)' y='(y)'/>
or
<Resequence keypt='(id)'/>
where (x), (y), and (id) are the same as defined above. Whichever method is used, it must be the last command in the single <GridBCs> block in the file.
Notes
The resequencing is done using the "GPS Algorithm, named after Gibbs, Poole, and Stockmeyer (1976).[1] Another bandwidth minimization method is the RCM method or the Reverse Cuthill-McKee method.[2] No method gets the absolute minimum. In testing, GPS and RCM get similar results but GPS is faster.
- It is best to start the resequencing at a node on the boundary of the object and probably on a corner. The final bandwidth may depend on the node selected for resequencing. The bandwidth is reported in FEA output results. You can vary the resequencing node to find the minimum value.
- Another use of this command is to verify mesh connectivity. Since disconnected sections of a static FEA mesh will cause a singular stiffness matrix, the calculations will fail. If you use a Resequence command on a disconnected mesh, it will detect the problem and abort the calculations.
References
- ↑ N. E. Gibbs, W. G. Poole, and P. K. Stockmeyer, "An Algorithm for Reducing the Bandwidth and Profile of a Sparse Matrix," SIAM Journal of Numerical Analysis, 13, 236-250 (1976).
- ↑ E. Cuthill and J. McKee. "Reducing the bandwidth of sparse symmetric matrices," In Proc. 24th Nat. Conf. ACM, 157–172 (1969).