SMS:Renumber: Difference between revisions

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Renumbering a mesh improves the computational efficiency (how fast a model produces a result) of a numeric mesh but should not affect the end results.
Renumbering a mesh improves the computational efficiency (how fast a model produces a result) of a numeric mesh but should not affect the end results.  


To renumber a mesh:
To renumber a mesh select the renumber command in the nodes menu.
# Select a boundary nodestring to start the renumbering process.
# Select Nodestring | Renumber from the SMS menu.


Upon execution of this command, the nodes and elements are renumbered by a wave that passes through the mesh. This wave proceeds from elements connected to the selected nodestring and continues through the entire mesh. If a section of elements or nodes are disjoint, the wave will not continue and a warning message is given. Disjoint mesh sections are assigned arbitrary numbers, but before running the analysis, there should be no disjoint sections. Nodes which are not connected to any elements can be found and selected automatically.
Upon execution of this command, the nodes and elements are renumbered using a global renumbering process known as the Cuthill-McKee or Inverse Cuthill-McKee scheme. Other global resequencing methods may be added in future versions. The Cuthill-McKee method searches for a global optimum, but since are often multiple options with the same efficiency level (bandwidth), invoking the command multiple times usually results in different numbering patterns.  Each time a mesh is generated, SMS invokes a renumbering command. When nodes are manually added/removed from a mesh, it should be renumbered.


It is important to realize that after renumbering the finite element mesh, any previous boundary condition file or solution file is no longer valid!
It is important to realize that after renumbering the finite element mesh, any previous boundary condition file or solution file is no longer valid! They must be resaved with the new indices.


== Front Width and Band Width ==
==Front Width and Band Width==  
There are two measures of efficiency of a matrix.  These include front width and band width.  Both can be computed in multiple ways from the grid.  The Cuthill-McKee scheme has its own method of computing band width and reports the band width before and after renumbering.  In addition,  SMS provides an estimate as to how large the front width and half band width may become when running the finite element solver. These estimates are shown in the Mesh Information dialog, which can be opened by performing the "File | Get Info" command while in the Mesh Module.


SMS contains two similar algorithms for renumbering a mesh from a boundary nodestring. These algorithms are called the front width option and the band width option. The option to use can be specified in the [[SMS:Nodestring Options|Nodestring Options dialog]].
Due to the number of questions that are asked regarding this subject, this section will attempt to describe, in a broad sense, why renumbering is important.  


Due to the number of questions that are asked regarding this subject, this section will attempt to describe, in a broad sense, why renumbering is important.
The finite element solvers use an iterative, banded numerical solver to solve the governing differential equations. If the computer had to simultaneously solve the thousands of equations, it would run out of memory. This is why it uses a banded solver. The front width and the half-band width determine the size of the matrix which is used by the finite element solvers. A smaller front width and band width lead to a smaller required matrix. The front width and band width depend on the node and element numbering of the finite element mesh. To minimize the front width and band width, the mesh should be renumbered.  
 
The finite element solvers use an iterative, banded numerical solver to solve the governing differential equations. If the computer had to simultaneously solve the thousands of equations, it would run out of memory. This is why it uses a banded solver. The front width and the half-band width determine the size of the matrix which is used by the finite element solvers. A smaller front width and band width lead to a smaller required matrix. The front width and band width depend on the node and element numbering of the finite element mesh. To minimize the front width and band width, the mesh should be renumbered.
 
SMS provides an estimate as to how large the front width and half band width may become when running the finite element solver. These estimates are shown in the Mesh Information dialog, which can be opened by performing the "File | Get Info" command while in the Mesh Module. There is not a single renumbering scheme which always produces the lowest values for these, so it is suggested that you renumber from various locations in the mesh and check the mesh information before deciding which renumbering scheme to use. As a guideline, the mesh should be renumbered using a nodestring which extends across a small section of the mesh, such as a river inflow boundary.


== Related Topics ==
== Related Topics ==

Revision as of 21:23, 30 October 2012

Renumbering a mesh improves the computational efficiency (how fast a model produces a result) of a numeric mesh but should not affect the end results.

To renumber a mesh select the renumber command in the nodes menu.

Upon execution of this command, the nodes and elements are renumbered using a global renumbering process known as the Cuthill-McKee or Inverse Cuthill-McKee scheme. Other global resequencing methods may be added in future versions. The Cuthill-McKee method searches for a global optimum, but since are often multiple options with the same efficiency level (bandwidth), invoking the command multiple times usually results in different numbering patterns. Each time a mesh is generated, SMS invokes a renumbering command. When nodes are manually added/removed from a mesh, it should be renumbered.

It is important to realize that after renumbering the finite element mesh, any previous boundary condition file or solution file is no longer valid! They must be resaved with the new indices.

Front Width and Band Width

There are two measures of efficiency of a matrix. These include front width and band width. Both can be computed in multiple ways from the grid. The Cuthill-McKee scheme has its own method of computing band width and reports the band width before and after renumbering. In addition, SMS provides an estimate as to how large the front width and half band width may become when running the finite element solver. These estimates are shown in the Mesh Information dialog, which can be opened by performing the "File | Get Info" command while in the Mesh Module.

Due to the number of questions that are asked regarding this subject, this section will attempt to describe, in a broad sense, why renumbering is important.

The finite element solvers use an iterative, banded numerical solver to solve the governing differential equations. If the computer had to simultaneously solve the thousands of equations, it would run out of memory. This is why it uses a banded solver. The front width and the half-band width determine the size of the matrix which is used by the finite element solvers. A smaller front width and band width lead to a smaller required matrix. The front width and band width depend on the node and element numbering of the finite element mesh. To minimize the front width and band width, the mesh should be renumbered.

Related Topics


SMS

Modules: Mesh Module · Cartesian Grid Module · Scatter Module · Map Module · GIS Module · Particle Module
Models: ADCIRC · BOUSS-2D · CGWAVE · CMS-Flow · CMS-Wave · FESWMS · FVCOM · Generic Mesh Model · GENESIS · HYDRO AS-2D · PTM · SRH-2D · Steering · STWAVE · TABS · TUFLOW

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