SMS:Renumber

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to realize that after renumbering the finite element mesh, any previous boundary condition file or solution file is no longer valid!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.

Renumbering Nodes and Elements

Meshes with gaps in numbering or with random numbering can lead to errors or inefficient solutions with many finite element solvers. The nodes and the elements can be renumbered simultaneously in an efficient manner by selecting the Renumber item from the Nodestrings menu. A node string must be selected before renumbering the mesh.

The selected node string is used to specify where the renumbering process begins. The "row" of elements and nodes adjacent to the string is numbered first. The elements and nodes adjacent to the first set of nodes and elements are numbered next, and so on until all of the nodes and elements have been renumbered.

The nodes and elements are renumbered in a sequence that can be envisioned as a "moving front" that passes through the mesh. Since the front proceeds from one set of elements to an adjacent set of elements, disjoint portions of the mesh will not be visited in the renumbering process. Unvisited nodes and elements are numbered arbitrarily.

Related Topics

• Nodestrings Menu