Traditional Nodal Description

This format is based on the age-old way of doing things in Engineering Science and is basically and XML-isation of CMGUI's .exelem and .exnode file formats. The files currently necessary to describe a one-element cube can be found here: the .exelem file contains the mesh, element bases and map (implied) information, and the .exnode file contains the ensemble field parameters for the problem.

With the separation of mesh and field information in FieldML, the field description reduces to:

• Element Bases - definitions of the set of basis functions used for field interpolation within each element (see Specifying Element Bases.
• Node Vector - the ensemble field parameters in the traditional model description are the field values (and possibly derivatives) at the nodes.
• Node Indexing - a list containing the indices of the nodes in the global node vector that correspond to the local nodes for each element. Currently the order is implied, based on the local coordinates of the element.

Continuity is implied when two elements reference the same global node. The level of continuity at common nodes is implied from the order of the element bases in the elements referencing that node; for instance, C¹ continuity is possible between elements with cubic basis functions. It is currently possible to specify different levels of continuity independent of the element bases by using versions (??).

The advantages of the traditional nodal description are in the simplicity of creating a mesh, defining the continuity of a field, and modifying the field through direct graphical manipulation of field values and derivatives at the nodes. The disadvantages are that, in comparison to the general linear map, some continuity constraints cannot be easily specified.

A Simple Example

<field
    name                = "temperature"
    description-method  = "traditional-nodal"
    type                = "data">

  <element-bases>
    <use-bases>linear-Lagrange, linear-Lagrange</use-bases>
  </element-bases>

  <node-information>
    <node-values>
      <vector>
        <cn>5.0</cn> <cn>3.0</cn> <cn>4.0</cn>
        <cn>4.0</cn> <cn>5.0</cn> <cn>3.0</cn>
      </vector>
    </node-values>

    <node-indexing>
      <node-index
          element  = "1">
        <vector>
          <cn>1</cn> <cn>2</cn> <cn>4</cn> <cn>5</cn>
        </vector>
      </node-index>
      <node-index
          element  = "2">
        <vector>
          <cn>1</cn> <cn>2</cn> <cn>4</cn> <cn>5</cn>
        </vector>
      </node-index>
    </node-indexing>

  </node-information>

</field>