Use Adapt () to modify an existing mesh based on an expression, typically by refining the mesh based on error information from a solution, as shown in Figure 8-27. The Adapt operation is used when setting up adaptive mesh refinement in the solver. The operation can also be used to modify the element size in a mesh based on a size expression, without the need for a solution.

Adapt nodes are part of meshing sequences that the adaptive solver creates. You can also add Adapt nodes by selecting entities in the Graphics window, then choose one of the following:

The Adapt node’s Settings window contains the following sections.

From the Geometric entity list, choose Entire geometry (the default), Domain, Boundary, or Edge to select a set of entities for which the adaptation is active. Choose Manual in the Selection list to select the entities in the Graphics window or choose a named selection to refer to a previously defined selection.

From the Solution list, select the solution to use for evaluation, or choose None to not use any solution, but instead use the input mesh for the operation to evaluate on.

From the Solution selection list, select which solution to use to evaluate error estimates:

In the Weights field (only available when Solution selection is Manual or All), enter weights as a space-separated list of positive (relative) weights so that the error estimate is a weighted sum of the error estimates for the various solutions (eigenmodes). The default value is 1, which means that all the weight is put on the first solution (eigenmode). That is, any omitted weight components are treated as zero weight.

From the Type of expression list, choose Error indicator (the default), Absolute size, or Anisotropic metric.

If you select Error indicator, the following settings appear:

The Error expression list, where you can add expressions for the error, for example, in terms of the dependent variables (including the variables for error estimation). You can use any expression, including field variables and their derivatives, defined in the domain. Use the Active column to control which error expressions are active by selecting or clearing the corresponding check box.

The Error order column is available when Element selection is set to Rough global minimum and forms an array of h-exponents for the decrease of the error expression. This array has the same indexing as the error expression’s indexing (for an error expression with two expressions, such as errexpr1, errexpr2, and error orders = 2, 3, it means that errexpr1 = O(h2) and errexpr2 = O(h3)). When the adaptation method is used, these numbers are filled in automatically based on the Residual order and Error estimate settings (on the adaptation study). The shape functions can also influence this order. Note that these order numbers need to be positive to generate additional elements (element growth).

Use the Move Up (), Move Down (), Add ()and Delete () buttons as needed. If you use several expressions, such as one for each solution component, the error expressions are added to form the sum of all of them. Or right-click a table cell and select Move Up, Move Down, Add, or Delete.

Use the Adaptation method list (2D and 3D only) to control how to adaptively refine mesh elements. Select one of these methods:

Enter a value for the Maximum number of refinements (default: 5 in 2D and 3D; 16 in 1D), if needed.

Use the Element selection list to specify how the element refinement vector is determined from the error expression. Select:

If you select Absolute size, the following settings appear:

In the Size expression field, type an expression for the element size (in terms of variables defined by the solution).

In 2D and 3D, use the Adaptation method list to control how to refine mesh elements. Select one of the following methods:

If you select Anisotropic metric (2D and 3D only), the following settings appear:

In the matrix (2-by-2 in 2D; 3-by-3 in 3D) that appears, you can enter a metric in upper-triangular parts (the matrix is a positive definite symmetric matrix). The expressions for the metric can vary in space and include the local mesh element size h. The default value is a diagonal matrix with the diagonal elements set to 1/h, which means “no modification” for an isotropic mesh. The interpretation of the matrix is as follows: The vector representing an edge of an element is transformed by the matrix in that point, and the length of the transformed vector is measured. If the length is shorter than 1.0, it is considered too short. If it is longer than 1.0, it is considered too long. This measure is used to control the adaptation.

The following settings are available under External changes if the Solution list is set to None.

There is a caching scheme that caches various data required to compute the mesh size field. If you have changed something in the model that has not been picked up by the code and thus invalidated the cache, you can clear the cache by clicking Reevaluate with Updated Model.

The selection in the Update when parameter is changed list provides the possibility to have the cache cleared whenever the values of the selected parameter are changed.