3 \page smoothing_page Smoothing
5 \n Smoothing is used to improve quality of 2D mesh by adjusting the
6 locations of element corners (nodes).
8 \note Depending on the chosen method and mesh geometry
9 the smoothing can actually decrease the quality of elements and even
10 make some elements inverted.
12 <em>To apply smoothing to the elements of your mesh:</em>
15 <li>In the \b Modification menu select the \b Smoothing item or click
16 <em>"Smoothing"</em> button in the toolbar.
18 \image html image84.png
19 <center><em>"Smoothing" button</em></center>
21 The following dialog will appear:
23 \image html smoothing.png
28 <li>specify the IDs of the elements which will be smoothed:
30 <li><b>Select the whole mesh, sub-mesh or group</b> activating this
32 <li>choose mesh elements with the mouse in the 3D Viewer. It is
33 possible to select a whole area with a mouse frame; or</li>
34 <li>input the element IDs directly in <b>ID Elements</b> field. The
35 selected elements will be highlighted in the viewer; or</li>
36 <li>apply Filters. <b>Set filters</b> button allows to apply a filter
37 to the selection of elements. See more about filters in the
38 \ref filtering_elements "Selection filter library" page.</li>
42 <li>define the <b>Fixed nodes ids</b> that should remain at their
43 location during smoothing. If a mesh is built on a shape, the nodes
44 built on its geometric edges are always fixed. If the smoothing is
45 applied to a part of the mesh (a set of element), the nodes on
46 boundary of the element set are also fixed. It is possible to
47 additionally fix any other nodes. The fixed nodes can be selected
48 manually or by filters, just as the smoothed elements.</li>
49 <li>choose the <b>Smoothing Method:</b>
51 <li>\b Laplacian smoothing pulls a node toward the center of
52 surrounding nodes directly connected to that node along an element
54 <li>\b Centroidal smoothing pulls a node toward the
55 element-area-weighted centroid of the surrounding elements. </li>
57 Laplacian method will produce the mesh with the least element
58 edge length. It is also the fastest method. Centroidal smoothing
59 produces a mesh with more uniform element sizes.</li>
62 \image html image83.gif
65 <li>specify the <b>Iteration limit</b>. Both smoothing methods iterate
66 through a number of steps to produce the resulting smoothed mesh. At
67 each new step the smoothing is reevaluated with the updated nodal
68 locations. This process continues till the limit of iterations has
69 been exceeded, or till the aspect ratio of all element is less than
70 or equal to the specified one.</li>
71 <li>specify the <b>Max. aspect ratio</b> - the target mesh quality at
72 which the smoothing algorithm should stop the iterations.</li>
73 <li>activate <b>in parametric space</b> check-box if it is necessary to
74 improve the shape of faces in the parametric space of geometrical
75 surfaces on which they are generated, else the shape of faces in the
76 3D space is improved that is suitable for <b>planar meshes only</b>. </li>
79 <li>Click \b Apply or <b> Apply and Close</b> button to confirm the operation.</li>
82 \image html smoothing1.png "The initial mesh"
84 \image html smoothing2.png "The smoothed mesh"
86 <br><b>See Also</b> a sample TUI Script of a
87 \ref tui_smoothing "Smoothing" operation.