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<h1>Smoothing</h1>
<p><img src="../i_blue.jpg" x-maintain-ratio="TRUE" width="30px" height="30px" border="0" class="img_whs1"> Smoothing is used to adjust the locations of element
corners (nodes) to reduce distortions in these elements.</p>
<p> </p>
<p class=TODO>To apply smoothing to the elements of your mesh:</p>
<p class=TODO> </p>
<p class="whs2">1. Display a mesh or a submesh in the 3D
viewer.</p>
<p class="whs2"> </p>
<p class="whs2">2. In the <span style="font-weight: bold;"><B>Modification
</B></span>menu select the <span style="font-weight: bold;"><B>Smoothing </B></span>item
or click <img src="../image84.gif" width="24px" height="25px" border="0" class="img_whs3"> button in the toolbar. The following dialog box
will appear:</p>
<p> </p>
<p class="whs2"><img src="../image85.gif" width="319px" height="369px" border="0" class="img_whs4"></p>
<p class="whs2"> </p>
<p class="whs2">This dialog box contains the following fields
which should be specified:</p>
<p> </p>
<ul type="disc" class="whs5">
<li class=kadov-p><p class="whs6"><span
style="font-weight: bold;"><B>Id Elements </B></span><span>field allows to specify
the elements which should be smoothed by selecting them in the 3D viewer.
Note: to select several elements press </span><span style="font-weight: bold;"><B>Shift
</B></span><span>button.</span></p></li>
<ul type="disc" class="whs5">
<li class=kadov-p><p class="whs7">Smoothing is applied
to the whole mesh or its part</p></li>
<li class=kadov-p><p><span style="font-weight: bold;"><B>Fixed nodes
ids</B></span>: some nodes keep their location during smoothing. If a mesh
is built on a geometry shape, the nodes built on geometrical edges are
always fixed. If smoothing is applied to a part of a mesh then the boundary
nodes of an elements set are also fixed. Any other nodes may be additionally
fixed.</p></li>
<li class=kadov-p><p> </p></li>
<li class=kadov-p><p><span style="font-weight: bold;"><B>Smoothing
method</B></span>:</p></li>
<ul type="disc" class="whs5">
<li class=kadov-p><p><span style="font-weight: bold;"><B>Laplacian</B></span>
smoothing pulls a node toward the center of surrounding nodes directly
connected to that node along an element edge. Centroidal smoothing pulls
a node toward the element-area-weighted centroid of the surrounding elements.
Typically, the Laplacian method will produce the mesh with the least element
distortion. It is also the faster method. </p></li>
<li class=kadov-p><p><span style="font-weight: bold;"><B>Centroidal</B></span>
smoothing usually produces a mesh that has more uniform element sizes.
Both methods produce good results with "free" meshes.</p></li>
</ul>
</ul>
</ul>
<p class="whs8"><img src="../image83.gif" width="527px" height="281px" border="0" class="img_whs9"></p>
<ul type="disc" class="whs5">
<li class=kadov-p><p class="whs6"><span
style="font-weight: bold;"><B>Iteration limit: </B></span>both of the smoothing
methods use an iterative procedure to converge toward a smoothed mesh.
All nodes are smoothed according to one of the techniques shown above.
Then the smoothing is reevaluated with the updated nodal locations. This
process continues until the maximum number of iterations has been exceeded,
or all elements has aspect ratio less or equal than the specified one.</p></li>
<li class=kadov-p><p class="whs6"><span
style="font-weight: bold;"><B>Max. aspect ratio</B></span>.</p></li>
</ul>
<p class="whs2"> </p>
<p class="whs2">3. Click the <span style="font-weight: bold;"><B>Apply
</B></span>or <span style="font-weight: bold;"><B>OK </B></span>button to confirm
the operation.</p>
<p> </p>
<p> </p>
<p> </p>
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