refine.html

有限元学习研究用源代码(老外的),供科研人员参考

<title>IBG: Refinement Control</title>

<h1>Refinement Control</h1>

 <P>For some simple applications, the possibilities of refinement
control using an <A HREF="extern.html">external file</A> for the
definition of some control parameters may be sufficient. Other, more
complex applications have the possibility to define <A
HREF="#callbacks"> own refinement criteria</A>.

<H1>Refinement Parameter</H1>

<h2> 
<a name="min"> min</a>,
<a name="xmin"> xmin</a>,
<a name="ymin"> ymin</a>,
<a name="zmin"> zmin</a>: 
minimal refinement</h2>

<p>It is possible to fix a minimal refinement distance in each direction.
This minimal refinement paremeters allow to avoid infinite loops in the case
of geometries with infinite complexity or other refinement criteria which
require an infinite grid.

<p>The minimal refinement parameters may be different for each direction.
The parameter setting

<pre>
min=value;
</pre>

<p>is simply an abbreviation for 

<pre>
xmin=value; ymin=value; zmin=value;
</pre>

<p>The minimal distances between nodes in the grid may be much smaller than
the values defined here near the boundary, because the definition of the
boundary nodes is independent of these parameters.

<h2>
<a name="fnorm"> fnorm</a>,
<a name="lnorm"> lnorm</a>,
<a name="ftang"> ftang</a>,
<a name="ltang"> ltang</a>:
refinement near boundary faces and lines</h2>

<p> These four scalar paramters define some homogeneous refinement around
the intersection with boundary faces (fnorm, ftang) and boundary lines
(lnorm, ltang). They are the maximal length of an edge resp. rectangle with
an intersection with the related boundary (fnorm, lnorm) or of edges resp.
rectangles orthogonal to them (ftang, ltang).

<h2>
<a name="refine"> refine</a>,
<a name="refineX"> refineX</a>,
<a name="refineY"> refineY</a>,
<a name="refineZ"> refineZ</a>,
<a name="refineU"> refineU</a>,
<a name="refineV"> refineV</a>,
<a name="refineW"> refineW</a>:
local refinement around a point</h2>

<p>These calls allow to define local refinement around a point. An
isotropical refinement will be defined by the keyword <b>refine</b>
and has following parameters:

<pre>
refine(v,r,x,fx,y,fy,z,fz);
</pre>

<p>Anisotropical refinement will be defined by the keywords
<b>refineX</b>, <b>refineY</b>, <b>refineZ</b>, <b>refineU</b>,
<b>refineV</b> and <b>refineW</b>. The same parameter set is the
same. The parameters are:

 <ul>

 <li>v: the maximal length analogical to <a href="#max> max</a> in the
point.
 <li>r: an integer value which defines a region. The criterion will be
applied only inside the region. If omitted (or set to 0) it will be applied
for all regions.
 <li>x,y,z: the coordinates of the point.
 <li>fx,fy,fz: parameters for the definition of the region around the point
which has to be refined. The value has to be between 0 and 1. 0 means that
the whole direction has to be defined, 1 means the minimal possible region
around the point.
 </ul>

 <p>In the region defined by r, x, y, z, fx, fy and fz, <B>refine</B>
refines isotropically, <B>refineX</B>, <B>refineY</B> and
<B>refineZ</B> refine in x-, y- resp. z-direction. <B>refineU</B>,
<B>refineV</B> and <B>refineW</B> refine in gradient direction of the
functions u, v, w defined on the points.

<p>The distances between the points of the resulting grid may be
greater than the values defined here. First, because only orthogonal
edges will be tested, thus the diagonal edges are longer. Second, near
the boundary grid points may be moved, and this movement will be
controlled by other parameters. Last not least, The point of highest
refinement (x,y,z) is usually not in the grid.