tutorial.html

有限元学习研究用源代码(老外的),供科研人员参考

<TITLE>Tutorial</TITLE>

<H1>Tutorial</H1>

 <P>I hope, the technical problems of <A HREF="install.html">
installation</A> of COG have been solved.  Now you want to learn how
to use COG.  In my experience, the best way to learn something is by
modification of working code examples.  That's why I have designed the
documentation in this way: as a collection of documented working code
examples.

 <P>In this tutorial, we start with simple geometries and ad, step by
step, new features:

<H2>Simple Standard Geometries</H2>

 <OL>

 <LI>
 <A HREF="mainstarttest.html">the simplest grid examples</A>: unit
cube, square, segment.

 <LI>
 <A HREF="mainoctreetest.html">2D rectangular geometries</A>: unions
and intersections of rectangles.

 <LI> 
 <A HREF="mainoctree3dtest.html">3D rectangular geometries</A>: unions
and intersections of cubes (see also
 FBH example <A HREF="mainfbh1test.html">Nr.1</A>).

 <LI> Definition of
 <A HREF="mainfacetest.html">boundary conditions</A>.

 <LI> 
 <A HREF="mainreftest.html">Local refinement</A>.

 <LI> Usage of curved coordinates, starting with
 <A HREF="mainpolartest.html">polar coordinates</A> (see also 
 <A HREF="mainspheretest.html">spherical coordinates</A>,
 <A HREF="mainshuktest.html">Shukowski transformations</A>).

 <LI> Combination of different geometries defined in different
coordinates, starting with the
 <A HREF="mainuniontest.html">union</A> (see also
 TEAM example <A HREF="mainteam7test.html"> Nr.7</A>,
 FBH example
 <A HREF="mainfbh2test.html">Nr.2</A>)

 </OL>

<H2>Separation between Cogenerator and Cogeometry</H2>

 <P>Until now, we have created the geometry description and the grid
generator input together.  But an essential property of the algorithm
is that these two parts are independent.  The geometry description
used in COG - named <B>cogeometry</B> - may be defined independently.

 <P>Then, a grid generator which allows a cogeometry as geometry
description - a <B>cogenerator</B> - defines, for which part of this
cogeometry we want to create a grid and how to do this.  For a given
cogeometry, it is possible to define different cogenerators:

 <UL>
 <LI> intersection with the <A HREF="maincogtest.html">cube [-1,1]<SUP>3</SUP></A>,
 <LI> intersection with the <A HREF="maincog3dtest.html">cube [0,1]<SUP>3</SUP></A>,
 <LI> intersection with the <A HREF="maincog2dtest.html">rectangle [-1,1]<SUP>2</SUP></A> at z=0.4,
 <LI> intersection with the <A HREF="maincog1dtest.html">segment [-1,1]</A> at y=z=0.4,
 <LI> intersection with a <A HREF="maincogpolartest.html">unit disc</A> at z=0.2,
 </UL>

 <P>Then, every cogenerator may be applied to every cogeometry.

<H2>External Cogeometries</H2>

 <P>For the previously considered standard cogenerators we can 
 <A HREF="cogcogentest.html">extract the related cogeometry</A>.
 This already defines a large class of geometries: rectangular
domains, their images in curved coordinates, and unions and
intersections of these objects.

 <P>Nonetheless, a cogeometry may be defined also by other
methods. Here we have listed some of them:

 <UL>
 <LI> <A HREF="cogregiontest.html">using a function region(x)</A>;
 <LI> <A HREF="cogfacetest.html">defining boundary conditions with a function face(x)</A>;
 </UL>


 <P><B><A NAME=warranty>Warning</A>:</B>This distribution contains
also some other direct methods.  They should be considered as
obsolete. The reason is that for cogeometries with a more or less
natural choice of a cogenerator I plan to implement such a
cogenerator. In this case, the direct method will be replaced by the
 <A HREF="cogcogentest.html">extraction of the cogeometry</A> from the
new standard cogenerator.