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<!doctype html>
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<title>p4est 2020 HCM Summer School: Forest</title>
<meta name="author" content="Carsten Burstedde">
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<h1><tt>p4est</tt> 2020 HCM Summer School: Forest</h1>
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<p>
We are organizing a <tt>p4est</tt> summer school
sponsored by the
<a href="https://www.hcm.uni-bonn.de">Hausdorff Center for Mathematics</a>
at the <a href="https://www.uni-bonn.de/">University of Bonn</a>, Germany.
Please see also the school's <a
href="https://www.hcm.uni-bonn.de/events/eventpages/hausdorff-school/hausdoff-school-2020/the-p4est-software-for-parallel-amr/">home
page and application forms</a>.
</p>
<article>
<section>
<h2>Create and manipulate a forest of octrees</h2>
<p class="book">
<tt>p4est</tt> represents a mesh topology as a forest of octrees. This
forest can be created by <tt>p4est</tt> given a
<a href="tutorial-connectivity.html">connectivity</a>. In this tutorial,
we talk about the typical workflow in <tt>p4est</tt> to create and manipulate
a forest of quadtrees (2D) or octrees (3D) to represent a mesh topology.
</p>
</p>
<dl class="spec">
<dt>Required skills</dt><dd><a href="tutorial-build.html">Build</a>,
<a href="tutorial-connectivity.html">connectivity</a> and optional
the <a href="tutorial-io.html">VTK graphics tutorial</a>.</dd>
<dt>Skills acquired</dt><dd>Create a forest of quadtrees and change the
refinement structure of the created forest.</dd>
<dt>Additional material</dt><dd>For an example that covers the content
of this tutorial see <a href="https://github.com/cburstedde/p4est/blob/prev3-develop/example/simple/simple2.c">simple2.c</a>.</dd>
<dt>Next steps (with links?)</dt><dd>
Reference to more advanced tutorials when they exist.</dd>
</dl>
</section>
<section id="create">
<h3>Create a forest of octrees</h3>
<p class="book">
A fundamental step of a typical workflow with <tt>p4est</tt> is to create a forest
of octrees or quadtrees. The <tt>p4est</tt> libary offers the functions
<code>p4est_new</code> and <code>p4est_new_ext</code> (a version with more
parameters) to create such a forest.
</p>
<pre class="book">
typedef my_user_data {
int foo;
} my_user_data_t;
static void my_quadrant_init (p4est, which_tree, quadrant) {
((my_user_data_t *) quadrant->p.user_data)->foo = *(int *) p4est->user_pointer;
}
static int foo = 17489;
void *user_pointer = &foo;
p4est = p4est_new_ext (mpicomm, connectivity, 0, level, 1,
sizeof (my_user_data_t), my_quadrant_init, user_pointer);
</pre>
<p class="book">
<code>mpicomm</code> is an MPI communicator (see the <a
href="https://github.com/cburstedde/p4est/blob/prev3-develop/example/simple/simple2.c">example
simple</a> for a usage example).
<!--
By <code>min_quadtrants</code> the user can prescribe the minimal intial number of quadrants per
processor.
//-->
The highest occurring <code>level</code> of refinement is specified.
If it is zero or negative, there will be no refinement beyond the coarse
mesh connectivity at this point.
<!--
The quasi Boolean value <code>fill_uniform</code> determines if the forest
is filled with a uniform mesh for <code>fill_uniform</code> true or the
coarstest possible mesh is created for <code>fill_uniform</code> false.
//-->
We provide an optional callback mechanism to initialize the
user data that we allocate inside any forest leaf.
The <code>user_pointer</code> is assigned to the
member of the same name in the <code>p4est</code> created (before the init
callback function is called the first time).
This is a way to keep application state referenced in a <tt>p4est</tt> object.
For more details see
<code><a href="https://github.com/cburstedde/p4est/blob/prev3-develop/src/p4est.h#L253-L276">p4est.h</a></code> and
<code><a href="https://github.com/cburstedde/p4est/blob/prev3-develop/src/p4est_extended.h#L113-L131">p4est_extended.h</a></code>
(as always, the 3D equivalents are prefixed with <code>p8est</code>).
</p>
<p class="exer">
Exercise F1:
Choose in
<code><a href="https://github.com/cburstedde/p4est/blob/prev3-develop/src/p4est_connectivity.h#L360-L436">p4est_connectivity.h</a></code>
a connectivity that you like and create a forest of quadtrees.
</p>
</section>
<section>
<h3>Manipulate the refinement structure and the partition</h3>
<p class="book">
The hypercubic elements for the dimensions two and three are called quadrants
(the code uses this term also for three dimensional octants).
In <code><a href="https://github.com/cburstedde/p4est/blob/prev3-develop/src/p4est.h#L68-L109">p4est.h</a></code>
the <code>struct p4est_quadrant</code> is declared and documented.
</p>
<p class="book">
Our next step in the workflow is to manipulate the refinement structure. The <tt>p4est</tt> libary offers the
following functions to manipulate the forest of quadtrees (2D) or octrees (3D).
They are collective over the MPI communicator passed to <code>p4est_new</code>.
</p>
<dl class="book">
<dt><code><a href="https://github.com/cburstedde/p4est/blob/prev3-develop/src/p4est.h#L316-L335">p4est_refine</a></code></dt>
<dd>Refinement of specific hypercubes given a refinement criterion, i.e. a
user-defined callback function.
While it is possible (and fun) to turn on recursive refinement, in practice
we set it to non-recursive and loop around the function.
This has the advantage that we can repartition in parallel after every iteration.
</dd>
<dt><code><a href="https://github.com/cburstedde/p4est/blob/prev3-develop/src/p4est.h#L337-L348">p4est_coarsen</a></code></dt>
<dd>Coarsen a family of hypercubes given a coarsening criterion, i.e. a
user-defined callback function.</dd>
<dt><code><a href="https://github.com/cburstedde/p4est/blob/prev3-develop/src/p4est.h#L350-L360">p4est_balance</a></code></dt>
<dd>This function ensures a 2:1 balance of the size differences of
neigboring elements in a forest by refining quadrants.
This is accomplished by adding some more refinement where needed.
</dd>
<dt><code><a href="https://github.com/cburstedde/p4est/blob/prev3-develop/src/p4est.h#L362-L382">p4est_partition</a></code></dt>
<dd>Partition the forest in parallel, equally or according to a given
user-defined weight per quadrant.</dd>
</dl>
<p class="exer">
Exercise F2:
Use <code>p4est_refine</code> in a loop to refine at the boundary
(choose a boundary thickness) of a circle until the quadrants there reach
the refinement level six, and then redistribute the quadrants between the processes
using <code>p4est_partition</code>.
Verify your program using the VTK output.
</p>
<p class="exer">
Exercise F3:
Coarsen all families of quadrants that have a level greater than four and
call <code>p4est_balance</code> on the forest.
In parallel, examine the difference between standard partition and
<code>partition_ext (p4est, 1, NULL)</code>.
Verify your program using the VTK output.
</p>
<p class="exer">
Exercise F4:
Formulate a weight function for <code>p4est_partition_ext</code>.
Tweak it in such a way that you can have from 0 to 15 elements on process zero
chosen by command line argument, and the rest of them partitioned evenly acress
the other processes.
</p>
</section>
</article>
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