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thirdParty/Zoltan/docs/ug_html/ug_alg_oct.html
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<!-------- @HEADER
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!
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! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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!
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! Zoltan Toolkit for Load-balancing, Partitioning, Ordering and Coloring
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! Copyright 2012 Sandia Corporation
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!
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! Under the terms of Contract DE-AC04-94AL85000 with Sandia Corporation,
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! the U.S. Government retains certain rights in this software.
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!
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! Redistribution and use in source and binary forms, with or without
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! modification, are permitted provided that the following conditions are
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! met:
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!
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! 1. Redistributions of source code must retain the above copyright
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! notice, this list of conditions and the following disclaimer.
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!
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! 2. Redistributions in binary form must reproduce the above copyright
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! notice, this list of conditions and the following disclaimer in the
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! documentation and/or other materials provided with the distribution.
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!
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! 3. Neither the name of the Corporation nor the names of the
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! contributors may be used to endorse or promote products derived from
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! this software without specific prior written permission.
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!
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! THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY
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! EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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! IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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! PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL SANDIA CORPORATION OR THE
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! CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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! EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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! PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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! PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
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! LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
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! NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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! SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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!
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! Questions? Contact Karen Devine kddevin@sandia.gov
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! Erik Boman egboman@sandia.gov
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!
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! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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!
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! @HEADER
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------->
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<HTML>
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<HEAD>
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<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso-8859-1">
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<META NAME="GENERATOR" CONTENT="Mozilla/4.04 [en] (X11; U; SunOS 5.6 sun4m) [Netscape]">
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<meta name="sandia.approval_type" content="formal">
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<meta name="sandia.approved" content="SAND2007-4748W">
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<meta name="author" content="Zoltan PI">
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<TITLE>Zoltan User's Guide: Octree Partitioning</TITLE>
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</HEAD>
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<BODY BGCOLOR="#FFFFFF">
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<div ALIGN=right><b><i><a href="ug.html">Zoltan User's Guide</a> | <a href="ug_order.html">Next</a> | <a href="ug_alg_patoh.html">Previous</a></i></b></div>
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<H2>
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<A NAME="Octree"></A>Octree Partitioning (OCTPART)</H2>
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The Octree Partitioning algorithm is based upon work in load balancing
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for parallel mesh generation at Rensselaer Polytechnic Institute [<A HREF="ug_refs.html#flaherty">Flaherty,
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Loy et al.</A>]. It was implemented in Zoltan by Luis Gervasio, Department
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of Computer Science, Rensselaer Polytechnic Institute, as his summer project
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in 1998 [<A HREF="ug_refs.html#gervasio">Gervasio</A>]. An octree is a spatial
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decomposition of the computational domain in which the root of the tree,
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representing the entire domain, is recursively divided by two in each coordinate
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direction (producing eight or four "child" octants in 3D or 2D, respectively)
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until each subregion holds at most an application-specified number of objects.
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These subregions are represented by the leaves of the octree. The octree
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data structure is widely used in mesh generation and adaptive mesh refinement
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[<U><A HREF="ug_refs.html#baehmann">Baehmann et al.</A></U>, <U><A HREF="ug_refs.html#shephard">Shephard
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and Georges</A></U>]. The octree resulting from such a spatial decomposition
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of the domain can be used to partition an application's work [<A HREF="ug_refs.html#edwards">Edwards</A>,
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<A HREF="ug_refs.html#pilkington">Pilkington and Baden</A>, <A HREF="ug_refs.html#warren">Warren
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and Salmon</A>]. To partition an octree, a traversal of the tree is used
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to define a global ordering on the leaves of the octree. This global ordering
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is often referred to as a Space-Filling Curve (SFC). The leaves of the
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octree can be easily assigned to processors in a manner which equally distributes
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work by assigning slices of the ordered list to processors. Different tree-traversal
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algorithms produce different global orderings or SFCs, with some SFCs having
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better connectivity and partition quality properties than others. Currently,
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Morton Indexing (i.e., Z-curve), Grey Code, and Hilbert SFCs are supported.
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Morton Indexing and Grey Code SFCs are the simplest (and currently, the
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fastest) of the SFC algorithms, but they produce lower-quality partitions
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than the Hilbert SFC.
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<BR>
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<TABLE WIDTH="100%" NOSAVE >
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<TR>
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<TD VALIGN=TOP><B>Method String:</B></TD>
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<TD><B>OCTPART</B></TD>
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</TR>
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<TR>
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<TD><B>Parameters:</B></TD>
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<TD></TD>
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</TR>
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<TR>
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<TD VALIGN=TOP> <I>OCT_DIM</I></TD>
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<TD>Specifies whether the 2D or 3D Octree algorithms should be used. The
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3D algorithms can be used for 2D problems, but much memory will be wasted
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to allow for a non-existent third dimension. Similarly, a 2D algorithm
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can be used for 3D surface meshes provided that the surface can be projected
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to the <I>xy</I>-plane without overlapping points.
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<BR>2 = use 2D algorithm; 3 = use 3D algorithm.</TD>
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</TR>
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<TR>
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<TD VALIGN=TOP><I> OCT_METHOD</I></TD>
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<TD>The SFC to be used.
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<BR>0 = Morton Indexing; 1 = Grey Code; 2 = Hilbert.</TD>
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</TR>
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<TR>
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<TD VALIGN=TOP> <I>OCT_MINOBJECTS</I></TD>
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<TD>The minimum number of objects to allow in a leaf octant of the octree.
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These objects will be assigned as a group to a processor, so this parameter
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helps define the granularity of the load-balancing problem. Values greater than
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or equal to one are allowable.</TD>
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</TR>
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<TR>
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<TD VALIGN=TOP> <I>OCT_MAXOBJECTS</I></TD>
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<TD>The maximum number of objects to allow in a leaf octant of the octree.
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These objects will be assigned as a group to a processor, so this parameter
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helps define the granularity of the load-balancing problem. Values greater than
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or equal to one are allowable.</TD>
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</TR>
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<TR>
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<TD VALIGN=TOP> <I>OCT_OUTPUT_LEVEL</I></TD>
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<TD>Amount of output the load-balancing algorithm should produce.
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<BR>0 = no statistics; 1 = statistics summary; 2 = debugging information; 3 = data for generating plots.</TD>
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</TR>
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<TR>
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<TD VALIGN=TOP><B>Default:</B></TD>
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<TD></TD>
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</TR>
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<TR>
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<TD></TD>
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<TD><I>OCT_DIM</I> = 3</TD>
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</TR>
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<TR>
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<TD></TD>
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<TD><I>OCT_METHOD</I> = 2</TD>
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</TR>
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<TR>
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<TD></TD>
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<TD><I>OCT_MINOBJECTS</I> = 10</TD>
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</TR>
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<TR>
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<TD></TD>
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<TD><I>OCT_MAXOBJECTS</I> = 40</TD>
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</TR>
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<TR>
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<TD></TD>
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<TD><I>OCT_OUTPUT_LEVEL</I> = 0</TD>
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</TR>
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<TR>
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<TD VALIGN=TOP><B>Required Query Functions:</B></TD>
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<TD></TD>
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</TR>
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<TR>
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<TD></TD>
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<TD><B><A HREF="ug_query_lb.html#ZOLTAN_NUM_OBJ_FN">ZOLTAN_NUM_OBJ_FN</A></B></TD>
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</TR>
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<TR>
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<TD></TD>
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<TD><B><A HREF="ug_query_lb.html#ZOLTAN_OBJ_LIST_FN">ZOLTAN_OBJ_LIST_FN</A></B>
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</TD>
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</TR>
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<TR>
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<TD></TD>
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<TD><B><A HREF="ug_query_lb.html#ZOLTAN_NUM_GEOM_FN">ZOLTAN_NUM_GEOM_FN</A></B></TD>
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</TR>
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<TR>
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<TD></TD>
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<TD>
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<b><a href="ug_query_lb.html#ZOLTAN_GEOM_MULTI_FN">ZOLTAN_GEOM_MULTI_FN</a></b>
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or <b><a href="ug_query_lb.html#ZOLTAN_GEOM_FN">ZOLTAN_GEOM_FN</a></b>
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</TD>
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</TR>
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</TABLE>
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<P>
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<HR WIDTH="100%">[<A HREF="ug.html">Table of Contents</A> |
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<A HREF="ug_order.html">Next: Ordering </A>
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| <A HREF="ug_alg_patoh.html">Previous: ParKway</A> | <a href="https://www.sandia.gov/general/privacy-security/index.html">Privacy and Security</a>]
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</BODY>
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</HTML>
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