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graeser
dune-functions-debug
Commits
e87a8a26
Commit
e87a8a26
authored
Feb 28, 2018
by
oliver.sander_at_tu-dresden.de
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Scrap a few obsolete phrases
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doc/manual/dune-functions-manual.bib
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doc/manual/dune-functions-manual.bib
doc/manual/dune-functions-manual.tex
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@@ -59,3 +59,11 @@ year = {1990}
primaryClass
=
{cs.MS}
,
preprinturl
=
{http://arxiv.org/abs/1512.06136}
}
@Book
{
bader:2013
,
title
=
{Space-Filling Curves -- An Introduction with Applications in Scientific Computing}
,
publisher
=
{Springer}
,
year
=
{2013}
,
author
=
{Michael Bader}
}
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doc/manual/dune-functions-manual.tex
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@@ -594,23 +594,15 @@ to derive such index trees from the finite element tree.
\todosander
{
Rewrite this section to match the new section title
}
To work with the basis of a finite element space, the basis vectors need to be indexed. Indexing the basis functions
is what allows to address the corresponding vector and matrix coefficients in suitable vector and matrix data structures.
In simple cases, indexing means simply enumerating the basis functions with natural numbers, but for hierarchically
constructed spaces more general ways to index are possible.
There are two aspects to what we just have loosely called ``indexing''. The first is that the set of all basis functions
in the tree need to be given a global order. There are several reasonable choices to do this, which we discuss
in this section.
Given an order of the basis functions, there is then a natural indexing by simply enumerating the basis functions in
their specific order.
This is what we call the
{
\em
flat
}
numbering, and very often this is what we want to use. However, as the FE basis
is constructed hierarchically (and so may be the linear algebra data structures; see Chapter~
\ref
{
sec:dune
_
istl:dune
_
istl
}
),
it may make sense to use hierarchical indices as well. We discuss this in Section~
\ref
{
sec:dune
_
functions:blocking
}
.
their specific order. This can be flat or hierarchical.
Consider first a leaf basis consisting of
$
n
$
basis functions. We suppose that these basis functions are given in a fixed
order (even though being able to change this ordering can improve the performance of a numerical
algorithm, see for example
\cite
{
space
_
filling
_
curves
,ordering
_
for
_
gauss
_
seidel
}
for more on this).
algorithm, see for example
\cite
{
bader:2013
,ordering
_
for
_
gauss
_
seidel
}
for more on this).
Consider now a tree of finite element bases with a given root
$
R
$
. This root has
$
m
$
children, and suppose that for
each of the subtrees rooted in these children we have already chosen an ordering. Suppose further that the children themselves are given
in a fixed ordering (One may of course create different overall orderings by permuting the children, but in our view
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