From e87a8a266e00f10ff97927ac4b00355e791d3b5e Mon Sep 17 00:00:00 2001
From: Oliver Sander <oliver.sander@tu-dresden.de>
Date: Wed, 28 Feb 2018 21:51:38 +0100
Subject: [PATCH] Scrap a few obsolete phrases
---
doc/manual/dune-functions-manual.bib | 8 ++++++++
doc/manual/dune-functions-manual.tex | 12 ++----------
2 files changed, 10 insertions(+), 10 deletions(-)
diff --git a/doc/manual/dune-functions-manual.bib b/doc/manual/dune-functions-manual.bib
index 74fd04d..6276d62 100644
--- a/doc/manual/dune-functions-manual.bib
+++ b/doc/manual/dune-functions-manual.bib
@@ -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}
+}
+
diff --git a/doc/manual/dune-functions-manual.tex b/doc/manual/dune-functions-manual.tex
index 7e43794..eeb8a6a 100644
--- a/doc/manual/dune-functions-manual.tex
+++ b/doc/manual/dune-functions-manual.tex
@@ -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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