Documentation and style changes.

git-svn-id: https://svn.dealii.org/trunk@21311 0785d39b-7218-0410-832d-ea1e28bc413d

diff --git a/deal.II/examples/step-45/doc/intro.dox b/deal.II/examples/step-45/doc/intro.dox
index 9c2eb80b373f902d9943462342ac7f938607f479..73f5e84f035c7fde7155735b2f3c5855312217cc 100644 (file)
--- a/deal.II/examples/step-45/doc/intro.dox
+++ b/deal.II/examples/step-45/doc/intro.dox
@@ -12,11 +12,11 @@ solve some equation on a representative piece of a larger domain that repeats
 in one or more direction; an example is the simulation of the electronic
 structure of photonic
 crystals, because they have a lattice-like structure and, thus, it often
-suffices to do the actual computation on only one cell. To be able to proceed
-this way one has to assume that the computation can be periodically extended
-to the other cells. This requires the solution to be periodic w.r.t. the
-cells. Hence the solution has to obtain the same nodal values on opposite parts of the
-boundary. In the figure below we show this
+suffices to do the actual computation on only one cell of the lattice. To be
+able to proceed this way one has to assume that the computation can be periodically
+extended to the other cells. This requires the solution to be periodic with respect
+to the cells. Hence the solution has to obtain the same nodal values on opposite
+parts of the boundary. In the figure below we show this
 concept in two space-dimensions. There, all dashed faces with the same color should
 have the same boundary values:
 
@@ -45,14 +45,14 @@ periodic unless this is explicitly enforced.
 The way one has to see these periodic boundary conditions $u(x,0) = u(x,1)$ is
 as follows: Assume for a moment (as we do in this program) that we have a
 uniformly refined mesh. Then, after discretization there are a number of nodes
-(degrees of freedom) with indices $i \in {\cal I}_b$ on the bottom boundary of
-the domain, and  a second set of nodes at the top boundary $j \in {\cal
+(degrees of freedom) with indices $i \in {\cal I}_b$ on the left boundary of
+the domain, and  a second set of nodes at the right boundary $j \in {\cal
 I}_t$. Since we have assumed that the mesh is uniformly refined, there is
 exactly one node $j \in {\cal I}_t$ for each $i \in {\cal I}_b$ so that
 ${\mathrm x}_j = {\mathrm x}_i + (0,1)^T$, i.e. the two of them match with
 respect to the periodicity. We will then write that $j=\text{periodic}(i)$
 (and, if you want, $i=\text{periodic}(j)$).
-If now $U_k, k=0,\ldots,N-1$ are the unknowns of our discretized problem, then
+If now $U_k, k=0,\ldots,N-1,$ are the unknowns of our discretized problem, then
 the periodic boundary condition boils down to the following set of
 constraints:
 @f{align*}

diff --git a/deal.II/examples/step-45/doc/results.dox b/deal.II/examples/step-45/doc/results.dox
index 4fc57f22a3fbe6d0c0f0e766bb11e52b02f62a99..b4f55e3127fb93dca9200e6e1b3c53032742cf83 100644 (file)
--- a/deal.II/examples/step-45/doc/results.dox
+++ b/deal.II/examples/step-45/doc/results.dox
@@ -1,8 +1,8 @@
 <h1>Results</h1>
 
 The textual output the program generates is not very surprising. It just
-prints out the usual information on degrees of freedom, active cells and
-iteration steps of the solver, in much the same way as step-3 did:
+prints out the usual information on degrees of freedom and active cells,
+in much the same way as step-3 did:
 
 @code
 Number of active cells: 1024