From 3d54c67dc497ce2851ca6a2cbe2f567576a48084 Mon Sep 17 00:00:00 2001 From: bangerth Date: Thu, 24 Jun 2010 12:20:53 +0000 Subject: [PATCH] Adjust indices. git-svn-id: https://svn.dealii.org/trunk@21313 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/examples/step-45/doc/intro.dox | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/deal.II/examples/step-45/doc/intro.dox b/deal.II/examples/step-45/doc/intro.dox index 73f5e84f03..47e175733f 100644 --- a/deal.II/examples/step-45/doc/intro.dox +++ b/deal.II/examples/step-45/doc/intro.dox @@ -45,18 +45,18 @@ 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 left boundary of +(degrees of freedom) with indices $i \in {\cal I}_l$ 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 +I}_r$. Since we have assumed that the mesh is uniformly refined, there is +exactly one node $j \in {\cal I}_r$ for each $i \in {\cal I}_l$ so that +${\mathrm x}_j = {\mathrm x}_i + (1,0)^T$, 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 the periodic boundary condition boils down to the following set of constraints: @f{align*} - U_{\text{periodic}(i)} = U_i, \qquad \forall i \in {\cal I}_b. + U_{\text{periodic}(i)} = U_i, \qquad \forall i \in {\cal I}_l. @f} Now, this is exactly the sort of constraint that the ConstraintMatrix class, first introduced in step-6, -- 2.39.5