From c44ed8c7ba48f7ecbd09de6ccc0b86f12e90e7be Mon Sep 17 00:00:00 2001 From: frohne Date: Thu, 7 Feb 2013 21:59:40 +0000 Subject: [PATCH] fix the name Tremoliere again and add a note that B is symmetric git-svn-id: https://svn.dealii.org/trunk@28269 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/examples/step-41/doc/intro.dox | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/deal.II/examples/step-41/doc/intro.dox b/deal.II/examples/step-41/doc/intro.dox index ec35d89e7d..f98bbc5674 100644 --- a/deal.II/examples/step-41/doc/intro.dox +++ b/deal.II/examples/step-41/doc/intro.dox @@ -166,7 +166,7 @@ statement above only appears to have the wrong sign because we have $\mu-\lambda<0$ at points where $\lambda=0$, given the definition of $K$. The existence and uniqueness of $(u,\lambda)\in V\times K$ of this saddle -point problem has been stated in Glowinski, Lions and Tr{é}moli{è}res: Numerical Analysis of Variational +point problem has been stated in Glowinski, Lions and Trémolières: Numerical Analysis of Variational Inequalities, North-Holland, 1981. @@ -237,7 +237,7 @@ pp. 865-888.

The primal-dual active set algorithm

-The algorithm for the primal-dual active set method works as follows: +The algorithm for the primal-dual active set method works as follows (NOTE: $B = B^T$): - [(0)] Initialize $\mathcal{A}_k$ and $\mathcal{F}_k$, such that $\mathcal{S}=\mathcal{A}_k\cup\mathcal{F}_k$ and @@ -245,7 +245,7 @@ The algorithm for the primal-dual active set method works as follows: - [(1)] Find the primal-dual pair $(U^k,\Lambda^k)$ that satisfies @f{align*} AU^k + B\Lambda^k &= F,\\ - [BU^k]_i &= G\quad&&\forall i\in\mathcal{A}_k,\\ + [BU^k]_i &= G_i\quad&&\forall i\in\mathcal{A}_k,\\ \Lambda_i^k &= 0\quad&&\forall i\in\mathcal{F}_k. @f} Note that the second and third conditions imply that exactly $|S|$ unknowns -- 2.39.5