From: bangerth Date: Mon, 27 Feb 2012 10:21:39 +0000 (+0000) Subject: Add more pictures. X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=f3e4198cae76e2af8578f68e4ebedf0958603965;p=dealii-svn.git Add more pictures. git-svn-id: https://svn.dealii.org/trunk@25176 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/examples/step-41/doc/results.dox b/deal.II/examples/step-41/doc/results.dox index e871345f8a..0b87663985 100644 --- a/deal.II/examples/step-41/doc/results.dox +++ b/deal.II/examples/step-41/doc/results.dox @@ -171,6 +171,50 @@ course of the active set iterations, this unphysical membrane shape is smoothed out, the contact with the lower-most stair step disappears, and the solution stabilizes. +In addition to this, the program also outputs the values of the +Lagrange multipliers. Remember that these are the contact forces and +so should only be positive on the contact set, and zero outside. If, +on the other hand, a Lagrange multiplier is negative in the active +set, then this degree of freedom must be removed from the active +set. The following pictures show the multipliers in iterations 1, 9 +and 18, where we use red and browns to indicate positive values, and +blue for negative values. + + + + + + + + + + + + + +
+ @image html step-41.forces.01.png + + @image html step-41.forces.09.png + + @image html step-41.forces.18.png +
+ Iteration 1 + + Iteration 9 + + Iteration 18 +
+ +It is easy to see that the positive values converge nicely to moderate +values in the interior of the contact set and large upward forces at +the edges of the steps, as one would expect (to support the large +curvature of the membrane there); at the fringes of the active set, +multipliers are initially negative, causing the set to shrink until, +in iteration 18, there are no more negative multipliers and the +algorithm has converged. + +

Possibilities for extensions

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