From: Joerg Frohne Date: Mon, 28 Oct 2013 15:32:13 +0000 (+0000) Subject: fix a bug in linearized inequality and the residual in overall algorithm X-Git-Tag: v8.1.0~467 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=89b9dee57032942f1b59754b57bec8e4b3fa2430;p=dealii.git fix a bug in linearized inequality and the residual in overall algorithm git-svn-id: https://svn.dealii.org/trunk@31467 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/examples/step-42/doc/intro.dox b/deal.II/examples/step-42/doc/intro.dox index a7d4ab3e5b..5c9c2b9219 100644 --- a/deal.II/examples/step-42/doc/intro.dox +++ b/deal.II/examples/step-42/doc/intro.dox @@ -198,9 +198,9 @@ the following equation (still an inequality, but linearized): \label{eq:linearization} \left(I_{\Pi}\varepsilon(\tilde {\mathbf u}^{i}), \varepsilon(\varphi) - \varepsilon(\tilde {\mathbf u}^{i})\right) \geq - \left(\left(I_{\Pi}\varepsilon(\tilde {\mathbf u}^{i-1}), + \left(\left(I_{\Pi}\varepsilon({\mathbf u}^{i-1}), \varepsilon(\varphi) - \varepsilon(\tilde {\mathbf u}^{i})\right) - - \left(P_{\Pi}(C\varepsilon(\tilde {\mathbf u}^{i-1})), + \left(P_{\Pi}(C\varepsilon({\mathbf u}^{i-1})), \varepsilon(\varphi) - \varepsilon(\tilde {\mathbf u}^{i})\right)\right), \quad \forall \varphi\in V^+, @f} @@ -302,8 +302,11 @@ method for the contact. It works as follows: (1-\alpha^i_l)U^{i-1}@f} satisfies @f{gather*} - \vert F\left(U^{i}\right) \vert < \vert F\left(U^{i-1}\right) \vert. + \vert {\hat R}\left({\mathbf u}^{i}\right) \vert < \vert {\hat R}\left({\mathbf u}^{i-1}\right) \vert. \f} + with ${\hat R}\left({\mathbf u}\right)=\left(P_{Pi}(C\varepsilon(u)),\varepsilon(\varphi^{i}_p\right)$ with + the exceptions of (i) elements $p\in\mathcal{A}_i$ where we set ${\hat R}\left({\mathbf u}\right)=0$, + and (ii) elements that correpond to hanging nodes, which we eliminate in the usual manner.
  • Define the new active and inactive sets by @f{gather*}\mathcal{A}_{i+1}:=\lbrace p\in\mathcal{S}:\Lambda^i_p + @@ -324,8 +327,8 @@ method for the contact. It works as follows: where $g_{h,p}$ is the gap denoting the distance of the obstacle from the undisplaced configuration of the body. -
  • If $\mathcal{A}_{i+1} = \mathcal{A}_k$ and $\vert - F\left(U^{i}\right) \vert < \delta$ then stop, else set $i=i+1$ and go to +
  • If $\mathcal{A}_{i+1} = \mathcal{A}_k$ and $\left\| + {\hat R}\left({\mathbf u}^{i}\right)\right) \right\|_{\ell_2} < \delta$ then stop, else set $i=i+1$ and go to step (1). This step ensures that we only stop iterations if both the correct active set has been found and the plasticity has been iterated to sufficient accuracy.