From a2acb261b3c6dd400f23c416e3d81357c03b303d Mon Sep 17 00:00:00 2001 From: Luca Heltai Date: Thu, 10 May 2018 09:25:50 +0200 Subject: [PATCH] Fixed some issues with step-60 doc. --- doc/doxygen/tutorial/tutorial.h.in | 8 ++++++-- examples/step-60/doc/intro.dox | 28 ++++++++++++++-------------- examples/step-60/step-60.cc | 3 +++ 3 files changed, 23 insertions(+), 16 deletions(-) diff --git a/doc/doxygen/tutorial/tutorial.h.in b/doc/doxygen/tutorial/tutorial.h.in index 68a85a50cc..cd2cade0e0 100644 --- a/doc/doxygen/tutorial/tutorial.h.in +++ b/doc/doxygen/tutorial/tutorial.h.in @@ -781,7 +781,8 @@ * step-43, * step-55, * step-56, - * step-57 + * step-57, + * step-60 * * * @@ -812,7 +813,10 @@ * * Linear operators * - * step-44 + * + * step-44, + * step-60 + * * * * diff --git a/examples/step-60/doc/intro.dox b/examples/step-60/doc/intro.dox index 9bdf2cfde3..d61317a6d7 100644 --- a/examples/step-60/doc/intro.dox +++ b/examples/step-60/doc/intro.dox @@ -62,10 +62,10 @@ dimension of the embedding domain $\Omega$ (`spacedim`). We are going to solve the following differential problem: given a sufficiently regular function $g$ on $\Gamma$, find the solution $u$ to -@f{eqnarray*} -- \Delta u + \gamma^T \lambda &=& 0 & \text{ in } \Omega\\ -\gamma u &=& g & \text{ in } \Gamma \\ -u & = & 0 & \text{ on } \partial\Omega. +@f{eqnarray*}{ +- \Delta u + \gamma^T \lambda &=& 0 \text{ in } \Omega\\ +\gamma u &=& g \text{ in } \Gamma \\ +u & = & 0 \text{ on } \partial\Omega. @f} This is a constrained problem, where we are looking for a harmonic function $u$ @@ -97,9 +97,9 @@ Q(\Gamma)$, integrating by parts when possible, and exploiting the boundary conditions on $\partial\Omega$, we obtain the following variational problem: Given a sufficiently regular function $g$ on $\Gamma$, find the solution $u$ to -@f{eqnarray*} -(\nabla u, \nabla v)_{\Omega} + (\lambda, \gamma v)_{\Gamma} &=& 0 & \forall v \in V(\Omega) \\ -(\gamma u, q)_{\Gamma} &=& (g,q)_{\Gamma} & \forall q \in Q(\Gamma), +@f{eqnarray*}{ +(\nabla u, \nabla v)_{\Omega} + (\lambda, \gamma v)_{\Gamma} &=& 0 \qquad \forall v \in V(\Omega) \\ +(\gamma u, q)_{\Gamma} &=& (g,q)_{\Gamma} \qquad \forall q \in Q(\Gamma), @f} where $(\cdot, \cdot)_{\Omega}$ and $(\cdot, \cdot)_{\Gamma}$ represent, @@ -207,10 +207,10 @@ G where -@f{eqnarray*} -K_{ij} &:=& (\nabla v_j, \nabla v_i)_\Omega & i,j=1,\dots,n \\ -C_{\alpha j} &:=& (v_j, q_\alpha)_\Gamma &j=1,\dots,n, \alpha = 1,\dots, m \\\\ -G_{\alpha} &:=& (g, q_\alpha)_\Gamma & \alpha = 1,\dots, m. +@f{eqnarray*}{ +K_{ij} &:=& (\nabla v_j, \nabla v_i)_\Omega \qquad i,j=1,\dots,n \\ +C_{\alpha j} &:=& (v_j, q_\alpha)_\Gamma \qquad j=1,\dots,n, \alpha = 1,\dots, m \\\\ +G_{\alpha} &:=& (g, q_\alpha)_\Gamma \qquad \alpha = 1,\dots, m. @f} While the matrix $K$ is the standard stiffness matrix for the Poisson problem on @@ -242,9 +242,9 @@ of the matrix $C$. To evaluate $(v_j \circ F_{K}) (\hat x_i)$ the following steps needs to be taken (as shown in the picture below): -- For a given cell $K$ in $\Gamma$ compute the real point $y_i \coloneqq F_{K} -(\hat x_i)$, where $x_i$ is one of the quadrature points used for the integral -on $K \subseteq \Gamma$. +- For a given cell $K$ in $\Gamma$ compute the real point $y_i := F_{K} (\hat +x_i)$, where $x_i$ is one of the quadrature points used for the integral on $K +\subseteq \Gamma$. - Find the cell of $\Omega$ in which $y_i$ lies. We shall call this element $T$. diff --git a/examples/step-60/step-60.cc b/examples/step-60/step-60.cc index 627bb3e817..c71ff2b32c 100644 --- a/examples/step-60/step-60.cc +++ b/examples/step-60/step-60.cc @@ -436,6 +436,7 @@ namespace Step60 // organized as follows: // // @code + // # Example parameter file // subsection first // subsection second // subsection third @@ -457,6 +458,7 @@ namespace Step60 // absolute one (e.g. `ParameterAcceptor("/first/second/third/My Other Class")`), // obtaining: // @code + // # Example parameter file // subsection first // subsection second // subsection third @@ -479,6 +481,7 @@ namespace Step60 // resulting parameter file will look like: // // @code + // # Example parameter file // subsection first // subsection second // subsection third -- 2.39.5