From 2aa2b8378ede288de4fb0f55e16479910149eb8c Mon Sep 17 00:00:00 2001 From: bangerth Date: Sun, 22 Jun 2014 11:41:17 +0000 Subject: [PATCH] More minor adjustments. git-svn-id: https://svn.dealii.org/trunk@33074 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/examples/step-52/doc/intro.dox | 18 +++++++++++------- 1 file changed, 11 insertions(+), 7 deletions(-) diff --git a/deal.II/examples/step-52/doc/intro.dox b/deal.II/examples/step-52/doc/intro.dox index ccdff55a21..c3d93510ef 100644 --- a/deal.II/examples/step-52/doc/intro.dox +++ b/deal.II/examples/step-52/doc/intro.dox @@ -142,14 +142,14 @@ where {\cal A}_{ij} &= (\Sigma_a\psi_i,\psi_j)_\Omega, \\ {\cal S}_{i}(t) &= (\psi_i,S(x,t))_\Omega. @f} -Boundary terms are not necessary due to the chosen boundary conditions. +%Boundary terms are not necessary due to the chosen boundary conditions. To use the Runge-Kutta methods, we can then recast this as follows: @f{eqnarray*} -f(y) = -{\cal D)y - {\cal A}y + {\cal S} +f(y) = -{\cal D}y - {\cal A}y + {\cal S} @f} In the code, we will need to be able to evaluate this function $f(U)$ along with its derivative. However, in view of the linearity of $f$, we will be able -to use $\frac{\partial f}{\partial y} y = f(y)$. +to use that $\frac{\partial f}{\partial y} y = f(y)$.

Remarks

@@ -159,8 +159,12 @@ elements and the exact solution is quadratic). Going from a two dimensional domain to a three dimensional domain is not very challenging. However if the mesh must be adapted, it is important to remember to do the following:
    -
  1. Project the solution to the new mesh when the mesh is changed. The mesh - used should be the same at the beginning and at the end of the time step. -
  2. update the mass matrix and its inverse. +
  3. Project the solution to the new mesh when the mesh is changed. Of course, + the mesh + used should be the same at the beginning and at the end of the time step, + a question that arises because Runge-Kutta methods use multiple + evaluations of the equations within each time step. +
  4. You will need to update the mass matrix and its inverse every time the + mesh is changed.
-The techniques to do all of this are available in step-26. +The techniques for these steps are readily available by looking at step-26. -- 2.39.5