From: bangerth Date: Sun, 10 Sep 2006 04:09:13 +0000 (+0000) Subject: Finishing touches X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=4ce873a0882f7c4268b32a0f4a59eb09e290945d;p=dealii-svn.git Finishing touches git-svn-id: https://svn.dealii.org/trunk@13884 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/examples/step-24/doc/intro.dox b/deal.II/examples/step-24/doc/intro.dox index 96dd500d91..441c30ac71 100644 --- a/deal.II/examples/step-24/doc/intro.dox +++ b/deal.II/examples/step-24/doc/intro.dox @@ -186,3 +186,13 @@ G_{1}+(k\, \theta)G_{2}-(c_0k)^2\theta (\theta F^{n}+(1-\theta)F^{n-1}) \\ Mv^n & = & -(c_0^2\,k\, \theta\, A+c_0B)\bar{p}^{n}+ G_2 - c_0^2k(\theta F^{n}+(1-\theta)F^{n-1}) @f} + + +

What the program does

+ +Compared to @ref step_23 "step-23", this programs adds the treatment of a +simple absorbing boundary conditions. In addition, it deals with data obtained +from actual experimental measurements. To this end, we need to evaluate the +solution at points at which the experiment also evaluates a real pressure +field. We will see how to do that using the VectorTools::point_value function +further down below. diff --git a/deal.II/examples/step-24/doc/results.dox b/deal.II/examples/step-24/doc/results.dox index e997942ef4..45fe566502 100644 --- a/deal.II/examples/step-24/doc/results.dox +++ b/deal.II/examples/step-24/doc/results.dox @@ -103,6 +103,14 @@ figures: +Note that in the experimental data, the first signal (i.e. the left-most dark +line) results from absorption at the tissue boundary, and therefore reaches +the detectors first and before any of the signals from the interior. This +signal is also faintly visible at the end of the traces, around 30 $\my s$, +which indicates that the signal travelled through the entire tissue to reach +detectors at the other side, after all the signals originating from the +interior have reached them. + As before, the numerical result better matches experimental ones by applying a bandwidth filter that matches the actual behavior of detectors (left) and by choosing a finer mesh (right): @@ -118,7 +126,19 @@ choosing a finer mesh (right): - +One of the important differences between the left and the right figure is that +the curves look much less "angular" at the right. The angularity comes from +the fact that while waves in the continuous equation travel equally fast in +all directions, this isn't the case after discretization: there, waves that +travel diagonal to cells move at slightly different speeds to those that move +parallel to mesh lines. This anisotropy leads to wave fronts that aren't +perfectly circular (and would produce sinusoidal signals in the stacked +plots), but are bulged out in certain directions. To make things worse, the +circular mesh we use (see for example @ref step_6 "step-6" for a view of the +coarse mesh) is not isotropic either. The net result is that the signal fronts +are not sinusoidal unless the mesh is sufficiently fine. The right image is a +lot better in this respect, though artificts in the form of trailing spurious +waves can still be seen.