<TABLE WIDTH="60%" ALIGN="center">
<tr>
<td ALIGN="center">
- @image html step-1.grid-1.png
+ <img src="http://www.dealii.org/images/steps/developer/step-1.grid-1.png" alt="">
</td>
<td ALIGN="center">
- @image html step-1.grid-2.png
+ <img src="http://www.dealii.org/images/steps/developer/step-1.grid-2.png" alt="">
</td>
</tr>
</table>
<table "width=80%" align="center">
<tr>
<td>
- @image html step-10.ball_mapping_q1_ref0.png
+ <img src="http://www.dealii.org/images/steps/developer/step-10.ball_mapping_q1_ref0.png" alt="">
</td>
<td>
- @image html step-10.ball_mapping_q1_ref1.png
+ <img src="http://www.dealii.org/images/steps/developer/step-10.ball_mapping_q1_ref1.png" alt="">
</td>
</tr>
<tr>
<td>
- @image html step-10.ball_mapping_q2_ref0.png
+ <img src="http://www.dealii.org/images/steps/developer/step-10.ball_mapping_q2_ref0.png" alt="">
</td>
<td>
- @image html step-10.ball_mapping_q2_ref1.png
+ <img src="http://www.dealii.org/images/steps/developer/step-10.ball_mapping_q2_ref1.png" alt="">
</td>
</tr>
<tr>
<td>
- @image html step-10.ball_mapping_q3_ref0.png
+ <img src="http://www.dealii.org/images/steps/developer/step-10.ball_mapping_q3_ref0.png" alt="">
</td>
<td>
- @image html step-10.ball_mapping_q3_ref1.png
+ <img src="http://www.dealii.org/images/steps/developer/step-10.ball_mapping_q3_ref1.png" alt="">
</td>
</tr>
</table>
<table "width=80%" align="center">
<tr>
<td>
- @image html step-10.quarter-q1.png
+ <img src="http://www.dealii.org/images/steps/developer/step-10.quarter-q1.png" alt="">
</td>
<td>
- @image html step-10.quarter-q2.png
+ <img src="http://www.dealii.org/images/steps/developer/step-10.quarter-q2.png" alt="">
</td>
<td>
- @image html step-10.quarter-q3.png
+ <img src="http://www.dealii.org/images/steps/developer/step-10.quarter-q3.png" alt="">
</td>
</tr>
</table>
We show the solutions on the initial mesh, the mesh after two
and after five adaptive refinement steps.
-@image html step-12.sol-0.png
-@image html step-12.sol-2.png
-@image html step-12.sol-5.png
+<img src="http://www.dealii.org/images/steps/developer/step-12.sol-0.png" alt="">
+<img src="http://www.dealii.org/images/steps/developer/step-12.sol-2.png" alt="">
+<img src="http://www.dealii.org/images/steps/developer/step-12.sol-5.png" alt="">
Then we show the final grid (after 5 refinement steps) and the solution again,
sharpness of the jump on the refined mesh and the over- and undershoots of the
solution along the interface:
-@image html step-12.grid-5.png
-@image html step-12.3d-solution.png
+<img src="http://www.dealii.org/images/steps/developer/step-12.grid-5.png" alt="">
+<img src="http://www.dealii.org/images/steps/developer/step-12.3d-solution.png" alt="">
And finally we show a plot of a 3d computation.
-@image html step-12.sol-5-3d.png
+<img src="http://www.dealii.org/images/steps/developer/step-12.sol-5-3d.png" alt="">
<a name="dg-vs-cg"></a>
0
</td>
<td valign="top">
- @image html step-12.cg.sol-0.png
+ <img src="http://www.dealii.org/images/steps/developer/step-12.cg.sol-0.png" alt="">
</td>
<td valign="top">
1
</td>
<td valign="top">
- @image html step-12.cg.sol-1.png
+ <img src="http://www.dealii.org/images/steps/developer/step-12.cg.sol-1.png" alt="">
</td>
</tr>
2
</td>
<td valign="top">
- @image html step-12.cg.sol-2.png
+ <img src="http://www.dealii.org/images/steps/developer/step-12.cg.sol-2.png" alt="">
</td>
<td valign="top">
3
</td>
<td valign="top">
- @image html step-12.cg.sol-3.png
+ <img src="http://www.dealii.org/images/steps/developer/step-12.cg.sol-3.png" alt="">
</td>
</tr>
4
</td>
<td valign="top">
- @image html step-12.cg.sol-4.png
+ <img src="http://www.dealii.org/images/steps/developer/step-12.cg.sol-4.png" alt="">
</td>
<td valign="top">
5
</td>
<td valign="top">
- @image html step-12.cg.sol-5.png
+ <img src="http://www.dealii.org/images/steps/developer/step-12.cg.sol-5.png" alt="">
</td>
</tr>
</table>
<table width="80%" align="center">
<tr>
<td>
- @image html step-13.solution-kelly-0.png
+ <img src="http://www.dealii.org/images/steps/developer/step-13.solution-kelly-0.png" alt="">
</td>
<td>
- @image html step-13.solution-kelly-1.png
+ <img src="http://www.dealii.org/images/steps/developer/step-13.solution-kelly-1.png" alt="">
</td>
</tr>
<tr>
<td>
- @image html step-13.solution-kelly-2.png
+ <img src="http://www.dealii.org/images/steps/developer/step-13.solution-kelly-2.png" alt="">
</td>
<td>
- @image html step-13.solution-kelly-3.png
+ <img src="http://www.dealii.org/images/steps/developer/step-13.solution-kelly-3.png" alt="">
</td>
</tr>
<tr>
<td>
- @image html step-13.solution-kelly-4.png
+ <img src="http://www.dealii.org/images/steps/developer/step-13.solution-kelly-4.png" alt="">
</td>
<td>
- @image html step-13.solution-kelly-5.png
+ <img src="http://www.dealii.org/images/steps/developer/step-13.solution-kelly-5.png" alt="">
</td>
</tr>
<tr>
<td>
- @image html step-13.solution-kelly-6.png
+ <img src="http://www.dealii.org/images/steps/developer/step-13.solution-kelly-6.png" alt="">
</td>
<td>
- @image html step-13.solution-kelly-7.png
+ <img src="http://www.dealii.org/images/steps/developer/step-13.solution-kelly-7.png" alt="">
</td>
</tr>
<tr>
<td>
- @image html step-13.solution-kelly-8.png
+ <img src="http://www.dealii.org/images/steps/developer/step-13.solution-kelly-8.png" alt="">
</td>
<td>
- @image html step-13.solution-kelly-9.png
+ <img src="http://www.dealii.org/images/steps/developer/step-13.solution-kelly-9.png" alt="">
</td>
</tr>
</table>
viewed from top:
-@image html step-13.grid-kelly-8.png
+<img src="http://www.dealii.org/images/steps/developer/step-13.grid-kelly-8.png" alt="">
However, we are not yet finished with evaluation the point value
refinement criteria yields the following picture:
-@image html step-13.error.png
+<img src="http://www.dealii.org/images/steps/developer/step-13.error.png" alt="">
<table align="center">
<tr>
<td width="50%">
- @image html step-14.point-value.solution-5.png
+ <img src="http://www.dealii.org/images/steps/developer/step-14.point-value.solution-5.png" alt="">
</td>
<td width="50%">
- @image html step-14.point-value.solution-5-dual.png
+ <img src="http://www.dealii.org/images/steps/developer/step-14.point-value.solution-5-dual.png" alt="">
</td>
</tr>
</table>
<table align="center">
<tr>
<td width="50%">
- @image html step-14.point-value.grid-0.png
+ <img src="http://www.dealii.org/images/steps/developer/step-14.point-value.grid-0.png" alt="">
</td>
<td width="50%">
- @image html step-14.point-value.grid-2.png
+ <img src="http://www.dealii.org/images/steps/developer/step-14.point-value.grid-2.png" alt="">
</td>
</tr>
<tr>
<td width="50%">
- @image html step-14.point-value.grid-4.png
+ <img src="http://www.dealii.org/images/steps/developer/step-14.point-value.grid-4.png" alt="">
</td>
<td width="50%">
- @image html step-14.point-value.grid-5.png
+ <img src="http://www.dealii.org/images/steps/developer/step-14.point-value.grid-5.png" alt="">
</td>
</tr>
<tr>
<td width="50%">
- @image html step-14.point-value.grid-7.png
+ <img src="http://www.dealii.org/images/steps/developer/step-14.point-value.grid-7.png" alt="">
</td>
<td width="50%">
- @image html step-14.point-value.grid-8.png
+ <img src="http://www.dealii.org/images/steps/developer/step-14.point-value.grid-8.png" alt="">
</td>
</tr>
</table>
<table align="center">
<tr>
<td width="50%">
- @image html step-14.point-value.error.png
+ <img src="http://www.dealii.org/images/steps/developer/step-14.point-value.error.png" alt="">
</td>
<td width="50%">
- @image html step-14.point-value.error-estimation.png
+ <img src="http://www.dealii.org/images/steps/developer/step-14.point-value.error-estimation.png" alt="">
</td>
</tr>
</table>
is the distance to the evaluation point; it can be shown that this is
the optimal weight if we neglect the effects of boundaries):
-@image html step-14.point-value.error-comparison.png
+<img src="http://www.dealii.org/images/steps/developer/step-14.point-value.error-comparison.png" alt="">
<table align="center">
<tr>
<td width="50%">
- @image html step-14.point-derivative.solution-5-dual.png
+ <img src="http://www.dealii.org/images/steps/developer/step-14.point-derivative.solution-5-dual.png" alt="">
</td>
</table>
This time, the grids in refinement cycles 0, 5, 6, 7, 8, and 9 look
<table align="center">
<tr>
<td width="50%">
- @image html step-14.point-derivative.grid-0.png
+ <img src="http://www.dealii.org/images/steps/developer/step-14.point-derivative.grid-0.png" alt="">
</td>
<td width="50%">
- @image html step-14.point-derivative.grid-5.png
+ <img src="http://www.dealii.org/images/steps/developer/step-14.point-derivative.grid-5.png" alt="">
</td>
</tr>
<tr>
<td width="50%">
- @image html step-14.point-derivative.grid-6.png
+ <img src="http://www.dealii.org/images/steps/developer/step-14.point-derivative.grid-6.png" alt="">
</td>
<td width="50%">
- @image html step-14.point-derivative.grid-7.png
+ <img src="http://www.dealii.org/images/steps/developer/step-14.point-derivative.grid-7.png" alt="">
</td>
</tr>
<tr>
<td width="50%">
- @image html step-14.point-derivative.grid-8.png
+ <img src="http://www.dealii.org/images/steps/developer/step-14.point-derivative.grid-8.png" alt="">
</td>
<td width="50%">
- @image html step-14.point-derivative.grid-9.png
+ <img src="http://www.dealii.org/images/steps/developer/step-14.point-derivative.grid-9.png" alt="">
</td>
</tr>
</table>
<table align="center">
<tr>
<td width="50%">
- @image html step-14.point-derivative.error.png
+ <img src="http://www.dealii.org/images/steps/developer/step-14.point-derivative.error.png" alt="">
</td>
<td width="50%">
- @image html step-14.point-derivative.error-estimation.png
+ <img src="http://www.dealii.org/images/steps/developer/step-14.point-derivative.error-estimation.png" alt="">
</td>
</tr>
</table>
<table align="center">
<tr>
<td width="50%">
- @image html step-14.step-13.grid-9.png
+ <img src="http://www.dealii.org/images/steps/developer/step-14.step-13.grid-9.png" alt="">
</td>
<td width="50%">
- @image html step-14.step-13.grid-10.png
+ <img src="http://www.dealii.org/images/steps/developer/step-14.step-13.grid-10.png" alt="">
</td>
</tr>
</table>
<table align="center">
<tr>
<td width="50%" align="center">
- @image html step-14.step-13.solution-7.png
+ <img src="http://www.dealii.org/images/steps/developer/step-14.step-13.solution-7.png" alt="">
</td>
</tr>
</table>
The next point is to compare the new (duality based) mesh refinement
criterion with the old ones. These are the results:
-@image html step-14.step-13.error-comparison.png
+<img src="http://www.dealii.org/images/steps/developer/step-14.step-13.error-comparison.png" alt="">
<TABLE WIDTH="100%">
<tr>
<td>
- @image html step-15.solution-0.png
+ <img src="http://www.dealii.org/images/steps/developer/step-15.solution-0.png" alt="">
</td>
<td>
- @image html step-15.solution-1.png
+ <img src="http://www.dealii.org/images/steps/developer/step-15.solution-1.png" alt="">
</td>
</tr>
<tr>
<td>
- @image html step-15.solution-2.png
+ <img src="http://www.dealii.org/images/steps/developer/step-15.solution-2.png" alt="">
</td>
<td>
- @image html step-15.solution-3.png
+ <img src="http://www.dealii.org/images/steps/developer/step-15.solution-3.png" alt="">
</td>
</tr>
<tr>
<td>
- @image html step-15.solution-4.png
+ <img src="http://www.dealii.org/images/steps/developer/step-15.solution-4.png" alt="">
</td>
<td>
- @image html step-15.solution-5.png
+ <img src="http://www.dealii.org/images/steps/developer/step-15.solution-5.png" alt="">
</td>
</tr>
<tr>
<td>
- @image html step-15.solution-6.png
+ <img src="http://www.dealii.org/images/steps/developer/step-15.solution-6.png" alt="">
</td>
<td>
- @image html step-15.solution-7.png
+ <img src="http://www.dealii.org/images/steps/developer/step-15.solution-7.png" alt="">
</td>
</tr>
</table>
because there isn't much change in the solution. The final solution
and mesh are shown here:
-@image html step-15.grid.png
+<img src="http://www.dealii.org/images/steps/developer/step-15.grid.png" alt="">
least one colorful picture, here is, again, the solution:
<p align="center">
- @image html step-16.solution.png
+ <img src="http://www.dealii.org/images/steps/developer/step-16.solution.png" alt="">
</p>
When run, the output of this program is
300,000 unknowns:
-@image html step-17.12-ux.png
-@image html step-17.12-uy.png
+<img src="http://www.dealii.org/images/steps/developer/step-17.12-ux.png" alt="">
+<img src="http://www.dealii.org/images/steps/developer/step-17.12-uy.png" alt="">
though, is to look at the mesh and partition at this step:
-@image html step-17.12-grid.png
-@image html step-17.12-partition.png
+<img src="http://www.dealii.org/images/steps/developer/step-17.12-grid.png" alt="">
+<img src="http://www.dealii.org/images/steps/developer/step-17.12-partition.png" alt="">
Again, the mesh (left) shows the same refinement pattern as seen
we contend ourselves with showing output from cycle 4:
-@image html step-17.4-3d-partition.png
-@image html step-17.4-3d-ux.png
+<img src="http://www.dealii.org/images/steps/developer/step-17.4-3d-partition.png" alt="">
+<img src="http://www.dealii.org/images/steps/developer/step-17.4-3d-ux.png" alt="">
The left picture shows the partitioning of the cube into 16 processes, whereas
We can then visualize this one file with gnuplot, obtaining something like
this:
-@image html step-19.solution-0005.png
+<img src="http://www.dealii.org/images/steps/developer/step-19.solution-0005.png" alt="">
That's not particularly exciting, but the file we're looking at has only one
32nd of the entire domain anyway, so we can't expect much.
<TABLE WIDTH="60%" ALIGN="center">
<tr>
<td ALIGN="center">
- @image html step-2.sparsity-1.png
+ <img src="http://www.dealii.org/images/steps/developer/step-2.sparsity-1.png" alt="">
</td>
<td ALIGN="center">
- @image html step-2.sparsity-2.png
+ <img src="http://www.dealii.org/images/steps/developer/step-2.sparsity-2.png" alt="">
</td>
</tr>
</table>
solution, let us take a look at it. The following three images show (from left
to right) the x-velocity, the y-velocity, and the pressure:
-@image html step-20.u.png
-@image html step-20.v.png
-@image html step-20.p.png
+<img src="http://www.dealii.org/images/steps/developer/step-20.u.png" alt="">
+<img src="http://www.dealii.org/images/steps/developer/step-20.v.png" alt="">
+<img src="http://www.dealii.org/images/steps/developer/step-20.p.png" alt="">
x- and y-velocity:
-@image html step-20.u-wiggle.png
-@image html step-20.v-wiggle.png
+<img src="http://www.dealii.org/images/steps/developer/step-20.u-wiggle.png" alt="">
+<img src="http://www.dealii.org/images/steps/developer/step-20.v-wiggle.png" alt="">
It is obvious how fluids flow essentially only along the middle line, and not
inverse of this tensor (i.e., of <code>normalized_permeability</code>)
looks as follows:
-@image html step-20.k-random.png
+<img src="http://www.dealii.org/images/steps/developer/step-20.k-random.png" alt="">
With a permeability field like this, we would get x-velocities and pressures as
follows:
-@image html step-20.u-random.png
-@image html step-20.p-random.png
+<img src="http://www.dealii.org/images/steps/developer/step-20.u-random.png" alt="">
+<img src="http://www.dealii.org/images/steps/developer/step-20.p-random.png" alt="">
We will use these permeability fields again in step-21 and step-43.
The grids of fast and thermal energy groups at mesh iteration #9 are shown
in following figure.
-@image html step-28.grid-0.9.order2.png
+<img src="http://www.dealii.org/images/steps/developer/step-28.grid-0.9.order2.png" alt="">
-@image html step-28.grid-1.9.order2.png
+<img src="http://www.dealii.org/images/steps/developer/step-28.grid-1.9.order2.png" alt="">
We see that the grid of thermal group is much finner than the one of fast group.
The solutions on these grids are, (Note: flux are normalized with total fission
source equal to 1)
-@image html step-28.solution-0.9.order2.png
+<img src="http://www.dealii.org/images/steps/developer/step-28.solution-0.9.order2.png" alt="">
-@image html step-28.solution-1.9.order2.png
+<img src="http://www.dealii.org/images/steps/developer/step-28.solution-1.9.order2.png" alt="">
Then we plot the convergence data with polynomial order being equal to 1,2 and 3.
-@image html step-28.convergence.png
+<img src="http://www.dealii.org/images/steps/developer/step-28.convergence.png" alt="">
The estimated ``exact'' k-effective = 0.906834721253 which is simply from last
mesh iteration of polynomial order 3 minus 2e-10. We see that h-adaptive calculations
<TABLE WIDTH="60%" ALIGN="center">
<tr>
<td ALIGN="center">
- @image html step-3.solution-1.png
+ <img src="http://www.dealii.org/images/steps/developer/step-3.solution-1.png" alt="">
</td>
<td ALIGN="center">
- @image html step-3.solution-2.png
+ <img src="http://www.dealii.org/images/steps/developer/step-3.solution-2.png" alt="">
</td>
</tr>
</table>
<TABLE WIDTH="60%" ALIGN="center">
<tr>
<td ALIGN="center">
- @image html step-30.sol-1.iso.png
+ <img src="http://www.dealii.org/images/steps/developer/step-30.sol-1.iso.png" alt="">
</td>
<td ALIGN="center">
- @image html step-30.sol-1.aniso.png
+ <img src="http://www.dealii.org/images/steps/developer/step-30.sol-1.aniso.png" alt="">
</td>
</tr>
<tr>
<td ALIGN="center">
- @image html step-30.sol-5.iso.png
+ <img src="http://www.dealii.org/images/steps/developer/step-30.sol-5.iso.png" alt="">
</td>
<td ALIGN="center">
- @image html step-30.sol-5.aniso.png
+ <img src="http://www.dealii.org/images/steps/developer/step-30.sol-5.aniso.png" alt="">
</td>
</tr>
</table>
refinement. This observation is strengthened by the plot of the an adapted
anisotropic grid, e.g. the grid after three refinement steps.
-@image html step-30.grid-3.aniso.png
+<img src="http://www.dealii.org/images/steps/developer/step-30.grid-3.aniso.png" alt="">
In the whole left part of the domain refinement is only performed along the
y-axis of cells. In the right part of the domain the refinement is dominated by
domain. The combination of the two for the two dimensional case looks
like
-@image html step-34_2d.png
+<img src="http://www.dealii.org/images/steps/developer/step-34_2d.png" alt="">
while in three dimensions we show first the potential on the surface,
together with a contur plot,
-@image html step-34_3d.png
+<img src="http://www.dealii.org/images/steps/developer/step-34_3d.png" alt="">
and then the external contour plot of the potential, with opacity set to 25%:
-@image html step-34_3d-2.png
+<img src="http://www.dealii.org/images/steps/developer/step-34_3d-2.png" alt="">
<a name="extensions"></a>
<TABLE WIDTH="100%">
<tr>
<td>
- @image html step-36.default.eigenfunction.0.png
+ <img src="http://www.dealii.org/images/steps/developer/step-36.default.eigenfunction.0.png" alt="">
</td>
<td>
- @image html step-36.default.eigenfunction.1.png
+ <img src="http://www.dealii.org/images/steps/developer/step-36.default.eigenfunction.1.png" alt="">
</td>
</tr>
<tr>
<td>
- @image html step-36.default.eigenfunction.2.png
+ <img src="http://www.dealii.org/images/steps/developer/step-36.default.eigenfunction.2.png" alt="">
</td>
<td>
- @image html step-36.default.eigenfunction.3.png
+ <img src="http://www.dealii.org/images/steps/developer/step-36.default.eigenfunction.3.png" alt="">
</td>
</tr>
<tr>
<td>
- @image html step-36.default.eigenfunction.4.png
+ <img src="http://www.dealii.org/images/steps/developer/step-36.default.eigenfunction.4.png" alt="">
</td>
<td>
</td>
potential is the lowest, i.e. in the top right and bottom left sector of inner
circle of the potential):
-@image html step-36.mod.potential.png
+<img src="http://www.dealii.org/images/steps/developer/step-36.mod.potential.png" alt="">
The first five eigenfunctions are now like this:
<TABLE WIDTH="100%">
<tr>
<td>
- @image html step-36.mod.eigenfunction.0.png
+ <img src="http://www.dealii.org/images/steps/developer/step-36.mod.eigenfunction.0.png" alt="">
</td>
<td>
- @image html step-36.mod.eigenfunction.1.png
+ <img src="http://www.dealii.org/images/steps/developer/step-36.mod.eigenfunction.1.png" alt="">
</td>
</tr>
<tr>
<td>
- @image html step-36.mod.eigenfunction.2.png
+ <img src="http://www.dealii.org/images/steps/developer/step-36.mod.eigenfunction.2.png" alt="">
</td>
<td>
- @image html step-36.mod.eigenfunction.3.png
+ <img src="http://www.dealii.org/images/steps/developer/step-36.mod.eigenfunction.3.png" alt="">
</td>
</tr>
<tr>
<td>
- @image html step-36.mod.eigenfunction.4.png
+ <img src="http://www.dealii.org/images/steps/developer/step-36.mod.eigenfunction.4.png" alt="">
</td>
<td>
</td>
solution. We show a picture anyway, illustrating the size of the
solution through both isocontours and volume rendering:
-@image html "step-37.solution.png"
+<img src="http://www.dealii.org/images/steps/developer/step-37.solution.png" alt="">
Of more interest is to evaluate some aspects of the multigrid solver.
When we run this program in 2D for quadratic ($Q_2$) elements, we get the
Finally, the program produces graphical output that we can visualize. Here is
a plot of the results:
-@image html step-38.solution-3d.png
+<img src="http://www.dealii.org/images/steps/developer/step-38.solution-3d.png" alt="">
The program also works for 1d curves in 2d, not just 2d surfaces in 3d. You
can test this by changing the template argument in <code>main()</code> like
solution extruded into the third dimension, clearly showing the change in sign
as the curve moves from one quadrant of the domain into the adjacent one):
-@image html step-38.solution-2d.png
+<img src="http://www.dealii.org/images/steps/developer/step-38.solution-2d.png" alt="">
<a name="extensions"></a>
the x- and y-coordinates a bit. Let's show the computational domain and the
solution first before we go into details of the implementation below:
-@image html step-38.warp-1.png
+<img src="http://www.dealii.org/images/steps/developer/step-38.warp-1.png" alt="">
-@image html step-38.warp-2.png
+<img src="http://www.dealii.org/images/steps/developer/step-38.warp-2.png" alt="">
The way to produce such a mesh is by using the GridTools::transform
function. It needs a way to transform each individual mesh point to a
<h2>Postprocessing of the logfile</h2>
-@image html "step-39-convergence.png"
+<img src="http://www.dealii.org/images/steps/developer/step-39-convergence.png" alt="">
Using the perl script <tt>postprocess.pl</tt>, we extract relevant
data into <tt>output.dat</tt>, which can be used to plot graphs with
<tt>gnuplot</tt>. The graph above for instance was produced with
<TABLE WIDTH="100%">
<tr>
<td>
- @image html step-40.mesh.png
+ <img src="http://www.dealii.org/images/steps/developer/step-40.mesh.png" alt="">
</td>
<td>
- @image html step-40.solution.png
+ <img src="http://www.dealii.org/images/steps/developer/step-40.solution.png" alt="">
</td>
</tr>
</table>
<TABLE WIDTH="100%">
<tr>
<td>
- @image html step-40.strong2.png
+ <img src="http://www.dealii.org/images/steps/developer/step-40.strong2.png" alt="">
</td>
<td>
- @image html step-40.strong.png
+ <img src="http://www.dealii.org/images/steps/developer/step-40.strong.png" alt="">
</td>
</tr>
</table>
<TABLE WIDTH="100%">
<tr>
<td>
- @image html step-40.256.png
+ <img src="http://www.dealii.org/images/steps/developer/step-40.256.png" alt="">
</td>
<td>
- @image html step-40.4096.png
+ <img src="http://www.dealii.org/images/steps/developer/step-40.4096.png" alt="">
</td>
</tr>
</table>
concept in two space-dimensions. There, all dashed faces with the same color should
have the same boundary values:
-@image html step-45.periodic_cells.png
+<img src="http://www.dealii.org/images/steps/developer/step-45.periodic_cells.png" alt="">
To keep things simple, in this tutorial we will consider an academic,
simplified problem that allows us to focus on only that part that we are
required by the homogeneous Dirichlet boundary conditions. On the left and
right parts the values coincide with each other, just as we wanted:
-@image html step-45.solution.png
+<img src="http://www.dealii.org/images/steps/developer/step-45.solution.png" alt="">
Note also that the solution is clearly not left-right symmetric and so would
not likely have been periodic had we prescribed, for example, homogeneous
this is the mesh read from the .msh file and saved again by deal.II as an
image (see the grid_1 function):
-@image html step-49.grid-1.png
+<img src="http://www.dealii.org/images/steps/developer/step-49.grid-1.png" alt="">
<h3>Modifying a Mesh</h3>
<TABLE WIDTH="60%" ALIGN="center">
<tr>
<td ALIGN="center">
- @image html step-49.grid-5a.png regular input mesh
+ <img src="http://www.dealii.org/images/steps/developer/step-49.grid-5a.png" alt=""> regular input mesh
</td>
<td ALIGN="center">
- @image html step-49.grid-5.png output mesh
+ <img src="http://www.dealii.org/images/steps/developer/step-49.grid-5.png" alt=""> output mesh
</td>
</tr>
</TABLE>
<TABLE WIDTH="60%" ALIGN="center">
<tr>
<td ALIGN="center">
- @image html step-49.grid-6a.png regular input mesh
+ <img src="http://www.dealii.org/images/steps/developer/step-49.grid-6a.png" alt=""> regular input mesh
</td>
<td ALIGN="center">
- @image html step-49.grid-6.png wall-adapted output mesh
+ <img src="http://www.dealii.org/images/steps/developer/step-49.grid-6.png" alt=""> wall-adapted output mesh
</td>
</tr>
</TABLE>
<TABLE WIDTH="60%" ALIGN="center">
<tr>
<td ALIGN="center">
- @image html step-49.grid-7a.png regular input mesh
+ <img src="http://www.dealii.org/images/steps/developer/step-49.grid-7a.png" alt=""> regular input mesh
</td>
<td ALIGN="center">
- @image html step-49.grid-7.png perturbed output mesh
+ <img src="http://www.dealii.org/images/steps/developer/step-49.grid-7.png" alt=""> perturbed output mesh
</td>
</tr>
</TABLE>
<TABLE WIDTH="80%" ALIGN="center">
<tr>
<td ALIGN="center">
- @image html step-49.grid-2a.png input mesh 1
+ <img src="http://www.dealii.org/images/steps/developer/step-49.grid-2a.png" alt=""> input mesh 1
</td>
<td ALIGN="center">
- @image html step-49.grid-2b.png input mesh 2
+ <img src="http://www.dealii.org/images/steps/developer/step-49.grid-2b.png" alt=""> input mesh 2
</td>
<td ALIGN="center">
- @image html step-49.grid-2.png merged mesh
+ <img src="http://www.dealii.org/images/steps/developer/step-49.grid-2.png" alt=""> merged mesh
</td>
</tr>
</table>
<TABLE WIDTH="60%" ALIGN="center">
<tr>
<td ALIGN="center">
- @image html step-49.grid-3a.png input mesh
+ <img src="http://www.dealii.org/images/steps/developer/step-49.grid-3a.png" alt=""> input mesh
</td>
<td ALIGN="center">
- @image html step-49.grid-3.png top vertices moved upwards
+ <img src="http://www.dealii.org/images/steps/developer/step-49.grid-3.png" alt=""> top vertices moved upwards
</td>
</tr>
</table>
<TABLE WIDTH="60%" ALIGN="center">
<tr>
<td ALIGN="center">
- @image html step-49.grid-4base.png input mesh
+ <img src="http://www.dealii.org/images/steps/developer/step-49.grid-4base.png" alt=""> input mesh
</td>
<td ALIGN="center">
- @image html step-49.grid-4.png extruded output mesh
+ <img src="http://www.dealii.org/images/steps/developer/step-49.grid-4.png" alt=""> extruded output mesh
</td>
</tr>
</table>
here:
-@image html step-7.solution.png
+<img src="http://www.dealii.org/images/steps/developer/step-7.solution.png" alt="">
<TABLE WIDTH="100%">
<tr>
<td>
-@image html step-8.x.png
+<img src="http://www.dealii.org/images/steps/developer/step-8.x.png" alt="">
</td>
<td>
-@image html step-8.y.png
+<img src="http://www.dealii.org/images/steps/developer/step-8.y.png" alt="">
</td>
</tr>
</table>
$x=-0.5$, and of $y$-displacement at the origin. The next image shows the
final grid after eight steps of refinement:
-@image html step-8.grid.png
+<img src="http://www.dealii.org/images/steps/developer/step-8.grid.png" alt="">
What one frequently would like to do is to show the displacement as a vector
hundred vertices from which to draw the vectors; drawing them from each
individual vertex would make the picture unreadable):
-@image html step-8.vectors.png
+<img src="http://www.dealii.org/images/steps/developer/step-8.vectors.png" alt="">
We note that one may have intuitively expected the
displayed in the following picture:
-@image html step-9.grid.png
+<img src="http://www.dealii.org/images/steps/developer/step-9.grid.png" alt="">
solution itself:
-@image html step-9.solution.png
+<img src="http://www.dealii.org/images/steps/developer/step-9.solution.png" alt="">