<h1>Results</h1>
-Firstly, we present a comparison of a series of results with those
+Firstly, we present a comparison of a series of 3-d results with those
in the literature (see Reese et al (2000)) to demonstrate that the program works as expected.
We begin with a comparison of the convergence with mesh refinement for the $Q_1-DGPM_0-DGPM_0$ and
<td align="center">
<img src="http://www.dealii.org/images/steps/developer/step-44.Q1-P0_convergence.png" alt="">
<p align="center">
- Convergence of the $Q_1-DGPM_0-DGPM_0$ formulation.
+ Convergence of the $Q_1-DGPM_0-DGPM_0$ formulation in 3-d.
</p>
</td>
<td align="center">
<img src="http://www.dealii.org/images/steps/developer/step-44.Q2-P1_convergence.png" alt="">
<p align="center">
- Convergence of the $Q_2-DGPM_1-DGPM_1$ formulation.
+ Convergence of the $Q_2-DGPM_1-DGPM_1$ formulation in 3-d.
</p>
</td>
</tr>
<td align="center">
<img src="http://www.dealii.org/images/steps/developer/step-44.Q1-P0_gr_1_p_ratio_80-displacement.png" alt="">
<p align="center">
- Z-displacement solution.
+ Z-displacement solution for the 3-d problem.
</p>
</td>
<td align="center">
and the linear approximation of the pressure field allows a refined visualisation
of the pressure at the sub-element scale.
It should however be noted that the pressure field remains discontinuous
- and could be smoothed on a continuous grid for the post-processing purposes.
+and could be smoothed on a continuous grid for the post-processing purposes.
<td align="center">
<img src="http://www.dealii.org/images/steps/developer/step-44.Q2-P1_gr_3_p_ratio_80-displacement.png" alt="">
<p align="center">
- Z-displacement solution.
+ Z-displacement solution for the 3-d problem.
</p>
</td>
<td align="center">
This is shown in the graph below for a batch of tests run consecutively on a single 4-core (8-thread) machine.
The increase in computational time for the higher-order method is likely due to
the increased band-width required for the higher-order elements.
-As previously mentioned, the use of a better solver and precondtioner may mitigate the
+As previously mentioned, the use of a better solver and preconditioner may mitigate the
expense of using a higher-order formulation.
It was observed that for the given problem using the multithreaded Jacobi preconditioner can reduce the
computational runtime by up to 72% (for the worst case being a higher-order formulation with a large number
</tr>
</table>
+
+Lastly, results for the displacement solution for the 2-d problem are showcased below for
+two different levels of grid refinement.
+It is clear that due to the extra constraints imposed by simulating in 2-d that the resulting
+displacement field, although qualitatively similar, is different to that of the 3-d case.
+
+
+<table align="center" class="tutorial" cellspacing="3" cellpadding="3">
+
+ <tr>
+ <td align="center">
+ <img src="http://www.dealii.org/images/steps/developer/step-44.2d-gr_2.png" alt="">
+ <p align="center">
+ Y-displacement solution in 2-d for 2 global grid refinement levels.
+ </p>
+ </td>
+ <td align="center">
+ <img src="http://www.dealii.org/images/steps/developer/step-44.2d-gr_5.png" alt="">
+ <p align="center">
+ Y-displacement solution in 2-d for 5 global grid refinement levels.
+ </p>
+ </td>
+ </tr>
+</table>
+
<a name="extensions"></a>
<h3>Possibilities for extensions</h3>