In each cycle, the program furthermore writes the grid in EPS
format. These are shown in the following:
-
-
-<TABLE WIDTH="100%">
-<tr>
-<td>
- <img src="https://www.dealii.org/images/steps/developer/step-6.grid-0.png" alt="">
-</td>
-<td>
- <img src="https://www.dealii.org/images/steps/developer/step-6.grid-1.png" alt="">
-</td>
-</tr>
-
-<tr>
-<td>
- <img src="https://www.dealii.org/images/steps/developer/step-6.grid-2.png" alt="">
-</td>
-<td>
- <img src="https://www.dealii.org/images/steps/developer/step-6.grid-3.png" alt="">
-</td>
-</tr>
-
-<tr>
-<td>
- <img src="https://www.dealii.org/images/steps/developer/step-6.grid-4.png" alt="">
-</td>
-<td>
- <img src="https://www.dealii.org/images/steps/developer/step-6.grid-5.png" alt="">
-</td>
-</tr>
-
-<tr>
-<td>
- <img src="https://www.dealii.org/images/steps/developer/step-6.grid-6.png" alt="">
-</td>
-<td>
- <img src="https://www.dealii.org/images/steps/developer/step-6.grid-7.png" alt="">
-</td>
-</tr>
-</table>
-
+<div class="twocolumn" style="width: 80%">
+ <div>
+ <img src="https://www.dealii.org/images/steps/developer/step_6_grid_0.svg"
+ alt="Initial grid: the five-cell circle grid with one global refinement."
+ width="300" height="300">
+ </div>
+ <div>
+ <img src="https://www.dealii.org/images/steps/developer/step_6_grid_1.svg"
+ alt="First grid: the five-cell circle grid with two global refinements."
+ width="300" height="300">
+ </div>
+ <div>
+ <img src="https://www.dealii.org/images/steps/developer/step_6_grid_2.svg"
+ alt="Second grid: the five-cell circle grid with one adaptive refinement."
+ width="300" height="300">
+ </div>
+ <div>
+ <img src="https://www.dealii.org/images/steps/developer/step_6_grid_3.svg"
+ alt="Third grid: the five-cell circle grid with two adaptive
+ refinements, showing clustering around the inner circle."
+ width="300" height="300">
+ </div>
+ <div>
+ <img src="https://www.dealii.org/images/steps/developer/step_6_grid_4.svg"
+ alt="Fourth grid: the five-cell circle grid with three adaptive
+ refinements, showing clustering around the inner circle."
+ width="300" height="300">
+ </div>
+ <div>
+ <img src="https://www.dealii.org/images/steps/developer/step_6_grid_5.svg"
+ alt="Fifth grid: the five-cell circle grid with four adaptive
+ refinements, showing clustering around the inner circle."
+ width="300" height="300">
+ </div>
+ <div>
+ <img src="https://www.dealii.org/images/steps/developer/step_6_grid_6.svg"
+ alt="Sixth grid: the five-cell circle grid with five adaptive
+ refinements, showing clustering around the inner circle."
+ width="300" height="300">
+ </div>
+ <div>
+ <img src="https://www.dealii.org/images/steps/developer/step_6_grid_7.svg"
+ alt="Last grid: the five-cell circle grid with six adaptive
+ refinements, showing that most cells are clustered around the inner circle."
+ width="300" height="300">
+ </div>
+</div>
It is clearly visible that the region where the solution has a kink,
After a few global refinement steps, this would lead to a mesh of the following
kind:
-<img src="https://www.dealii.org/images/steps/developer/step-6.manifold-grid-4-bad.png" alt="">
+
+ <div class="onecolumn" style="width: 80%">
+ <div>
+ <img src="https://www.dealii.org/images/steps/developer/step_6_bad_grid_4.svg"
+ alt="Grid where some central cells are nearly triangular."
+ width="300" height="300">
+ </div>
+ </div>
This is not a good mesh: the central cell has been refined in such a way that
the children located in the four corners of the original central cell
This code then generates the following, much better sequence of meshes:
-<TABLE WIDTH="100%">
-<tr>
-<td>
- <img src="https://www.dealii.org/images/steps/developer/step-6.manifold-grid-0.png" alt="">
-</td>
-<td>
- <img src="https://www.dealii.org/images/steps/developer/step-6.manifold-grid-1.png" alt="">
-</td>
-</tr>
-
-<tr>
-<td>
- <img src="https://www.dealii.org/images/steps/developer/step-6.manifold-grid-2.png" alt="">
-</td>
-<td>
- <img src="https://www.dealii.org/images/steps/developer/step-6.manifold-grid-3.png" alt="">
-</td>
-</tr>
-
-<tr>
-<td>
- <img src="https://www.dealii.org/images/steps/developer/step-6.manifold-grid-4.png" alt="">
-</td>
-<td>
- <img src="https://www.dealii.org/images/steps/developer/step-6.manifold-grid-5.png" alt="">
-</td>
-</tr>
-
-<tr>
-<td>
- <img src="https://www.dealii.org/images/steps/developer/step-6.manifold-grid-6.png" alt="">
-</td>
-<td>
- <img src="https://www.dealii.org/images/steps/developer/step-6.manifold-grid-7.png" alt="">
-</td>
-</tr>
-</table>
-
+<div class="twocolumn" style="width: 80%">
+ <div>
+ <img src="https://www.dealii.org/images/steps/developer/step_6_grid_0_ladutenko.svg"
+ alt="Initial grid: the Ladutenko grid with one global refinement."
+ width="300" height="300">
+ </div>
+ <div>
+ <img src="https://www.dealii.org/images/steps/developer/step_6_grid_1_ladutenko.svg"
+ alt="First adaptively refined Ladutenko grid."
+ width="300" height="300">
+ </div>
+ <div>
+ <img src="https://www.dealii.org/images/steps/developer/step_6_grid_2_ladutenko.svg"
+ alt="Second adaptively refined Ladutenko grid."
+ width="300" height="300">
+ </div>
+ <div>
+ <img src="https://www.dealii.org/images/steps/developer/step_6_grid_3_ladutenko.svg"
+ alt="Third adaptively refined Ladutenko grid."
+ width="300" height="300">
+ </div>
+ <div>
+ <img src="https://www.dealii.org/images/steps/developer/step_6_grid_4_ladutenko.svg"
+ alt="Fourth adaptively refined Ladutenko grid. The cells are clustered
+ along the inner circle."
+ width="300" height="300">
+ </div>
+ <div>
+ <img src="https://www.dealii.org/images/steps/developer/step_6_grid_5_ladutenko.svg"
+ alt="Fifth adaptively refined Ladutenko grid: the cells are clustered
+ along the inner circle."
+ width="300" height="300">
+ </div>
+</div>
+
Creating good meshes, and in particular making them fit the geometry you
want, is a complex topic in itself. You can find much more on this in
step-49, step-53, and step-54, among other tutorial programs that cover