From ded5fe91367144b4629cb6e8a197905cf3339372 Mon Sep 17 00:00:00 2001 From: David Wells Date: Sat, 28 Apr 2018 17:39:29 -0400 Subject: [PATCH] Update images in step-6. --- examples/step-6/doc/results.dox | 169 +++++++++++++++++--------------- 1 file changed, 90 insertions(+), 79 deletions(-) diff --git a/examples/step-6/doc/results.dox b/examples/step-6/doc/results.dox index 5338b1542c..7c75a7540c 100644 --- a/examples/step-6/doc/results.dox +++ b/examples/step-6/doc/results.dox @@ -55,46 +55,53 @@ The final solution, as written by the program at the end of the In each cycle, the program furthermore writes the grid in EPS format. These are shown in the following: - - - - - - - - - - - - - - - - - - - - - - -
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- +
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+ Initial grid: the five-cell circle grid with one global refinement. +
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+ First grid: the five-cell circle grid with two global refinements. +
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+ Second grid: the five-cell circle grid with one adaptive refinement. +
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+ Third grid: the five-cell circle grid with two adaptive + refinements, showing clustering around the inner circle. +
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+ Fourth grid: the five-cell circle grid with three adaptive + refinements, showing clustering around the inner circle. +
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+ Fifth grid: the five-cell circle grid with four adaptive + refinements, showing clustering around the inner circle. +
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+ Sixth grid: the five-cell circle grid with five adaptive + refinements, showing clustering around the inner circle. +
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+ Last grid: the five-cell circle grid with six adaptive + refinements, showing that most cells are clustered around the inner circle. +
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It is clearly visible that the region where the solution has a kink, @@ -316,7 +323,14 @@ center of the mesh only fails for the central square of the mesh): After a few global refinement steps, this would lead to a mesh of the following kind: - + +
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+ Grid where some central cells are nearly triangular. +
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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 @@ -411,44 +425,41 @@ originally developed by Konstantin Ladutenko. We will use the following code: This code then generates the following, much better sequence of meshes: - - - - - - - - - - - - - - - - - - - - -
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- +
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+ Initial grid: the Ladutenko grid with one global refinement. +
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+ First adaptively refined Ladutenko grid. +
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+ Second adaptively refined Ladutenko grid. +
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+ Third adaptively refined Ladutenko grid. +
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+ Fourth adaptively refined Ladutenko grid. The cells are clustered + along the inner circle. +
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+ Fifth adaptively refined Ladutenko grid: the cells are clustered + along the inner circle. +
+
+ 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 -- 2.39.5