]> https://gitweb.dealii.org/ - dealii.git/commitdiff
Add 2d output. Add a few sentences.
authorWolfgang Bangerth <bangerth@math.tamu.edu>
Sat, 2 Feb 2008 02:58:46 +0000 (02:58 +0000)
committerWolfgang Bangerth <bangerth@math.tamu.edu>
Sat, 2 Feb 2008 02:58:46 +0000 (02:58 +0000)
git-svn-id: https://svn.dealii.org/trunk@15705 0785d39b-7218-0410-832d-ea1e28bc413d

deal.II/examples/step-31/doc/intro.dox
deal.II/examples/step-31/doc/results.dox

index aaa90cd687684eb7db0b948b8e747a328422e620..34a85e260b27427a83ade3d7f3bd1fb8f0de8e9d 100644 (file)
@@ -445,8 +445,27 @@ direct solver such as UMFPACK inefficient: only for problem sizes of a
 few 10,000 to maybe 100,000 unknowns can a sparse decomposition be
 computed using reasonable time and memory resources.
 
-SO WHAT TO DO HERE?
+What we do in that case is to use an incomplete LU decomposition (ILU) as a
+preconditioner, rather than actually computing complete LU factors. As it so
+happens, deal.II has a class that does this: SparseILU. Computing the ILU
+takes a time that only depends on the number of nonzero entries in the sparse
+matrix (or that we are willing to fill in the LU factors, if these should be
+more than the ones in the matrix), but is independent of the bandwidth of the
+matrix. It is therefore an operation that can efficiently also be computed in
+3d. On the other hand, an incomplete LU decomposition, by definition, does not
+represent an exact inverse of the matrix $A$. Consequently, preconditioning
+with the ILU will still require more than one iteration, unlike
+preconditioning with the sparse direct solver. The inner solver will therefore
+take more time when multiplying with the Schur complement, a tradeoff
+unavoidable.
+</ol>
 
 
-</ol>
+<h2>Implementation</h2>
+
+Note anything here that would be particular about this program.
+
+
+<h2>The testcase</h2>
 
+Describe the testcase we are dealing with here.
index b54aab4203ef1ea6b5c4e03dcf574176252cffb2..f1248247be5c3671458d7683cb164f00f531d377 100644 (file)
@@ -2,6 +2,59 @@
 <h1>Results</h1>
 
 
+
+
+
+
+
+
+<TABLE WIDTH="60%" ALIGN="center">
+  <tr>
+    <td ALIGN="center">
+      @image html step-31.2d.mesh-0.png
+    </td>
+
+    <td ALIGN="center">
+      @image html step-31.2d.mesh-1.png
+    </td>
+  </tr>
+
+  <tr>
+    <td ALIGN="center">
+      @image html step-31.2d.mesh-2.png
+    </td>
+
+    <td ALIGN="center">
+      @image html step-31.2d.mesh-3.png
+    </td>
+  </tr>
+
+  <tr>
+    <td ALIGN="center">
+      @image html step-31.2d.mesh-4.png
+    </td>
+
+    <td ALIGN="center">
+      @image html step-31.2d.mesh-5.png
+    </td>
+  </tr>
+
+  <tr>
+    <td ALIGN="center">
+      @image html step-31.2d.mesh-6.png
+    </td>
+
+    <td ALIGN="center">
+    </td>
+  </tr>
+</table>
+
+@image html step-31.2d.solution.png
+
+
+
+
+
 Output in 3d:
 @code
 Refinement cycle 0
@@ -61,23 +114,57 @@ Refinement cycle 6
    15 CG Schur complement iterations for pressure.
 @endcode
 
+Note that the number of (outer) iterations does not increase as we refine the
+mesh. 
+
 Compute times for each iteration alone: seconds, seconds, 1 minute, 8
 minutes, 33 minutes, 3h37, 24h55
 
 Pictures
 
-@image html step-31.3d.mesh-0.png
-
-@image html step-31.3d.mesh-1.png
+<TABLE WIDTH="60%" ALIGN="center">
+  <tr>
+    <td ALIGN="center">
+      @image html step-31.3d.mesh-0.png
+    </td>
+
+    <td ALIGN="center">
+      @image html step-31.3d.mesh-1.png
+    </td>
+  </tr>
+
+  <tr>
+    <td ALIGN="center">
+      @image html step-31.3d.mesh-2.png
+    </td>
+
+    <td ALIGN="center">
+      @image html step-31.3d.mesh-3.png
+    </td>
+  </tr>
+
+  <tr>
+    <td ALIGN="center">
+      @image html step-31.3d.mesh-4.png
+    </td>
+
+    <td ALIGN="center">
+      @image html step-31.3d.mesh-5.png
+    </td>
+  </tr>
+
+  <tr>
+    <td ALIGN="center">
+      @image html step-31.3d.mesh-6.png
+    </td>
+
+    <td ALIGN="center">
+    </td>
+  </tr>
+</table>
 
-@image html step-31.3d.mesh-2.png
-
-@image html step-31.3d.mesh-3.png
+@image html step-31.3d.solution.png
 
-@image html step-31.3d.mesh-4.png
 
-@image html step-31.3d.mesh-5.png
 
-@image html step-31.3d.mesh-6.png
 
-@image html step-31.3d.solution.png

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