Changes between Version 2 and Version 3 of MiscellaneousQuestions

Timestamp:

Oct 24, 2008, 10:04:02 AM (16 years ago)

Author:

ole

Comment:

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MiscellaneousQuestions

@@ -12 +12 @@
 part blank. Or perhaps you can discuss the question in more detail.
 
+
+== Why does ANUGA get so slow when meshes are refined ==
+
+Two reasons:
+
+ * With smaller triangles timesteps tend to become smaller due to the CFL condition
+ * The computation time per timestep grows more than linearly with the number of triangles. Here is why
+
+{{{
+Let h be the grid size. The number of cells (triangles) N will normally be proportional to h^{-2}
+The size of the timesteps will be proportional to the grid size, and so the number of timesteps is proportional to h^{-1} = N^{1/2}
+So the computational cost (solution time) will be proportional to 
+(number of cells) x (no of timesteps) = N x N^{1/2} = N^{3/2} 
+log (Time) = 3/2 log( N).
+
+So increasing the grid size from 100 cells to 1000 cells grows the computational time by 10^{3/2} (about 30).
+}}}
+
+
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