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Miscellaneous Questions

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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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