| 14 | |

| 15 | == Why does ANUGA get so slow when meshes are refined == |

| 16 | |

| 17 | Two reasons: |

| 18 | |

| 19 | * With smaller triangles timesteps tend to become smaller due to the CFL condition |

| 20 | * The computation time per timestep grows more than linearly with the number of triangles. Here is why |

| 21 | |

| 22 | {{{ |

| 23 | Let h be the grid size. The number of cells (triangles) N will normally be proportional to h^{-2} |

| 24 | 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} |

| 25 | So the computational cost (solution time) will be proportional to |

| 26 | (number of cells) x (no of timesteps) = N x N^{1/2} = N^{3/2} |

| 27 | log (Time) = 3/2 log( N). |

| 28 | |

| 29 | So increasing the grid size from 100 cells to 1000 cells grows the computational time by 10^{3/2} (about 30). |

| 30 | }}} |

| 31 | |

| 32 | |