Practice question · Numerical answer
A three-dimensional simulation halves its grid spacing in all three directions and also halves its time step. By what factor does the total amount of work grow?
Hints
- Halving the spacing doubles the number of cells along each of the three axes.
- Then account separately for twice as many time steps.
Show the answer
16
Why
Eight times as many cells, each advanced through twice as many time steps, gives a factor of 16. This is why resolution is so expensive in three dimensions and why numerical efficiency is not a luxury.
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