Computing time vs order of accuracy
Using a higher order implies using smaller time steps and using more basis functions. The expected increase in computed time can then be estimated as follow:
Here is an example of the theoretical increase of the compute time relative to order 3
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
|
---|---|---|---|---|---|---|---|---|
Increase due to time steps |
1 |
1.4 |
1.8 |
2.2 |
2.6 |
3 |
3.4 |
3.8 |
Increase due to number of basis functions |
1 |
2 |
3.5 |
5.6 |
8.4 |
12 |
16.5 |
22 |
theoretical increase relative to order 3 |
1 |
2.8 |
6.3 |
12.32 |
21.84 |
36 |
56.1 |
83.6 |
observed increase (on SM2) |
1 |
2.0 |
4.6 |
11.5 |
The last line shows the observed time increase on SuperMUC Phase 2 on a small run with dynamic rupture and LTS-DR. Low order calculation (up to order 5 included) are memory bounds, and are then less efficient. As a consequence, the higher-order simulations cost less than expected in comparison with order 3.