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 LTSDR. Low order calculation (up to order 5 included) are memory bounds, and are then less efficient. As a consequence, the higherorder simulations cost less than expected in comparison with order 3.