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
|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.