Mass Scaling to reduce computational time
MASS SCALING:
OBJECTIVE:
The objective of this project is to simulate a highly non-linear transient dynamics problem or any other type of analysis that would be computationally intensive. Since our example problem would be computationally expensive it would also be more time consuming provided the memory usage is well within that of the most systems.
Hence our aim is to reduce this time consumed by the solver processors by implementing the concept of MASS SCALING. Using this criterion, elements that are either beyond or far lower from the nominal time step is either increased/decreased to meet this criterion.
Hence by mass scaling the model, we can establish a solver time of relatively low while simultaneously not affecting the desired output results that could occur if the model was made to run using the default solver settings.
CRITERIA:
The mass scaling feature is accessed through the *CONTROL_TIMESTEP card. While mass scaling elements come at a cost of "scaling the mass", this scaling is set to a tolerance level of 5% i.e the computational time is effectively reduced by generating fictitious mass on the elements while this fictitious mass is maintained well within 5% of change.
The tssfac (TimeStep Scale Factor) parameter of *CONTROL_TIMESTEP is kept at a constant of 0.9 thereby to impart a considerable amount of weight to the time step which will be changed for each trial to get the desired value.
PROCEDURE:
Initially, the simulation is computed without the *CONTROL_TIMESTEP card. This simulation would give us the default value of the estimated time of completion by the solver based on the complexity of the problem and the amount of processor memory used by the solver.
Here we can notice that the estimated time is around 22hrs.
Hence from hereon, we aim to reduce this estimated time by mass scaling,
NOTE: This is a trial and error method and there is no fixed default value for a given type of simulation.
1. dt2ms = -1E-5
The estimated time is about 79hrs 48mins
2. dt2ms = -2E-5
The estimated time of completion is about 60hrs 32mins
3. dt2ms = -3.5E-5
The estimated time of completion is about 22hrs
4. dt2ms = -5E-5
The estimated time of completion is about 21hrs 32mins and an added mass of 0.013%
We can also notice that a mass of 0.01% is added to reduce this complexity and to attain the nominal value.
This added mass value also represents that elements fall within this range specified using dt2ms and tssfac.
5. dt2ms = -6E-5
The estimated time of completion is about 17hrs 57mins and an added mass of 0.022%
6. dt2ms = -8E-5
The estimated time of completion is about 82hrs 43mins and an added mass of 0.14%
7. dt2ms = -9E-5
The estimated time of completion is about 12hrs 34mins and an added mass of 2.74%
8. dt2ms = -10E-5
The estimated time of completion is about 14hrs 48mins and an added mass of 6.42%
The above results are briefed to get a clear overview of how the computational time and added mass vary as the mass scaling factors and parameters are increased.
The entire trial and error simulations performed along with their estimated time, added mass and its percentage are shown below,
The histogram of the above-recorded dta is plotted below,
While it might be clear that for a dt2ms value of -16E-5 or perhaps even higher might be the most suitable value for this simulation to reduce its complexity and attain a completion time of about 6hrs, the added mass factor must also be considered. While we can observe the computational time gradually decreasing with minor pullbacks, this decrease in computational time as mentioned before comes at a cost of sacrificing the desired data which in this case is altered by scaling the mass.
CONCLUSION:
Hence from the above-gathered data, we can conclude that a balance between the reduction in computation time and the added mass must be maintained. Thus this balance must be maintained within a given set of criteria which in this case is a scaled mass tolerance of about 5% thereby not affecting the end result.
While any value for dt2ms after -9E-5 has a significant reduction in computational time, it comes at a cost of addition of fictitious mass to the system which is above 5%. This fictitious mass for each element could be rather alarming as it could affect the end result of the simulation.
Hence it suffices to say that a dt2ms of -9E-5 would be the ideal value reason being it has significantly reduced the computational time of the simulation by 12hrs 34mins from 22hrs i.e almost by a factor of 2 while maintaining the percentage of added mass well within its criteria thereby not modifying the complexity of the model and hence the desired outcome.