Multi-Time Step Nodal Subcycling Observations

Having applied multi-time step nodal subcycling to various problems we can conclude that this method is able to provide a significant time savings at a minimal cost to the accuracy of the solution. Although it is most optimal for problems where the number of calculations (or nodes) in the non-subcycled region is at least twice more than in the subcycled region.

In addition, as the subcycling parameter, ${\it m}$, is increased, the savings also increases due to the decreased number of explicit updates for each cycle. In Figure 4.5, we present the comparison of the $\%$ savings obtained for the various subcycling parameters as a function of the region ratio. The biggest increase occurs as the region ratio is doubled, with an average increase of $15\%$ for each subcycling parameter; beyond this, the savings appears to plateau out.

Although subcycling is able to achieve significant time savings, it comes at the cost due to the increase in the size of the nodal arrays required to track the displacements, velocities and accelerations. Furthermore, as the subcycling parameter is increased, the number of approximations also increases which leads to a loss in accuracy of the solution. From our results, the subcycling parameter should not be be greater than half of the critical value for the subcycled nodal regions, to avoid many of the instabilities resulting from the nodal approximations.

Figure 4.5: Percent time savings vs region ratio for various subcycling parameters.