Conclusions

In this chapter we presented the results of applying the multi-time step nodal subcycling, dynamic cohesive element insertion and code parallelization methods to 2-D problems. From our subcycling results we have found that the most important factors leading to an accurate and stable solution are the subcycling parameter and the region ratio. The greatest time savings is achieved at higher subcycling parameter values although the stability of the solution decreases. Furthermore, the region ratio must be at least $2:1$ to ensure that the computational savings offsets the cost of the subcycling algorithm implementation.

The dynamic insertion algorithm has also proven to be extremely significant. Using both pre-stretching combined with stress based cohesive element insertion allows us to generate the greatest computational savings while still maintaining an accurate solution.

Finally, we applied the Charm++ parallelization technique to our code. The results have shown promising speedups although improvements in the pre-processing and mesh repartitioning can achieve better results.