Cause of MKL Pardiso convergence improvement with Parth-provided orderings in the Arma Roller IPC sequence

Determine whether MKL Pardiso’s improved ability to complete Newton time-step solves in the Arma Roller Incremental Potential Contact (IPC) benchmark when integrated with Parth arises from differences in the quality of permutation vectors generated by Parth compared to MKL’s custom METIS-based fill-reducing orderings, or from other MKL code-path or configuration changes triggered when MKL accepts user-supplied fill-reducing ordering vectors.

Background

Within the IPC benchmark, the authors observe that default MKL Pardiso sometimes fails to converge for the Arma Roller simulation due to numerical issues, a behavior consistent with prior IPC implementations. In contrast, when Parth is integrated and provides custom fill-reducing orderings, MKL completes more Newton time-step solves for this sequence.

The authors explicitly note uncertainty about the reason for this improvement—whether it stems from differences in the quality of Parth’s permutation vectors relative to MKL’s internal METIS routines, or from changes in MKL’s behavior when user-supplied orderings are provided. Clarifying this cause would inform both solver configuration and the interpretation of Parth’s numerical effects.

References

Interestingly, in contrast, we note that Parth-integrated MKL is able to complete more Newton time-step solves for the "Arma Roller" sequence. However, at this time we do not know if this change is due to differences in the quality between a few permutation vectors generated by Parth vs MKL's custom METIS routines or other code variations in the MKL settings that occur when we pass it custom fill-reducing orderings.

— Adaptive Algebraic Reuse of Reordering in Cholesky Factorization with Dynamic Sparsity Pattern  (2501.04011 - Zarebavani et al., 2024) in Section 5.6 (IPC: Parth Numerical Effect), after Table 3