Mechanism of reduced-precision failures in ill-conditioned multidimensional DSA systems

Investigate the common mechanism underlying the large solution changes and non-finite failures observed in ARDRA calculations using FP32 diffusion synthetic acceleration, particularly for poorly scaled or ill-conditioned two-dimensional DSA systems.

Background

The ARDRA automated test suite included 282 completed cases using FP64 transport calculations and FP32 hypre DSA solves. Although most cases passed, some two-dimensional criticality problems produced non-finite eigenvalues, while other calculations converged to solutions that differed measurably from the FP64 baseline. The paper associates these outcomes qualitatively with loss of accuracy or stability in ill-conditioned FP32 DSA systems, but does not establish a quantitatively verified common explanation. The unresolved issue is therefore to determine whether a single mechanism accounts for the observed non-finite failures and large solution perturbations, using simplified models to isolate the relevant conditioning and numerical-stability effects.

References

These observations do not quantitatively establish a common mechanism; further work with simplified models is warrented to investigate this.

— Reduced Precision Diffusion Synthetic Acceleration for S$_N$ Neutron Transport in LLNL's ARDRA using Hypre  (2609.04451 - Morgan et al., 3 Sep 2026) in Section 4.1, “Ardra's Automated Test Suite”