Numerical accuracy analysis in simulations on hybrid high-performance computing systems

Více o knize

Estimating the numerical accuracy of computed results in complex simulation software is often challenging due to various numerical effects, particularly in systems developed over many years. Current developers may lack detailed knowledge of numerical properties in large sections of the source code, which may not have been thoroughly investigated during initial implementation. Many high-performance computing systems utilize GPUs, FPGAs, and specialized processors like the Cell processor, where low precision (e.g., single precision) floating point performance significantly outpaces high precision (e.g., double precision) performance. Although newer GPU architectures enhance double precision performance, the associated costs remain high, maintaining the performance-price ratio that often favors single precision arithmetic. Mixed-precision approaches are gaining traction, particularly for solving linear equations, but the impact of low precision on numerical accuracy must be verified. Additionally, even double precision can exhibit instability in certain algorithms. As simulation technology evolves, particularly in hybrid high-performance computing systems, analyzing numerical accuracy becomes increasingly crucial due to the varying accuracy of floating point arithmetic. Rounding errors are expected to escalate with larger problem sizes in the approaching exascale computing era. This thesis explores methods to estimate the numeric