Accelerating the FlowSimulator: Influence of Mixed-Precision Preconditioning on GMRES

Abstract

This work highlights a potential drawback of applying mixedprecision techniques to the preconditioned GMRES iterative solver. When the preconditioner uses single-precision floating-point values, solution improvements beyond single-precision accuracy are lost during the solution update. The problem arises because the algorithm assumes the preconditioner to behave linearly in this phase. Using a preconditioner operating on single-precision vectors breaks this assumption and causes a loss of linearity, which limits the maximum achievable solution correction. While most studies show how mixed-precision may reduce runtime without losing accuracy, this work reveals a case where its blind use increases iterations or reduces accuracy. To the authors’ knowledge, this effect has not been previously investigated.