Evaluating Performance of Mixed Precision Linear Solvers with Iterative Refinement

Abstract

The solution of systems of linear algebraic equations is among the time-consuming problems when performing the numerical simulations. One of the possible ways of improving the corresponding solver performance is the use of reduced precision calculations, which, however, may affect the accuracy of the obtained solution. The current paper analyzes the potential of using the mixed precision iterative refinement procedure to solve the systems of equations occurring as a result of the discretization of elliptic differential equations. The paper compares several inner solver stopping criteria and proposes the one allowing to eliminate the residual deviation and minimize the number of extra iterations. The presented numerical calculation results demonstrate the efficiency of the adopted algorithm and show about the decrease in the solution time by a factor of 1.5 for the turbulent flow simulations when using the iterative refinement procedure to solve the corresponding pressure Poisson equation.