Discretization-Error-Accurate Mixed-Precision Multigrid Solvers

This paper shows how to obtain discretization-error-accurate solutions for linear elliptic partial differential equations (PDEs) by mixed-precision multigrid solvers. The key to this result is to balance quantization, algebraic, and discretization errors in the progressive-precision scheme proposed in the companion paper (Algebraic Error Analysis for Mixed-Precision Multigrid Solvers). Additionally, we show that the progressive precision scheme leads to memory savings of up to 50% compared to fixed precision.