Minisymposium Presentation

While most scientific applications are still computed in double precision, mixed-precision algorithms are becoming more commonplace as a way to improve the performance of an algorithm without overly increasing the resulting error. The impact of numerical precision on the results and stability of an algorithm however remain difficult to estimate.

We present a study on the impact of using mixed and variable numerical precision in the high-order ADER discontinuous Galerkin method for solving hyperbolic PDEs.As a baseline, the entire algorithm is computed in multiple precisions and the results compared. Then we measure the effects of changing the precision of individual kernels to estimate whether a mixed-precision approach could reduce the overall loss of accuracy.In addition, we simulate two stationary but numerically challenging scenarios in the isentropic vortex for the Euler equations and the resting lake scenario for the shallow water equations, to see whether variable precision can be used to resolve local stability issues.Finally we review the effects of numerical precision on the features of Lagrange interpolations, which are commonly used but are susceptible to small changes in the nodal values.