A variable-precision implementation of the ADER-DG algorithm

Efficient usage of mixed-precision can be used to accelerate numerical methods, but can also affect the convergence of high-order methods. Precision-induced errors in the solution however are often tied to specific areas of the domain. We present a variable-precision implementation of the high-order ADER-DG method (Discontinuous Galerkin with Arbitrary high-order DERivative time stepping) for solving hyperbolic systems of partial differential equations (PDEs) in the hyperbolic PDE engine ExaHyPE. This allows the computation of specific areas of the domain in higher or lower numerical precisions. The implementation is tested on three different scenarios to showcase properties of the method and how it can be used most efficiently.