Efficient implementation of ADER discontinuous Galerkin schemes for a scalable hyperbolic PDE engine
This work provides a scalable and efficient numerical method for solving a broad class of hyperbolic PDEs on exascale supercomputers, benefiting computational scientists in fields like fluid dynamics, elasticity, and general relativity.
The paper presents an efficient implementation of high-order ADER discontinuous Galerkin schemes for hyperbolic PDEs, achieving strong scaling up to 180,000 CPU cores, which are the largest runs ever carried out with such schemes.
In this paper we discuss a new and very efficient implementation of high order accurate ADER discontinuous Galerkin (ADER-DG) finite element schemes on modern massively parallel supercomputers. The numerical methods apply to a very broad class of nonlinear systems of hyperbolic partial differential equations. ADER-DG schemes are by construction communication avoiding and cache blocking and are furthermore very well-suited for vectorization, so that they appear to be a good candidate for the future generation of exascale supercomputers. We introduce the numerical algorithm and show some applications to a set of hyperbolic equations with increasing level of complexity, ranging from the compressible Euler equations over the equations of linear elasticity and the unified Godunov-Peshkov-Romenski (GPR) model of continuum mechanics to general relativistic magnetohydrodynamics (GRMHD) and the Einstein field equations of general relativity. We present strong scaling results of the new ADER-DG schemes up to 180,000 CPU cores. To our knowledge, these are the largest runs ever carried out with high order ADER-DG schemes for nonlinear hyperbolic PDE systems. We also provide a detailed performance comparison with traditional Runge-Kutta DG schemes.