ExaHyPE developed an engine to solve hyperbolic systems of partial differential equations (PDE) on exascale supercomputers. ExaHyPE particularly addressed problems in Seismology (e.g. earthquake simulation) and Astrophysics (systems of black holes or neutron stars, gravitational waves). As an “engine” ExahyPE supports a wide range of problems: solvers for more than 20 hyperbolic PDE systems have already been realised. Thus, ExaHyPE enables groups of computational domain scientists to realize grand challenge simulations in much quicker ”time to science”.
To address the challenges of exascale, ExaHyPE developed a novel, communication-avoiding high-order discontinuous-Galerkin scheme with high-order time stepping. At shocks and critical regions, the solver falls back to a robust Finite-Volume limiter. We feature tree-structured dynamical adaptive mesh refinement and express all numerical steps via task-based paradigms. We developed agile load balancing via lightweight work stealing across compute nodes and explored replication-based resiliency and the impact of a-posteriori limiting on detection and mitigation of soft faults.
As one of two demonstrators, we provide ExaSeis, for seismology, which includes (1) a linear model on curvilinear meshes, where the mesh is adapted to topography, material layers or fault planes, and (2) a novel non-linear diffused-interface model that expresses arbitrarily complex domains on Cartesian grids via a color function. As a second demonstrator, we provide solvers for the Einstein field equations of general relativity in first-order CCZ4 formulation, coupled to the general relativistic MHD equations. We thus enable relativistic simulation of black holes and neutron stars, which are being further developed towards mergers of binary systems.
