ExaHyPE: An engine for parallel dynamically adaptive simulations of wave problems

Abstract

ExaHyPE ("An Exascale Hyperbolic PDE Engine") is a software engine for solving systems of first-order hyperbolic partial differential equations (PDEs). Hyperbolic PDEs are typically derived from the conservation laws of physics and are useful in a wide range of application areas. Applications powered by ExaHyPE can be run on a student's laptop, but are also able to exploit thousands of processor cores on state-of-the-art supercomputers. The engine is able to dynamically increase the accuracy of the simulation using adaptive mesh refinement where required. Due to the robustness and shock capturing abilities of ExaHyPE's numerical methods, users of the engine can simulate linear and non-linear hyperbolic PDEs with very high accuracy.Users can tailor the engine to their particular PDE by specifying evolved quantities, fluxes, and source terms. A complete simulation code for a new hyperbolic PDE can often be realised within a few hours -a task that, traditionally, can take weeks, months, often years for researchers starting from scratch. In this paper, we showcase ExaHyPE's workflow and capabilities through real-world scenarios from our two main application areas: seismology and astrophysics.PDEs written in first order form. The systems may contain both conservative and non-conservative terms. Solution method:ExaHyPE employs the discontinuous Galerkin (DG) method combined with explicit one-step ADER (arbitrary high-order derivative) time-stepping. An a-posteriori limiting approach is applied to the ADER-DG solution, whereby spurious solutions are discarded and recomputed with a robust, patch-based finite volume scheme. ExaHyPE uses dynamical adaptive mesh refinement to enhance the accuracy of the solution around shock waves, complex geometries, and interesting features.

A simple diffuse interface approach for compressible flows around moving solids of arbitrary shape based on a reduced Baer–Nunziato model

“…Furthermore, in order to increase the resolution in the areas of interest, the ADER-DG scheme described above has been implemented on space-time adaptive Cartesian meshes, with a cell-by-cell refinement approach; for all the details we refer to [44,38,141,47,46,13,140,113].…”

Role-Oriented Code Generation in an Engine for Solving Hyperbolic PDE Systems

“…The ExaHyPE engine [1] can solve a large class of systems of first-order hyperbolic PDEs, which are expressed in the following canonical form:…”

“…The ADER-DG method consists of two phases, a predictor step in which the weak formulation of (1) is solved locally in each cell, and a corrector step in which the contributions of neighboring cells are taken into account. To derive the weak solution of the problem we insert the DG ansatz function from the space of piecewise polynomials into equation (1) and multiply with a test function from the same space of piecewise polynomials. We then integrate over a space-time control volume.…”

“…The canonical PDE system (1) can model a wide array of applications, including relativistic astrophysics [10], [11], seismic wave propagation [12], [13] or several variants of fluid equations (see [1] for an overview). All these problems can be formulated via Equation (1) via specific F(Q), B(Q) · ∇Q and S(Q).…”

“…exahype.eu) is an EU Horizon 2020 project to develop an exascale-ready general solver for hyperbolic systems of partial differential equations (PDEs). Intended as an engine (as in "game engine"), it concentrates on a dedicated numerical scheme and on a fixed mesh infrastructure, but provides flexibility in the PDE system to be solved [1]. Its mission statement is "to enable medium-sized interdisciplinary research teams to realize extreme-scale simulations of grand challenges modelled by hyperbolic conservation laws".…”