Communication-Avoiding Algorithms for a High-Performance Hyperbolic PDE
Engine

Abstract

The study of waves has always been an important subject of research. Earthquakes, for example,
have a direct impact on the daily lives of millions of people while gravitational waves reveal
insight into the composition and history of the Universe. These physical phenomena, despite
being tackled traditionally by different fields of physics, have in common that they are modelled
the same way mathematically: as a system of hyperbolic partial differential equations (PDEs).
The ExaHyPE project (“An Exascale Hyperbolic PDE Engine") translates this similarity into
a software engine that can be quickly adapted to simulate a wide range of hyperbolic partial
differential equations. ExaHyPE’s key idea is that the user only specifies the physics while the
engine takes care of the parallelisation and the interplay of the underlying numerical methods.
Consequently, a first simulation code for a new hyperbolic PDE can often be realised within a
few hours. This is a task that traditionally can take weeks, months, even years for researchers
starting from scratch.
My main contribution to ExaHyPE is the development of the core infrastructure. This
comprises the development and implementation of ExaHyPE’s solvers and adaptive mesh
refinement procedures, it’s MPI+X parallelisation as well as high-level aspects of ExaHyPE’s
application-tailored code generation, which allows to adapt ExaHyPE to model many different
hyperbolic PDE systems. Like any high-performance computing code, ExaHyPE has to tackle the
challenges of the coming exascale computing era, notably network communication latencies and
the growing memory wall. In this thesis, I propose memory-efficient realisations of ExaHyPE’s
solvers that avoid data movement together with a novel task-based MPI+X parallelisation
concept that allows to hide network communication behind computation in dynamically adaptive
simulations.