This thesis focuses on performance improvement strategies of a Flux Re-
construction solver. Two different approaches based on numerical and im-
plementation strategies are investigated. First, a numerical based strategy
is developed to enable a bigger time-step for the explicit inner iterations in
a dual time stepping scheme. A simplified preconditioner is developed par-
ticularly for the stretched elements located in the near wall region. The pre-
conditioner is constructed using the wall normal couplings only. Therefore,
it requires relatively low storage and the application of the preconditioner
increases a single iteration cost only around 10 to 30% while enabling a 4 to
15 times increase for the maximum time-step.
Next, an implementation based strategy that particularly focuses on cache
blocking approach is investigated. First, a data structure that will enable
cache blocking is implemented in PyFR. Then, a theoretical study is con-
ducted to predict the amount of bandwidth savings for three different kernel
grouping configurations for the Euler solver in PyFR. All three kernel group-
ing configurations are implemented in PyFR and the results are compared
against PyFR v1.11.0. The most performant configuration leads to a 2.81x
speedup in practice compared to PyFR v1.11.0. Subsequently, the cache
blocking approach is extended to Navier-Stokes equations and anti-aliasing.
Extension to Navier-Stokes solver requires forming a specific kernel grouping
configuration considering the additional kernels in the Navier-Stokes solver.
Anti-aliasing support on the other hand necessitates factorisation of the dense
interpolation matrices into sparse components so that they become band-
width bound and cache blocking approach can be used efficiently. Cache
blocking approach for the Navier-Stokes solver with full anti-aliasing yields
up to 3.88x speedup compared to PyFR v1.11.0. Furthermore, strong scala-
bility of cache blocking approach is also investigated and it is demonstrated
that PyFR with cache blocking achieves over 70% efficiency when scaled from
1 to 128 nodes on ARCHER2. Additionally, a cost analysis is carried out
based on Amazon AWS pricing and it shows that PyFR with cache blocking
on CPUs can be more cost efficient compared to PyFR on GPUs.