Abstract
The use of composable abstractions allows the application of new and
established algorithms to a wide range of problems while automatically
inheriting the benefits of well-known performance optimisations. This work
highlights the composition of the PETSc DMPlex domain topology abstraction with
the Firedrake automated finite element system to create a PDE solving
environment that combines expressiveness, flexibility and high performance. We
describe how Firedrake utilises DMPlex to provide the indirection maps required
for finite element assembly, while supporting various mesh input formats and
runtime domain decomposition. In particular, we describe how DMPlex and its
accompanying data structures allow the generic creation of user-defined
discretisations, while utilising data layout optimisations that improve cache
coherency and ensure overlapped communication during assembly computation.
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