Efficient mesh management in Firedrake using PETSc-DMPlex

Gerard J. Gorman; Lawrence Mitchell; Matthew G. Knepley; Michael Lange

Efficient mesh management in Firedrake using PETSc-DMPlex

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arxiv 1506.07749 v1 pith:KXOTMDOO submitted 2015-06-25 cs.MS

Michael Lange , Lawrence Mitchell , Matthew G. Knepley , Gerard J. Gorman This is my paper · ORCID

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keywords dmplexfiredrakewhileassemblydatadescribedomainelement

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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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