Efficient mesh management in firedrake using PETSc DMPlex. 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 optimizations. 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 utilizes 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 discretizations, while utilizing data layout optimizations that improve cache coherency and ensure overlapped communication during assembly computation.

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  1. Ferrero, Andrea; Iollo, Angelo; Larocca, Francesco: Field inversion for data-augmented RANS modelling in turbomachinery flows (2020)
  2. Wang, Lai; Gobbert, Matthias K.; Yu, Meilin: A dynamically load-balanced parallel (p)-adaptive implicit high-order flux reconstruction method for under-resolved turbulence simulation (2020)
  3. Prieto, Juan Luis; Carpio, Jaime: A-SLEIPNNIR: a multiscale, anisotropic adaptive, particle level set framework for moving interfaces. Transport equation applications (2019)
  4. Chang, Justin; Fabien, Maurice S.; Knepley, Matthew G.; Mills, Richard T.: Comparative study of finite element methods using the time-accuracy-size (TAS) spectrum analysis (2018)
  5. Creech, Angus C. W.; Jackson, Adrian; Maddison, James R.: Adapting and optimising fluidity for high-fidelity coastal modelling (2018)
  6. Adams, Mark F.; Hirvijoki, Eero; Knepley, Matthew G.; Brown, Jed; Isaac, Tobin; Mills, Richard: Landau collision integral solver with adaptive mesh refinement on emerging architectures (2017)
  7. Chang, J.; Karra, S.; Nakshatrala, K. B.: Large-scale optimization-based non-negative computational framework for diffusion equations: parallel implementation and performance studies (2017)
  8. Rathgeber, Florian; Ham, David A.; Mitchell, Lawrence; Lange, Michael; Luporini, Fabio; Mcrae, Andrew T. T.; Bercea, Gheorghe-Teodor; Markall, Graham R.; Kelly, Paul H. J.: Firedrake, automating the finite element method by composing abstractions (2017)
  9. Lange, Michael; Mitchell, Lawrence; Knepley, Matthew G.; Gorman, Gerard J.: Efficient mesh management in firedrake using PETSc DMPlex (2016)