Reference : Dynamic composition of solvers for coupled problems in DOLFINx
Scientific Presentations in Universities or Research Centers : Scientific presentation in universities or research centers
Engineering, computing & technology : Materials science & engineering
Computational Sciences
http://hdl.handle.net/10993/46711
Dynamic composition of solvers for coupled problems in DOLFINx
English
Rehor, Martin mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
Hale, Jack mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Engineering (DoE) >]
22-Mar-2021
International
FEniCS 2021
22-03-2021
University of Cambridge
[en] Recent developments in DOLFINx allow for the block assembly of linear algebraic systems arising from discretisations of coupled partial differential equations. Each algebraic block represents a subproblem associated with a coupling of the unknown fields. Designing and implementing robust and scalable solution and preconditioning strategies for block-structured linear systems is an active area of research.

In this contribution we show how DOLFINx can now exploit one of the most significant features of PETSc; the dynamic composition of the hierarchical solver and preconditioner options at runtime, see Brown et al [1]. The idea is inspired by the work of Kirby and Mitchell [2] that was originally implemented in the Firedrake Project.

One of the most significant benefits of the approach is the possibility to construct advanced preconditioners that require structure beyond a purely algebraic problem description, eg the pressure-convection-diffusion (PCD) approximation of the Schur complement for the Navier–Stokes equations, see Silvester et al [3].

We illustrate the capabilities of our implementation on examples ranging from incompressible flow of a viscous fluid, through temperature-driven convection, to flows described by rate-type viscoelastic fluid models.

References
[1] J. Brown, M. G. Knepley, D. A. May, L. C. McInnes, and B. Smith, "Composable Linear Solvers for Multiphysics," in 2012 11th International Symposium on Parallel and
Distributed Computing, Munich, Germany, Jun. 2012, pp. 55–62, doi: 10.1109/ISPDC.2012.16.
[2] R. C. Kirby and L. Mitchell, "Solver Composition Across the PDE/Linear Algebra Barrier," SIAM J. Sci. Comput., vol. 40, no. 1, pp. C76–C98, 2017, doi: 10.1137/17M1133208.
[3] H. C. Elman, D. J. Silvester, and A. J. Wathen, Finite elements and fast iterative solvers: with applications in incompressible fluid dynamics. 2014, doi: 10.1093/acprof:oso/9780199678792.001.0001.

Acknowledgements
The present work is supported by the National Research Fund, Luxembourg in the frame of the Industrial Fellowship project RIFLE (13754363). The experiments presented in this work were carried out using the HPC facilities of the University of Luxembourg.
University of Luxembourg: High Performance Computing - ULHPC
Fonds National de la Recherche - FnR
Researchers ; Students
http://hdl.handle.net/10993/46711
FnR ; FNR13754363 > Martin Rehor > RIFLE > Robust Incompressible FLow solver Enhancement > 01/01/2020 > 31/12/2021 > 2019

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