Anisotropic mesh adaptation in Firedrake with PETSc DMPlex
Barral, Nicolas, Matthew G. Knepley, Michael Lange, Matthew D. Piggott, Gerard J. Gorman
Research Note, 25th International Meshing Roundtable, Sandia National Laboratories, September 26-30 2016
25th International Meshing Roundtable
Washington DC, U.S.A.
September 26-30, 2016
Nicolas Barral, Imperial College London, GB, firstname.lastname@example.org
Matthew G. Knepley, Rice University, US, email@example.com
Michael Lange, Imperial College London, GB, firstname.lastname@example.org
Matthew D. Piggott, Imperial College London, GB, email@example.com
Gerard J. Gorman, Imperial College London, GB, firstname.lastname@example.org
Research Note Abstract
Despite decades of research in this area, mesh adaptation capabilities are still rarely found in numerical simulation software. We postulate that the primary reason for this is lack of usability. Integrating mesh adaptation into existing software is difficult as non-trivial operators, such as error metrics and interpolation operators, are required, and integrating available adaptive remeshers is not straightforward. Our approach presented here is to first integrate Pragmatic, an anisotropic mesh adaptation library, into DMPlex, a PETSc object that manages unstructured meshes and their interactions with PETSc’s solvers and I/O routines. As PETSc is already widely used, this will make anisotropic mesh adaptation available to a much larger community. As a demonstration of this we describe the integration of anisotropic mesh adaptation into Firedrake, an automated Finite Element based system for the portable solution of partial differential equations which already uses PETSc solvers and I/O via DMPlex. We present a proof of concept of this integration with a three-dimensional advection test case.
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