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DTSTAMP:20210916T132448Z
LOCATION:Louis Favre
DTSTART;TZID=Europe/Stockholm:20210705T160000
DTEND;TZID=Europe/Stockholm:20210705T163000
UID:submissions.pasc-conference.org_PASC21_sess111_msa127@linklings.com
SUMMARY:Flexible Computational Abstractions in the Design and Implementati
 on of Multiphysics Preconditioners
DESCRIPTION:Minisymposium\n\nFlexible Computational Abstractions in the De
 sign and Implementation of Multiphysics Preconditioners\n\nMitchell\n\nSma
 ll block overlapping, and non-overlapping, Schwarz methods are theoretical
 ly highly attractive as multigrid smoothers for a wide variety of problems
  that are not amenable to point relaxation methods. Examples include monol
 ithic Vanka smoothers for Stokes, overlapping vertex-patch decompositions 
 for $H(\text{div})$ and $H(\text{curl})$ problems, and line smoothers for 
 elliptic problems in thin domains. While it is possible to manually progra
 m these different schemes, their use in general purpose libraries has been
  held back by a lack of generic, composable interfaces. I present a new ap
 proach to the specification and development such additive Schwarz methods 
 in PETSc that cleanly separates the topological space decomposition from t
 he<br /> discretisation and assembly of the equations. This separation ena
 bles both linear and nonlinear smoothers to be supported through<br /> the
  same callback interface. The preconditioner is flexible enough to support
  overlapping and non-overlapping additive Schwarz methods, and can be used
  to formulate line, and plane smoothers, Vanka iterations, and others. I w
 ill illustrate the effectiveness with examples using the Firedrake finite 
 element library.\n\nDomain: CS and Math, Climate and Weather, Physics, Sol
 id Earth Dynamics
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