An algebraic multigrid method for Q2-Q1 mixed discretizations of the Navier-Stokes equations

Prokopenko, Andrey; Tuminaro, Raymond S.

doi:10.1002/nla.2109

Title: An algebraic multigrid method for Q2-Q1 mixed discretizations of the Navier-Stokes equations

Journal Article · Fri Jul 01 00:00:00 EDT 2016 · Numerical Linear Algebra with Applications (Online)

DOI:https://doi.org/10.1002/nla.2109· OSTI ID:1399874

Prokopenko, Andrey ^[1]; Tuminaro, Raymond S. ^[2]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research
Sandia National Lab. (SNL-CA), Livermore, CA (United States). Center for Computing Research

Algebraic multigrid (AMG) preconditioners are considered for discretized systems of partial differential equations (PDEs) where unknowns associated with different physical quantities are not necessarily colocated at mesh points. Specifically, we investigate a Q₂-Q₁ mixed finite element discretization of the incompressible Navier–Stokes equations where the number of velocity nodes is much greater than the number of pressure nodes. Consequently, some velocity degrees of freedom (DOFs) are defined at spatial locations where there are no corresponding pressure DOFs. Thus, AMG approaches leveraging this colocated structure are not applicable. This article instead proposes an automatic AMG coarsening that mimics certain pressure/velocity DOF relationships of the Q₂-Q₁ discretization. The main idea is to first automatically define coarse pressures in a somewhat standard AMG fashion and then to carefully (but automatically) choose coarse velocity unknowns so that the spatial location relationship between pressure and velocity DOFs resembles that on the finest grid. To define coefficients within the intergrid transfers, an energy minimization AMG (EMIN-AMG) is utilized. EMIN-AMG is not tied to specific coarsening schemes and grid transfer sparsity patterns, and so it is applicable to the proposed coarsening. Numerical results highlighting solver performance are given on Stokes and incompressible Navier–Stokes problems.

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Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sandia National Lab. (SNL-CA), Livermore, CA (United States); Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC04-94AL85000; AC05-00OR22725

OSTI ID:: 1399874

Alternate ID(s):: OSTI ID: 1394531

Report Number(s):: SAND-2016-6518J; 644837; TRN: US1703220

Journal Information:: Numerical Linear Algebra with Applications (Online), Vol. 24, Issue 6; ISSN 1099-1506

Publisher:: WileyCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 1 work

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