In this paper we give an overview of the present state of fast solvers
for the solution of the incompressible Navier-Stokes equations
discretized by the
finite element method and linearized by Newton or Picard's method.
It is shown that block preconditioners form an excellent approach for the
solution, however if the grids are not to fine preconditioning with
a Saddle point ILU matrix (SILU) may be an attractive alternative.
The applicability of all methods to stabilized elements is
investigated.
In case of the stand-alone Stokes equations special preconditioners
increase the efficiency considerably.
%0 Journal Article
%1 NMTMA-3-245
%A Segal, A.
%A ur Rehman, M.
%A Vuik, C.
%D 2010
%J Numerical Mathematics: Theory, Methods and Applications
%K 65f10-iterative-methods-for-linear-systems 65n30-pdes-bvps-finite-elements 76d05-incompressible-navier-stokes-equations
%N 3
%P 245--275
%R 10.4208/nmtma.2010.33.1
%T Preconditioners for Incompressible Navier-Stokes Solvers
%U http://global-sci.org/intro/article_detail/nmtma/5999.html
%V 3
%X In this paper we give an overview of the present state of fast solvers
for the solution of the incompressible Navier-Stokes equations
discretized by the
finite element method and linearized by Newton or Picard's method.
It is shown that block preconditioners form an excellent approach for the
solution, however if the grids are not to fine preconditioning with
a Saddle point ILU matrix (SILU) may be an attractive alternative.
The applicability of all methods to stabilized elements is
investigated.
In case of the stand-alone Stokes equations special preconditioners
increase the efficiency considerably.
@article{NMTMA-3-245,
abstract = {In this paper we give an overview of the present state of fast solvers
for the solution of the incompressible Navier-Stokes equations
discretized by the
finite element method and linearized by Newton or Picard's method.
It is shown that block preconditioners form an excellent approach for the
solution, however if the grids are not to fine preconditioning with
a Saddle point ILU matrix (SILU) may be an attractive alternative.
The applicability of all methods to stabilized elements is
investigated.
In case of the stand-alone Stokes equations special preconditioners
increase the efficiency considerably.},
added-at = {2020-05-25T01:56:00.000+0200},
author = {Segal, A. and ur Rehman, M. and Vuik, C.},
biburl = {https://www.bibsonomy.org/bibtex/243fcdccfa2607269c73e6a152bd601fc/gdmcbain},
doi = {10.4208/nmtma.2010.33.1},
interhash = {87b16a07bddabfd86b3ceb4e1c7e0eaa},
intrahash = {43fcdccfa2607269c73e6a152bd601fc},
issn = {2079-7338},
journal = {Numerical Mathematics: Theory, Methods and Applications},
keywords = {65f10-iterative-methods-for-linear-systems 65n30-pdes-bvps-finite-elements 76d05-incompressible-navier-stokes-equations},
number = 3,
pages = {245--275},
timestamp = {2020-05-25T01:56:00.000+0200},
title = {Preconditioners for Incompressible Navier-Stokes Solvers},
url = {http://global-sci.org/intro/article_detail/nmtma/5999.html},
volume = 3,
year = 2010
}