%0 Conference Paper %1 citeulike:11271604 %A John, Volker %B Scientific Computing and Applications %C Huntington, New York %D 2001 %E Minev, Par P. %E Lin, Yanping %I Nova Science Publishers, Inc. %K 65y05-parallel-computation 65n55-pdes-bvps-multigrid-methods-domain-decomposition 65n22-pdes-bvps-solution-of-discretized-equations 65m55-pdes-ibvps-multigrid-methods-domain-decomposition %P 75+ %T On Smoothers in Parallel Coupled Multigrid Methods for Incompressible Navier--Stokes Equations %U http://books.google.fr/books?id=cyiQChiG17UC&\#38;pg=PA75&\#38;lpg=PA75&\#38;dq=vanka+stokes&\#38;source=bl&\#38;ots=qTU31KsjlC&\#38;sig=hu7J5i8r7C9YYoBBEZtjpzjxqtg&\#38;hl=fr\#v=onepage&\#38;q=vanka\%20stokes&\#38;f=false %V 7 %X We present a numerical study of two types of smoothers in parallelized coupled multigrid methods for the solution of incompressible Navier--Stokes equations. The Vanka smoother is characterized by the solution of many small linear systems of equations in each smoothing step whereas the Braess--Sarazin smoother solves one large linear saddle point problem. Our study is based on the nonconforming \$P\_1/P\_0\$-finite element discretization in space and th Crank--Nicolson discretization in time. The computations were performed on parallel computer HP N-Class with RISC 8500 processors using the communication interface MPI. The Vanka smoother shows a better efficiency in this framework.

@inproceedings{citeulike:11271604, abstract = {{We present a numerical study of two types of smoothers in parallelized coupled multigrid methods for the solution of incompressible Navier--Stokes equations. The Vanka smoother is characterized by the solution of many small linear systems of equations in each smoothing step whereas the Braess--Sarazin smoother solves one large linear saddle point problem. Our study is based on the nonconforming \$P\_1/P\_0\$-finite element discretization in space and th Crank--Nicolson discretization in time. The computations were performed on parallel computer HP N-Class with RISC 8500 processors using the communication interface MPI. The Vanka smoother shows a better efficiency in this framework.}}, added-at = {2017-06-29T07:13:07.000+0200}, address = {Huntington, New York}, author = {John, Volker}, biburl = {https://www.bibsonomy.org/bibtex/2f3fdb19abbfd13feee790b86a38df822/gdmcbain}, booktitle = {Scientific Computing and Applications}, citeulike-article-id = {11271604}, citeulike-linkout-0 = {http://books.google.fr/books?id=cyiQChiG17UC\&\#38;pg=PA75\&\#38;lpg=PA75\&\#38;dq=vanka+stokes\&\#38;source=bl\&\#38;ots=qTU31KsjlC\&\#38;sig=hu7J5i8r7C9YYoBBEZtjpzjxqtg\&\#38;hl=fr\#v=onepage\&\#38;q=vanka\%20stokes\&\#38;f=false}, comment = {treats the "Vanka smoother" mentioned by Jed Brown on 'libmesh-users 2012-09-17T2302':http://sourceforge.net/mailarchive/message.php?msg\_id=29822734 \% an example of a good smoother is due to Vanka. It is a multiplicative overlapping Schwarz method that uses domains obtained by taking a pressure node, adding all velocity dofs that touch it, then assembling that block problem (or extracting it from the matrix), solving, updating the state vector for all dofs under the block solve, then moving to the next pressure node. Efficiently implementing these with assembled matrices or continuous finite elements is unfortunately, somewhat problematic.}, editor = {Minev, Par P. and Lin, Yanping}, interhash = {694a077bc1710e11c0e06f05ceaf8e73}, intrahash = {f3fdb19abbfd13feee790b86a38df822}, keywords = {65y05-parallel-computation 65n55-pdes-bvps-multigrid-methods-domain-decomposition 65n22-pdes-bvps-solution-of-discretized-equations 65m55-pdes-ibvps-multigrid-methods-domain-decomposition}, pages = {75+}, posted-at = {2012-09-18 11:09:14}, priority = {2}, publisher = {Nova Science Publishers, Inc.}, series = {Advances in Computation: Theory and Practice}, timestamp = {2019-04-04T01:14:26.000+0200}, title = {On Smoothers in Parallel Coupled Multigrid Methods for Incompressible {N}avier--{S}tokes Equations}, url = {http://books.google.fr/books?id=cyiQChiG17UC\&\#38;pg=PA75\&\#38;lpg=PA75\&\#38;dq=vanka+stokes\&\#38;source=bl\&\#38;ots=qTU31KsjlC\&\#38;sig=hu7J5i8r7C9YYoBBEZtjpzjxqtg\&\#38;hl=fr\#v=onepage\&\#38;q=vanka\%20stokes\&\#38;f=false}, volume = 7, year = 2001 }