%0 Report %1 citeulike:13665237 %A Elman, Howard C. %C College Park, Maryland %D 1996 %K 76m20-finite-difference-methods-in-fluid-mechanics 35q30-navier-stokes-equations 65f08-preconditioners-for-iterative-methods 76d05-incompressible-navier-stokes-equations 65f10-iterative-methods-for-linear-systems 65n20-pdes-bvps-illposed-problems 15a06-linear-equations %R 10.1137/s1064827596312547 %T Preconditioning for the Steady-State Navier--Stokes Equations with Low Viscosity %U http://dx.doi.org/10.1137/s1064827596312547 %X We introduce a preconditioner for the linearized Navier-Stokes equations that is effective when either the discretization mesh size or the viscosity approaches zero. For constant coecient problems with periodic boundary conditions, we show that the preconditioning yields a system with a single eigenvalue equal to one, so that performance is independent of both viscosity and mesh size. For other boundary conditions, we demonstrate empirically that convergence depends only mildly on these parameters and we give a partial analysis of this phenomenon. We also show that some expensive subsidiary computations required by the new method can be replaced by inexpensive approximate versions of these tasks based on iteration, with virtually no degradation of performance.

@techreport{citeulike:13665237, abstract = {{We introduce a preconditioner for the linearized Navier-Stokes equations that is effective when either the discretization mesh size or the viscosity approaches zero. For constant coecient problems with periodic boundary conditions, we show that the preconditioning yields a system with a single eigenvalue equal to one, so that performance is independent of both viscosity and mesh size. For other boundary conditions, we demonstrate empirically that convergence depends only mildly on these parameters and we give a partial analysis of this phenomenon. We also show that some expensive subsidiary computations required by the new method can be replaced by inexpensive approximate versions of these tasks based on iteration, with virtually no degradation of performance.}}, added-at = {2017-06-29T07:13:07.000+0200}, address = {College Park, Maryland}, author = {Elman, Howard C.}, biburl = {https://www.bibsonomy.org/bibtex/2a30a7774c9d64111c687a91cd06a292f/gdmcbain}, citeulike-article-id = {13665237}, citeulike-attachment-1 = {elman_96_preconditioning_1024898.pdf; /pdf/user/gdmcbain/article/13665237/1024898/elman_96_preconditioning_1024898.pdf; 62549f77c89cd4fd1c86c2c13ad94abdf1fba767}, citeulike-linkout-0 = {http://dx.doi.org/10.1137/s1064827596312547}, doi = {10.1137/s1064827596312547}, file = {elman_96_preconditioning_1024898.pdf}, howpublished = {Report CS-TR-3712}, institution = {Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland}, interhash = {b5f56faef10008fb6db0c7dae568b2b7}, intrahash = {a30a7774c9d64111c687a91cd06a292f}, keywords = {76m20-finite-difference-methods-in-fluid-mechanics 35q30-navier-stokes-equations 65f08-preconditioners-for-iterative-methods 76d05-incompressible-navier-stokes-equations 65f10-iterative-methods-for-linear-systems 65n20-pdes-bvps-illposed-problems 15a06-linear-equations}, month = nov, posted-at = {2015-07-06 01:14:16}, priority = {2}, timestamp = {2019-05-03T08:35:29.000+0200}, title = {Preconditioning for the Steady-State {N}avier--{S}tokes Equations with Low Viscosity}, url = {http://dx.doi.org/10.1137/s1064827596312547}, year = 1996 }