%0 Journal Article %1 citeulike:13665231 %A Hemmingsson-Frändén, Lina %A Wathen, Andrew %D 2001 %J Numerical Linear Algebra with Applications %K 76m20-finite-difference-methods-in-fluid-mechanics 35q30-navier-stokes-equations 76m10-finite-element-methods-in-fluid-mechanics 65f08-preconditioners-for-iterative-methods 76d05-incompressible-navier-stokes-equations 65f10-iterative-methods-for-linear-systems %N 4 %P 229--243 %R 10.1002/nla.239 %T A Nearly Optimal Preconditioner for the Navier--Stokes Equations %U http://dx.doi.org/10.1002/nla.239 %V 8 %X We present a preconditioner for the linearized Navier–Stokes equations which is based on the combination of a fast transform approximation of an advection diffusion problem together with the recently introduced 'BFBTT' preconditioner of Elman (SIAM Journal of Scientific Computing, 1999; 20:1299–1316). The resulting preconditioner when combined with an appropriate Krylov subspace iteration method yields the solution in a number of iterations which appears to be independent of the Reynolds number provided a mesh Péclet number restriction holds, and depends only mildly on the mesh size. The preconditioner is particularly appropriate for problems involving a primary flow direction.

@article{citeulike:13665231, abstract = {{We present a preconditioner for the linearized Navier–Stokes equations which is based on the combination of a fast transform approximation of an advection diffusion problem together with the recently introduced 'BFBTT' preconditioner of Elman (SIAM Journal of Scientific Computing, 1999; 20:1299–1316). The resulting preconditioner when combined with an appropriate Krylov subspace iteration method yields the solution in a number of iterations which appears to be independent of the Reynolds number provided a mesh P\'{e}clet number restriction holds, and depends only mildly on the mesh size. The preconditioner is particularly appropriate for problems involving a primary flow direction.}}, added-at = {2017-06-29T07:13:07.000+0200}, author = {Hemmingsson-Fr\"{a}nd\'{e}n, Lina and Wathen, Andrew}, biburl = {https://www.bibsonomy.org/bibtex/233248d22124a763167d1532ba495cc0a/gdmcbain}, citeulike-article-id = {13665231}, citeulike-attachment-1 = {hemmingson-fraenden_01_nearly.pdf; /pdf/user/gdmcbain/article/13665231/1024897/hemmingson-fraenden_01_nearly.pdf; b2dc79a0a5c6ce88a07ce298255537285605e657}, citeulike-linkout-0 = {http://dx.doi.org/10.1002/nla.239}, doi = {10.1002/nla.239}, file = {hemmingson-fraenden_01_nearly.pdf}, interhash = {ecb603d93d14d04a2af4559084d81e34}, intrahash = {33248d22124a763167d1532ba495cc0a}, issn = {1070-5325}, journal = {Numerical Linear Algebra with Applications}, keywords = {76m20-finite-difference-methods-in-fluid-mechanics 35q30-navier-stokes-equations 76m10-finite-element-methods-in-fluid-mechanics 65f08-preconditioners-for-iterative-methods 76d05-incompressible-navier-stokes-equations 65f10-iterative-methods-for-linear-systems}, month = jun, number = 4, pages = {229--243}, posted-at = {2015-07-06 01:06:27}, priority = {0}, timestamp = {2019-02-28T23:43:44.000+0100}, title = {A Nearly Optimal Preconditioner for the {N}avier--{S}tokes Equations}, url = {http://dx.doi.org/10.1002/nla.239}, volume = 8, year = 2001 }