%0 Journal Article %1 Ho_2017 %A Ho, Nguyenho %A Olson, Sarah D. %A Walker, Homer F. %D 2017 %I Society for Industrial & Applied Mathematics (SIAM) %J SIAM Journal on Scientific Computing %K 65b10-acceleration-of-convergence-summation-of-series 65f08-preconditioners-for-iterative-methods 65f10-iterative-methods-for-linear-systems 65n22-pdes-bvps-solution-of-discretized-equations 76d07-stokes-and-related-oseen-etc-flows 65h10-systems-of-nonlinear-algebraic-equations %N 5 %P S461–S476 %R 10.1137/16m1076770 %T Accelerating the Uzawa Algorithm %U https://doi.org/10.1137%2F16m1076770 %V 39 %X The Uzawa algorithm is an iterative method for the solution of saddle-point problems, which arise in many applications, including fluid dynamics. Viewing the Uzawa algorithm as a fixed-point iteration, we explore the use of Anderson acceleration (also known as Anderson mixing) to improve the convergence. We compare the performance of the preconditioned Uzawa algorithm with and without acceleration on several steady Stokes and Oseen problems for incompressible flows. For perspective, we include in our comparison GMRES with two different preconditioners. The results indicate that the accelerated preconditioned Uzawa algorithm converges significantly faster than the algorithm without acceleration and is competitive with the other methods considered.

@article{Ho_2017, abstract = {The Uzawa algorithm is an iterative method for the solution of saddle-point problems, which arise in many applications, including fluid dynamics. Viewing the Uzawa algorithm as a fixed-point iteration, we explore the use of Anderson acceleration (also known as Anderson mixing) to improve the convergence. We compare the performance of the preconditioned Uzawa algorithm with and without acceleration on several steady Stokes and Oseen problems for incompressible flows. For perspective, we include in our comparison GMRES with two different preconditioners. The results indicate that the accelerated preconditioned Uzawa algorithm converges significantly faster than the algorithm without acceleration and is competitive with the other methods considered.}, added-at = {2019-05-02T01:41:06.000+0200}, author = {Ho, Nguyenho and Olson, Sarah D. and Walker, Homer F.}, biburl = {https://www.bibsonomy.org/bibtex/27e9bc870fa27b2cd89e8c1618682d6c1/gdmcbain}, doi = {10.1137/16m1076770}, interhash = {d287dc722faa3d6c9608c401f355e2fc}, intrahash = {7e9bc870fa27b2cd89e8c1618682d6c1}, journal = {{SIAM} Journal on Scientific Computing}, keywords = {65b10-acceleration-of-convergence-summation-of-series 65f08-preconditioners-for-iterative-methods 65f10-iterative-methods-for-linear-systems 65n22-pdes-bvps-solution-of-discretized-equations 76d07-stokes-and-related-oseen-etc-flows 65h10-systems-of-nonlinear-algebraic-equations}, month = jan, number = 5, pages = {S461–S476}, publisher = {Society for Industrial {\&} Applied Mathematics ({SIAM})}, timestamp = {2020-07-28T09:23:35.000+0200}, title = {Accelerating the Uzawa Algorithm}, url = {https://doi.org/10.1137%2F16m1076770}, volume = 39, year = 2017 }