Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 39, Issue 5, Pages S461-S476Publisher
SIAM PUBLICATIONS
DOI: 10.1137/16M1076770
Keywords
Uzawa algorithm; saddle-point problems; preconditioning; Anderson acceleration; Stokes problems; Oseen problems; incompressible flows
Categories
Funding
- U.S. National Science Foundation [DMS 1455270, DMS 1337943]
- U.S. Department of Energy [DE-SC0004880]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1337943, 1455270] Funding Source: National Science Foundation
- U.S. Department of Energy (DOE) [DE-SC0004880] Funding Source: U.S. Department of Energy (DOE)
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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.
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