Analysis of a new dimension-wise splitting iteration with selective relaxation for saddle point problems
We propose a new dimension-wise splitting with selective relaxation (DSSR) method for saddle point systems arising from the discretization of the incompressible Navier–Stokes equations. Using Fourier analysis, we determine the optimal choice of the relaxation parameter that leads to the best performance of the iterative method for the Stokes and the steady Oseen equations. We also explore numerically the influence of boundary conditions on the optimal choice of the parameter, the use of inner and outer iterations, and the performance for a lid driven cavity flow.
KeywordsSplitting iterations Optimized relaxation parameter Stokes Oseen
Mathematics Subject Classification65F10 65N22
The authors would like to thank the organizing committee for the wonderful conference NASC2014, where the authors met each other and started their collaboration on this interesting topic. They are also very thankful for the constructive comments of the anonymous referees, which substantially enhanced the content and structure of this manuscript.
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