A FETI-DP Algorithm for Saddle Point Problems in Three Dimensions
A FETI-DP algorithm is proposed for solving the system of linear equations arising from the mixed finite element approximations of a three dimensional saddle problem. A preconditioned conjugate gradient method is used in the algorithm with either a lumped or a Dirichlet preconditioner, and scalable convergence rates are proved without a divergence free condition for the coarse space. Numerical experiments of solving a three-dimensional incompressible Stokes problem demonstrate the performance of the proposed algorithm.
KeywordsMixed Finite Element Saddle Point Problem Finite Element Space Coarse Space Preconditioned Conjugate Gradient Method
This work was supported in part by National Science Foundation Contracts No. DMS-1115759 and DMS-1419069.
- 6.X. Tu, J. Li, A FETI-DP algorithm for incompressible stokes equations with continuous pressures, in Proceedings of the 21th Domain International Conference on Domain Decomposition Methods, 2012Google Scholar