# Deflation-accelerated preconditioning of the Poisson-Neumann Schur problem on long domains with a high-order discontinuous element-based collocation method

@article{Joshi2016DeflationacceleratedPO, title={Deflation-accelerated preconditioning of the Poisson-Neumann Schur problem on long domains with a high-order discontinuous element-based collocation method}, author={Sumedh M. Joshi and Greg N. Thomsen and Peter J. Diamessis}, journal={J. Comput. Phys.}, year={2016}, volume={313}, pages={209-232} }

A combination of block-Jacobi and deflation preconditioning is used to solve a high-order discontinuous element-based collocation discretization of the Schur complement of the Poisson-Neumann system as arises in the operator splitting of the incompressible Navier-Stokes equations. The preconditioners and deflation vectors are chosen to mitigate the effects of ill-conditioning due to highly-elongated domains typical of simulations of strongly non-hydrostatic environmental flows, and to achieve… CONTINUE READING

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