English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

A combination of block-Jacobi and deflation preconditioning is used to solvea high-order discontinuous element-based collocation discretization of theSchur complement of the Poisson-Neumann system as arises in the operatorsplitting of the incompressible Navier-Stokes equations. The ill-posedness ofthe Poisson-Neumann system manifests as an inconsistency of the Schurcomplement problem, but it is shown that this can be accounted for withappropriate projections out of the null space of the Schur complement matrixwithout affecting the accuracy of the solution. The block-Jacobipreconditioner, combined with deflation, is shown to yield GMRES convergenceindependent of the polynomial order of expansion within an element. Finally,while the number of GMRES iterations does grow as the element size is reduced(e.g. $h$-refinement), the dependence is very mild; the number of GMRESiterations roughly doubles as the element size is divided by a factor of six.In light of these numerical results, the deflated Schur complement approachseems practicable, especially for high-order methods given its convergenceindependent of polynomial order.

A deflated Schur complement method for the iterative solution of a high-order discontinuous element discretization of the Poisson equation