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

We present a scalable block preconditioning strategy for the trace systemcoming from the high-order hybridized discontinuous Galerkin (HDG)discretization of incompressible resistive magnetohydrodynamics (MHD). Weconstruct the block preconditioner with a least squares commutator (BFBT)approximation for the inverse of the Schur complement that segregates out thepressure unknowns of the trace system. The remaining velocity, magnetic field,and Lagrange multiplier unknowns form a coupled nodal unknown block (the upperblock), for which a system algebraic multigrid (AMG) is used for theapproximate inverse. The complexity of the MHD equations together with thealgebraic nature of the statically condensed HDG trace system makes the choiceof smoother in the system AMG part critical for the convergence and performanceof the block preconditioner. Our numerical experiments show GMRESpreconditioned by ILU(0) of overlap zero as a smoother inside system AMGperforms best in terms of robustness, time per nonlinear iteration and memoryrequirements. With several transient test cases in 2D and 3D including theisland coalescence problem at high Lundquist number we demonstrate therobustness and parallel scalability of the block preconditioner. Additionallyfor the upper block a preliminary study of an alternate nodal block systemsolver based on a multilevel approximate nested dissection is presented. On a2D island coalescence problem the multilevel approximate nested dissectionpreconditioner shows better scalability with respect to mesh refinement thanthe system AMG, but is relatively less robust with respect to Lundquist numberscaling.

A Multilevel Block Preconditioner for the HDG Trace System Applied to Incompressible Resistive MHD