BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Colin Cotter (Imperial College) DTSTART:20210720T070000Z DTEND:20210720T080000Z DTSTAMP:20260423T052708Z UID:CMWebinar/8 DESCRIPTION:Title: Hybridised implicit solvers for the Gung Ho dynamical core\nby Colin Cotter (Imperial College) as part of Australian Seminar on Computational Mathematics\n\n\nAbstract\nGung Ho is the name of the Met Office project t o build a new dynamical core (fluid dynamics component) for their weather/ climate prediction system. Gung Ho is built around compatible finite eleme nt methods as the apparently unique solution to the question of how to fin d a consistent gridpoint (i.e. non-spectral) discretisation that supports various essential wave propagation properties at the discrete level on gri ds with near-equal edge lengths "pseudo-uniform" on the sphere. One downsi de of this approach versus their current finite difference approach is the non-diagonal mass matrix for the velocity component\, which means that th e usual strategy of eliminating velocity to get an elliptic problem for pr essure results in a non-sparse matrix. The solution to this\, known for de cades\, is to "hybridise" the mixed system by breaking continuity constrai nts to get a discontinuous velocity space\, and to introduce Lagrange mult ipliers as trace variables supported on cell facets to enforce continuity of the solution. The system can then be eliminated down to a sparse reduce d system for the trace variables only. The question then arises of how to efficiently iteratively solve this system when the domain is very thin (li ke the Earth's atmosphere). This question can be answered by combining var ious results from (a) the analysis of hybridised mixed finite element meth ods and (b) the analysis of additive Schwarz methods. I will briefly intro duce these\, describe a solver algorithm and sketch a proof that it gives iteration counts that are independent of depth in the thin layer limit\, b efore illustrating with some numerical results produced using Firedrake an d PETSc.\n LOCATION:https://researchseminars.org/talk/CMWebinar/8/ END:VEVENT END:VCALENDAR