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SUMMARY:Optimal and Scalable Augmented Lagrangian preconditioners for Fict
 itious Domain problems
DTSTART:20250513T090000Z
DTEND:20250513T100000Z
DTSTAMP:20260518T212200Z
UID:indico-event-321@events.dm.unipi.it
DESCRIPTION:Speakers: Federica Mugnaioni (Scuola Normale Superiore)\n\nOne
  of the major drawbacks of using Fictitious Domain methods is the computat
 ional demands of solving the associated large-scale linear systems\, both 
 in terms of time and memory. To address this issue\, we propose two augmen
 ted Lagrangian-based preconditioners for efficiently solving linear system
 s of equations with a block two-by-two and three-by-three structure arisin
 g from fictitious domain problems and from finite element discretizations 
 of immersed boundary methods. We consider two relevant examples to illustr
 ate the performance of these preconditioners when used in conjunction with
  flexible GMRES: the Poisson and the Stokes fictitious domain problems.  
 We provide a detailed spectral analysis\, deriving lower and upper bounds 
 for the eigenvalues of the preconditioned matrix and showing their indepen
 dence with respect to discretization parameters. Furthermore\, we discuss 
 the eigenvalue distribution when inexact versions of the preconditioners a
 re employed. We show the effectiveness of the proposed approach and the r
 obustness of our preconditioning strategies through extensive numerical te
 sts in both two and three dimensions\, using different immersed geometries
 .M. Benzi\, M. Feder\, L. Heltai and F. Mugnaioni. Optimal and Scalable Au
 gmented Lagrangian preconditioners for Fictitious Domain problems. arXiv:
 2504.11339\, 2025\n\nhttps://events.dm.unipi.it/event/321/
LOCATION:Saletta Riunioni (Dipartimento di Matematica)
URL:https://events.dm.unipi.it/event/321/
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