April 2025 - NumPI - Mailing list — Dipartimento di Matematica, UniPI

[Indico] Federica Mugnaioni, Optimal and Scalable Augmented Lagrangian preconditioners for Fictitious Domain problems, 13/05/2025, 11:00 Europe/Rome
by fabio.durastante＠unipi.it 28 Apr '25

28 Apr '25

Title: Optimal and Scalable Augmented Lagrangian preconditioners for Fictitious Domain problems, Speaker(s): Federica Mugnaioni, Scuola Normale Superiore, Date and time: 13 May 2025, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Saletta Riunioni). You can access the full event here: https://events.dm.unipi.it/e/321 Abstract -------- One of the major drawbacks of using Fictitious Domain methods is the computational demands of solving the associated large-scale linear systems, both in terms of time and memory. To address this issue, we propose two augmented Lagrangian-based preconditioners for efficiently solving linear systems of equations with a block two-by-two and three-by-three structure arising from fictitious domain problems and from finite element discretizations of immersed boundary methods. We consider two relevant examples to illustrate 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 independence with respect to discretization parameters. Furthermore, we discuss the eigenvalue distribution when inexact versions of the preconditioners are employed. We show the effectiveness of the proposed approach and the robustness of our preconditioning strategies through extensive numerical tests in both two and three dimensions, using different immersed geometries.M. Benzi, M. Feder, L. Heltai and F. Mugnaioni. Optimal and Scalable Augmented Lagrangian preconditioners for Fictitious Domain problems. arXiv:2504.11339, 2025 -- Indico :: Email Notifier https://events.dm.unipi.it/e/321

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Colloquium 17 aprile ore 16.00
by Stefano Massei 15 Apr '25

15 Apr '25

Cari tutti, a nome della Commissione Colloquia di Dipartimento, vi ricordo che giovedì 17 aprile alle 16.00 in AULA MAGNA Virginie Ehrlacher<https://team.inria.fr/matherials/team-members/virginie-ehrlacher-galland/> (Ecole des Ponts ParisTech) terrà un <https://www.dm.unipi.it/en/seminar/?id=67a64aff762f5b32f7b4dfd3> colloquium<https://www.dm.unipi.it/en/seminar/?id=67a64aff762f5b32f7b4dfd3> sul tema: “A sparse approximation of the Lieb functional with moment constraints”. Cordiali saluti, Stefano Massei

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Next NUMPI seminar: set the date
by Fabio Durastante 15 Apr '25

15 Apr '25

Good morning, We would like to fix the date for the next NUMPI seminar in May. It will be a seminar held by Federica Mugnaioni (Ph.D. Scuola Normale Superiore) on the topic of preconditioners for discretization of fictitious domain problems. Please reply with your availability for the days of May 12/13 and we will try to organize it at a time convenient for most of us: https://date.dm.unipi.it/Vh6AwjL3MKGWBESp Best, Fabio

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[Indico] Raf Vandebril, On inverse eigenvalue problems for multiple orthogonal polynomials, 14/04/2025, 11:30 Europe/Rome
by leonardo.robol＠unipi.it 14 Apr '25

14 Apr '25

Title: On inverse eigenvalue problems for multiple orthogonal polynomials, Speaker(s): Raf Vandebril, KU Leuven, Date and time: 14 Apr 2025, 11:30 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Saletta Riunioni). You can access the full event here: https://events.dm.unipi.it/e/318 Abstract -------- Multiple orthogonal polynomials (MOP's) arise in various applications, including approximation theory, random matrix theory, and numerical integration. To define MOP's, one needs multiple inner products, leading to two types of MOP’s, which are mutually biorthogonal. These MOP's satisfy recurrence relations, which can be linked to linear algebra, via discretization. As a result we get an inverse eigenvalue problem to retrieve the matrix of recurrences directly. We provide two algorithms for solving the inverse eigenvalue problem, one based on classical equivalence transformations and one linked to (block) Krylov methods. Numerical illustrations are provided to demonstrate correctness of the approach and also reveal the strong sensitivity of the problem. -- Indico :: Email Notifier https://events.dm.unipi.it/e/318

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[Indico] Raf Vandebril, On inverse eigenvalue problems for multiple orthogonal polynomials, 14/04/2025, 11:30 Europe/Rome
by leonardo.robol＠unipi.it 08 Apr '25

08 Apr '25

Title: On inverse eigenvalue problems for multiple orthogonal polynomials, Speaker(s): Raf Vandebril, KU Leuven, Date and time: 14 Apr 2025, 11:30 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Saletta Riunioni). You can access the full event here: https://events.dm.unipi.it/e/318 Abstract -------- Multiple orthogonal polynomials (MOP's) arise in various applications, including approximation theory, random matrix theory, and numerical integration. To define MOP's, one needs multiple inner products, leading to two types of MOP’s, which are mutually biorthogonal. These MOP's satisfy recurrence relations, which can be linked to linear algebra, via discretization. As a result we get an inverse eigenvalue problem to retrieve the matrix of recurrences directly. We provide two algorithms for solving the inverse eigenvalue problem, one based on classical equivalence transformations and one linked to (block) Krylov methods. Numerical illustrations are provided to demonstrate correctness of the approach and also reveal the strong sensitivity of the problem. -- Indico :: Email Notifier https://events.dm.unipi.it/e/318

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