NumPI October 2021

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Annuncio di seminario, 25/10 (Cecilia Pagliantini)
by Leonardo Robol 25 Oct '21

25 Oct '21

Speaker: Cecilia Pagliantini Affiliation: TU Eindhoven Venue: Sala Seminari, Dipartimento di Matematica Time: Monday, 25/10/2021, 15:00 Title: Structure-preserving dynamical model order reduction of parametric Hamiltonian systems In real-time and many-query simulations of parametric differential equations, computational methods need to face high computational costs to provide sufficiently accurate and stable numerical solutions. To address this issue, model order reduction techniques aim at constructing low-complexity high-fidelity surrogate models that allow rapid and accurate solutions under parameter variation. In this talk, we will consider reduced basis methods (RBM) for the model order reduction of parametric Hamiltonian dynamical systems describing nondissipative phenomena. The development of RBM for Hamiltonian systems is challenged by two main factors: (i) failing to preserve the geometric structure encoding the physical properties of the dynamics, such as invariants of motion or symmetries, might lead to instabilities and unphysical behaviors of the resulting approximate solutions; (ii) the \emph{local} low-rank nature of transport-dominated and nondissipative phenomena demands large reduced spaces to achieve sufficiently accurate approximations. We will discuss how to address these aspects via a structure-preserving nonlinear reduced basis approach based on dynamical low-rank approximation. The gist of the proposed method is to evolve low-dimensional surrogate models on a phase space that adapts in time while being endowed with the geometric structure of the full model. Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Annuncio di seminario, 15/10 (Igor Simunec)
by Leonardo Robol 15 Oct '21

15 Oct '21

Cari tutti, a breve ricominceremo con i tradizionali seminari NumPi, questa volta in forma "ibrida". Per tutti quelli che vorranno ci sarà la possibilità di seguire in presenza in Aula Magna del Dipartimento di Matematica (compilando questa form: https://forms.gle/AaMgajhKhroXdHqY6). Per gli altri, organizzeremo lo streaming tramite il solito link ( https://hausdorff.dm.unipi.it/b/leo-xik-xu4). Qui sotto trovate l'annuncio del primo seminario; a breve vi farò avere un Doodle per provare a scegliere un giorno che torni il più comodo possibile a tutti, da utilizzare per quelli successivi. Trovate tutte le informazioni sulla pagina dei seminari del sito NumPi (https://numpi.dm.unipi.it/seminars). A presto, -- Leonardo. Speaker: Igor Simunec Affiliation: Scuola Normale Superiore, Pisa Time: Friday, 15/10/2021, 16:30 Title: Computation of generalized matrix functions with rational Krylov methods Generalized matrix functions [3] are an extension of the notion of standard matrix functions to rectangular matrices, defined using the singular value decomposition instead of an eigenvalue decomposition. In this talk, we consider the computation of the action of a generalized matrix function on a vector and we present a class of algorithms based on rational Krylov methods [2]. These algorithms incorporate as a special case previous methods based on the Golub-Kahan bidiagonalization [1]. By exploiting the quasiseparable structure of the projected matrices, we show that the basis vectors can be updated using a short recurrence, which can be seen as a generalization to the rational case of the Golub-Kahan bidiagonalization. We also prove error bounds that relate the error of these methods to uniform rational approximation on an interval containing the singular values of the matrix. The effectiveness of the algorithms and the accuracy of the bounds is illustrated with numerical experiments. This is joint work with Angelo A. Casulli (Scuola Normale Superiore). [1] F. Arrigo, M. Benzi, and C. Fenu, Computation of generalized matrix functions, SIAM J. Matrix Anal. Appl. 37 (2016), no. 3, 836–860. [2] A. A. Casulli, I. Simunec, Computation of generalized matrix functions with rational Krylov methods, arXiv:2107.12074 (2021). [3] J. B. Hawkins and A. Ben-Israel, On generalized matrix functions, Linear and Multilinear Algebra 1 (1973), no. 2, 163–171. Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Orario per seminari NumPi
by Leonardo Robol 13 Oct '21

13 Oct '21

Cari tutti, a partire dal prossimo seminario (dopo quello di Igor venerdì) cercheremo di scegliere un orario compatibile con gli impegni di tutti, e mantere una cadenza indicativamente bisettimanale. Ho creato un Doodle [1] per la settimana 25/10 - 29/10, dove chiederei (a chi è interessato a seguire i seminari in presenza e/o online) di indicare le preferenze di orario. Sebbene il Doodle sia per quella settimana specifica, è da intendersi come le preferenze in base ai vostri impegni settimanali. Vi chiederei di farci avere una risposta entro venerdì, così che possiamo organizzare il seminario seguente basandoci sulle risposte. Grazie! A presto, -- Leonardo (e Fabio). [1] https://doodle.com/poll/dtvyu6uakv3exdp8

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NumPI October 2021