- NumPI - Mailing list — Dipartimento di Matematica, UniPI

[Indico] [Event reminder] The GLT class as a Generalized Fourier Analysis and applications (26/05/2022, 15:00 Europe/Rome)
by francesco.tudisco＠gssi.it 23 May '22

23 May '22

Please note that the event "The GLT class as a Generalized Fourier Analysis and applications" will start on 26 May 2022, 15:00 (Europe/Rome). It will take place at GSSI (Rectorate-Building-Auditorium). You can access the full event here: https://indico.gssi.it/e/394 Description ----------- Stefano Serra-Capizzano University of Insubria, Italy http://scienze-como.uninsubria.it/serra/ Title of the talk: The GLT class as a Generalized Fourier Analysis and applications Abstract: Recently, the class of Generalized Locally Toeplitz (GLT) sequences has been introduced as a generalization both of classical Toeplitz sequences and of variable coefficient differential operators and, for every sequence of the class, it has been demonstrated that it is possible to give a rigorous description of the asymptotic spectrum in terms of a function (the symbol) that can be easily identified. This generalizes the notion of a symbol for differential operators also of fractional type (discrete and continuous) or for Toeplitz sequences for which it is identified through the Fourier coefficients and is related to the classical Fourier Analysis. The GLT class has nice algebraic properties and indeed it has been proven that it is stable under linear combinations, products, and inversion when the sequence which is inverted shows a sparsely vanishing symbol (sparsely vanishing symbol = a symbol which vanishes at most in a set of zero Lebesgue measure). Furthermore, the GLT class virtually includes any approximation by local methods (Finite Difference, Finite Element, Isogeometric Analysis of partial differential equations (PDEs) and, based on this, we demonstrate that our results on GLT sequences can be used in a PDE setting in various directions. Detailed PDF version of the abstract: HERE The seminar will take place in the Auditorium, but remote participation will also be possible via the zoom link: https://us02web.zoom.us/j/89664583638?pwd=MTluRndSWUhoMG5VbU80Rlcydmg2dz09 Note ---- Dear all, It is our pleasure to invite you all to the next Math Colloquium on Thursday May 19 at 3pm in the Main Auditorium. The speaker will be Stefano Serra-Capizzano, from the University of Insubria (Como, Italy) with a talk on Generalized Fourier Analysis and Applications. We look forward to seeing you all there! Please feel free to share this announcement as you see fit. Best, Paolo Antonelli, Marielle Simon, Francesco Tudisco and Francesco Viola -- Indico :: Email Notifier https://indico.gssi.it/e/394 -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/165331080936.1432.1…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

1 0

Reminder: Seminario 24/5, 15:00 - Andrew Wathen
by Leonardo Robol 23 May '22

23 May '22

Cari tutti, vi ricordo il Colloquio de Giorgi di domani 24/5 alle 15:00, che sarà tenuto da Andrew Wathen. https://www.crm.sns.it/course/6307/ La registrazione per partecipare (stando a quanto indicato sul sito e sul poster, che allego) è obbligatoria per poter partecipare in presenza. -- Leonardo Robol.

1 0

Fwd: Fwd: Modern Techniques of Very Large Scale Optimization, Edinburgh, 19th - 20th May 2022
by Fabio Durastante 12 May '22

12 May '22

FYI -------- Messaggio Inoltrato -------- Oggetto: Fwd: Modern Techniques of Very Large Scale Optimization, Edinburgh, 19th - 20th May 2022 Data: Thu, 12 May 2022 17:14:04 +0100 Mittente: Stefano Cipolla <scipolla(a)ed.ac.uk> A: fabio.durastante(a)unipi.it ======================== Dear Colleagues, we are delighted to inform you that the workshop "Modern Techniques of Very Large Scale Optimization" will be held in Edinburgh, 19th - 20th May 2022; please see https://www.maths.ed.ac.uk/~gondzio/admm2020/home.html for more information. Although the capacity of in-person attendance is already reached we are happy for online participants to follow the talks. If you are interested and would like to attend the workshop online, then please register (free of charge) at your earliest convenience but not later than Friday 13th May. We will send you a Zoom link. Very Best regards, Jacek, Stefano, Filippo ======================== -- Stefano Cipolla Postdoctoral Research Associate School of Mathematics University of Edinburgh James Clerk Maxwell Building Peter Guthrie Tait Road Edinburgh, EH9 3FD email: scipolla(a)ed.ac.uk The University of Edinburgh is a charitable body, registered in Scotland, with registration number SC005336. Is e buidheann carthannais a th’ ann an Oilthigh Dhùn Èideann, clàraichte an Alba, àireamh clàraidh SC005336.

1 0

Fwd: CENTRO DE GIORGI -- ANNOUNCEMENT -- COLLOQUIO DE GIORGI (24 May 2022)
by Fabio Durastante 12 May '22

12 May '22

*********************************************************************************** CENTRO DI RICERCA MATEMATICA "ENNIO DE GIORGI" ********************************************************************************** COLLOQUIO DE GIORGI Centro De Giorgi, Pisa, 24 May 2022 Aula Dini: 3.00 pm The event will take place in person. Andrew Wathen University of Oxford Title:“Numerical solutions methods for problems of PDE-constrained optimisation” Abstract:Since the advent of computers there has been interest in numerical methods for solving partial differential equations (PDE) problems---both methods of approximation and numerical linear algebra for the resulting sets of equations which are usually of very large dimension. Sometimes it is the solutions themselves that are of interest, but there is a significant class of problems where there is a design optimization criterion with physical constraints that are expressed in terms of PDEs; it is always the motion of fluids described by flow equations which provide the principal constraints when an engineer designs an aerodynamic structure with minimal drag and acceptable lift for example. In this talk I will consider numerical methods for such optimization problems with PDE constraints, in particular methods of iterative numerical linear algebra that render feasible the solution of such problems on advanced computers. Web site:http://www.crm.sns.it/course/6307/ <http://www.crm.sns.it/course/6307/> Please note that for organizational purposes, registration <http://www.crm.sns.it/event/493/registration.html>is mandatory. CRM Secretariat STG Puteano Centro di Ricerca Matematica "Ennio De Giorgi" Scuola Normale Superiore Piazza dei Cavalieri, 3 56126 Pisa, Italy

1 0

Seminario di oggi (link)
by Leonardo Robol 05 May '22

05 May '22

Cari tutti/e, Il seminario di oggi sarà disponibile, oltre che in presenza, anche in streaming al solito link https://meetings.dm.unipi.it/b/leo-xik-xu4. A dopo, -- Leonardo Robol

1 0

[Indico] Stefano Massei, Improved parallel-in-time integration via low-rank updates and interpolation, 05/05/2022, 11:00 Europe/Rome
by leonardo.robol＠unipi.it 04 May '22

04 May '22

Title: Improved parallel-in-time integration via low-rank updates and interpolation, Speaker(s): Stefano Massei, Università di Pisa, Date and time: 5 May 2022, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/89 Abstract -------- This work is concerned with linear matrix equations that arise from the space-time discretization of time-dependent linear partial differential equations (PDEs). Such matrix equations have been considered, for example, in the context of parallel-in-time integration leading to a class of algorithms called ParaDiag. We develop and analyze two novel approaches for the numerical solution of such equations. Our first approach is based on the observation that the modification of these equations performed by ParaDiag in order to solve them in parallel has low rank. Building upon previous work on low-rank updates of matrix equations, this allows us to make use of tensorized Krylov subspace methods to account for the modification. Our second approach is based on interpolating the solution of the matrix equation from the solutions of several modifications. Both approaches avoid the use of iterative refinement needed by ParaDiag and related space-time approaches in order to attain good accuracy. In turn, our new approaches have the potential to outperform, sometimes significantly, existing approaches. This potential is demonstrated for several different types of PDEs. -- Indico :: Email Notifier https://events.dm.unipi.it/e/89

1 0

[Indico] Stefano Massei, Improved parallel-in-time integration via low-rank updates and interpolation, 05/05/2022, 11:00 Europe/Rome
by leonardo.robol＠unipi.it 27 Apr '22

27 Apr '22

Title: Improved parallel-in-time integration via low-rank updates and interpolation, Speaker(s): Stefano Massei, Università di Pisa, Date and time: 5 May 2022, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/89 Abstract -------- This work is concerned with linear matrix equations that arise from the space-time discretization of time-dependent linear partial differential equations (PDEs). Such matrix equations have been considered, for example, in the context of parallel-in-time integration leading to a class of algorithms called ParaDiag. We develop and analyze two novel approaches for the numerical solution of such equations. Our first approach is based on the observation that the modification of these equations performed by ParaDiag in order to solve them in parallel has low rank. Building upon previous work on low-rank updates of matrix equations, this allows us to make use of tensorized Krylov subspace methods to account for the modification. Our second approach is based on interpolating the solution of the matrix equation from the solutions of several modifications. Both approaches avoid the use of iterative refinement needed by ParaDiag and related space-time approaches in order to attain good accuracy. In turn, our new approaches have the potential to outperform, sometimes significantly, existing approaches. This potential is demonstrated for several different types of PDEs. -- Indico :: Email Notifier https://events.dm.unipi.it/e/89

1 0

Ph.D. Course: An introduction to fractional calculus: fundamental ideas and numerics
by Fabio Durastante 27 Apr '22

27 Apr '22

Dear all, Monday 2 May we begin with the Ph.D. course "An introduction to fractional calculus: fundamental ideas and numerics" from 2.00 pm to 4.00 pm in the Aula Seminari. Find the latest information at: https://fdurastante.github.io/courses/introfracalculus.html#about The plan is to schedule the other lessons with those present that day. If there are people that wish to attend, but have difficulties being in person, please let me know at fabio.durastante(a)unipi.it and I'll try activating a streaming of the lecture. For any other question, feel free to write an E-mail. Best, Fabio Durastante

1 0

[Indico] Raf Vandebril,
by leonardo.robol＠unipi.it 12 Apr '22

12 Apr '22

Title: Construction of a sequence of orthogonal rational functions, Speaker(s): Raf Vandebril, Department of Computer Science, KU Leuven, Date and time: 13 Apr 2022, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/86 Abstract -------- Orthogonal polynomials are an important tool to approximate functions. Orthogonal rational functions provide a powerful alternative if the function of interest is not well approximated by polynomials. Polynomials orthogonal with respect to certain discrete inner products can be constructed by applying the Lanczos or Arnoldi iteration to appropriately chosen diagonal matrix and vector. This can be viewed as a matrix version of the Stieltjes procedure. The generated nested orthonormal basis can be interpreted as a sequence of orthogonal polynomials. The corresponding Hessenberg matrix, containing the recurrence coefficients, also represents the sequence of orthogonal polynomials. Alternatively, this Hessenberg matrix can be generated by an updating procedure. The goal of this procedure is to enforce Hessenberg structure onto a matrix which shares its eigenvalues with the given diagonal matrix and the first entries of its eigenvectors must correspond to the elements of the given vector. Plane rotations are used to introduce the elements of the given vector one by one and to enforce Hessenberg structure. The updating procedure is stable thanks to the use of unitary similarity transformations. In this talk rational generalizations of the Lanczos and Arnoldi iterations are discussed. These iterations generate nested orthonormal bases which can be interpreted as a sequence of orthogonal rational functions with prescribed poles. A matrix pencil of Hessenberg structure underlies these iterations. We show that this Hessenberg pencil can also be used to represent the orthogonal rational function sequence and we propose an updating procedure for this case. The proposed procedure applies unitary similarity transformations and its numerical stability is illustrated. -- Indico :: Email Notifier https://events.dm.unipi.it/e/86

1 0

[Indico] Construction of a sequence of orthogonal rational functions,
by leonardo.robol＠unipi.it 05 Apr '22

05 Apr '22

Title: Construction of a sequence of orthogonal rational functions, Speaker(s): Raf Vandebril, Department of Computer Science, KU Leuven, Date and time: 13 Apr 2022, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/86 Abstract -------- Orthogonal polynomials are an important tool to approximate functions. Orthogonal rational functions provide a powerful alternative if the function of interest is not well approximated by polynomials. Polynomials orthogonal with respect to certain discrete inner products can be constructed by applying the Lanczos or Arnoldi iteration to appropriately chosen diagonal matrix and vector. This can be viewed as a matrix version of the Stieltjes procedure. The generated nested orthonormal basis can be interpreted as a sequence of orthogonal polynomials. The corresponding Hessenberg matrix, containing the recurrence coefficients, also represents the sequence of orthogonal polynomials. Alternatively, this Hessenberg matrix can be generated by an updating procedure. The goal of this procedure is to enforce Hessenberg structure onto a matrix which shares its eigenvalues with the given diagonal matrix and the first entries of its eigenvectors must correspond to the elements of the given vector. Plane rotations are used to introduce the elements of the given vector one by one and to enforce Hessenberg structure. The updating procedure is stable thanks to the use of unitary similarity transformations. In this talk rational generalizations of the Lanczos and Arnoldi iterations are discussed. These iterations generate nested orthonormal bases which can be interpreted as a sequence of orthogonal rational functions with prescribed poles. A matrix pencil of Hessenberg structure underlies these iterations. We show that this Hessenberg pencil can also be used to represent the orthogonal rational function sequence and we propose an updating procedure for this case. The proposed procedure applies unitary similarity transformations and its numerical stability is illustrated. -- Indico :: Email Notifier https://events.dm.unipi.it/e/86

1 0