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[Indico] Cecilia Pagliantini, Model order reduction of parametric Hamiltonian systems on matrix manifolds, 28/03/2023, 16:00 Europe/Rome
by leonardo.robol＠unipi.it 21 Mar '23

21 Mar '23

Title: Model order reduction of parametric Hamiltonian systems on matrix manifolds, Speaker(s): Cecilia Pagliantini, University of Pisa, Date and time: 28 Mar 2023, 16:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Seminari). You can access the full event here: https://events.dm.unipi.it/e/176 Abstract -------- Model order reduction of parametric differential equations aims at constructing low-complexity high-fidelity surrogate models that allow rapid and accurate solutions under parameter variation. The development of reduced order models for Hamiltonian systems is challenged by several 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 slowly decaying Kolmogorov n-width of transport-dominated and non-dissipative phenomena demands large reduced spaces to achieve sufficiently accurate approximations; and (iii) nonlinear operators require hyper-reduction techniques that preserve the gradient structure of the flow velocity.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 adapt in time an approximate low-dimensional phase space endowed with the geometric structure of the full model and to ensure that the reduced flow is still Hamiltonian. -- Indico :: Email Notifier https://events.dm.unipi.it/e/176

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[Indico] Prof. Lloyd N. Trefethen, Applications of AAA Rational Approximation, 21/02/2023, 11:00 Europe/Rome
by fabio.durastante＠unipi.it 20 Feb '23

20 Feb '23

Title: Applications of AAA Rational Approximation, Speaker(s): Prof. Lloyd N. Trefethen, Mathematical Institute, University of Oxford, Date and time: 21 Feb 2023, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Scuola Normale Superiore (Aula Volterra). Address: Piazza dei Cavalieri, 7 - 56126 Pisa You can access the full event here: https://events.dm.unipi.it/e/158 Abstract -------- Abstract:For the first time, a method has recently become available for fast computation of near-best rational approximations on arbitrary sets in the real line or complex plane: the AAA algorithm (Nakatsukasa-Sete-T. 2018). We will present the algorithm and then demonstrate a number of applications, includingdetection of singularities, model order reduction, analytic continuation, functions of matrices, nonlinear eigenvalue problems, interpolation of equispaced data, smooth extension of multivariate real functions, extrapolation of ODE and PDE solutions into the complex plane, solution of Laplace problems, conformal mapping, Wiener-Hopf factorization. Note ---- A reminder of tomorrow's seminar. -- Indico :: Email Notifier https://events.dm.unipi.it/e/158

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[Indico] Prof. Lloyd N. Trefethen, Applications of AAA Rational Approximation, 21/02/2023, 11:00 Europe/Rome
by fabio.durastante＠unipi.it 13 Feb '23

13 Feb '23

Title: Applications of AAA Rational Approximation, Speaker(s): Prof. Lloyd N. Trefethen, Mathematical Institute, University of Oxford, Date and time: 21 Feb 2023, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Scuola Normale Superiore (Aula Volterra). Address: Piazza dei Cavalieri, 7 - 56126 Pisa You can access the full event here: https://events.dm.unipi.it/e/158 Abstract -------- Abstract:For the first time, a method has recently become available for fast computation of near-best rational approximations on arbitrary sets in the real line or complex plane: the AAA algorithm (Nakatsukasa-Sete-T. 2018). We will present the algorithm and then demonstrate a number of applications, includingdetection of singularities, model order reduction, analytic continuation, functions of matrices, nonlinear eigenvalue problems, interpolation of equispaced data, smooth extension of multivariate real functions, extrapolation of ODE and PDE solutions into the complex plane, solution of Laplace problems, conformal mapping, Wiener-Hopf factorization. -- Indico :: Email Notifier https://events.dm.unipi.it/e/158

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Colloquio De Giorgi - Volker Mehrmann, Dirac and Lagrange structures in energy-based mathematical modeling 24/02/23, 16:00
by Fabio Durastante 01 Feb '23

01 Feb '23

We apologize in advance for cross-posting. ******************************************************************************** CENTRO DI RICERCA MATEMATICA "ENNIO DE GIORGI" ******************************************************************************** COLLOQUIO DE GIORGI Centro De Giorgi, Pisa, 24th February 2023 Aula Dini: 4.00 pm The event will take place in person. Volker Mehrmann Technische Universität Berlin Title:“Dirac and Lagrange structures in energy-based mathematical modeling” Abstract: Most real world dynamical systems consist of subsystems from different physical domains, modelled by partial-differential equations, ordinary differential equations, and algebraic equations, combined with input and output connections. To deal with such complex system, in recent years the class of dissipative port-Hamiltonian (pH) descriptor systems has emerged as a very successful modeling methodology. The main reasons are that the network based interconnection of pH systems is again pH, Galerkin projection in PDE discretization and model reduction preserve the pH structure and the physical properties are encoded in the geometric properties of the flow as well as the algebraic properties of the equations. Furthermore, dissipative pH system form a very robust representation under structured perturbations and directly indicate Lyapunov functions for stability analysis. Using global geometric and algebraic points of view, via Dirac and Lagrange spaces or manifolds, translations between different representations are presented. Characterizations are also derived when a general differential-algebraic system can be transformed into one of these structured representations. Numerical approaches for computing the structural information and the described transformations are derived and the results are demonstrated with some real world examples. Web site: http://www.crm.sns.it/course/6529/ <https://es.sonicurlprotection-fra.com/click?PV=2&MSGID=20230131222506106602…> Please note that for organizational purposes, registration <https://es.sonicurlprotection-fra.com/click?PV=2&MSGID=20230131222506106602…>is mandatory. CRM Secretariat Scuola Normale Superiore Piazza dei Cavalieri, 3 56126 Pisa, Italy

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[Indico] Dr Gianluca Ceruti, Robust numerical integrators for dynamical low-rank approximation, 15/12/2022, 11:00 Europe/Rome
by leonardo.robol＠unipi.it 14 Dec '22

14 Dec '22

Title: Robust numerical integrators for dynamical low-rank approximation, Speaker(s): Dr Gianluca Ceruti, École Polytechnique Fédérale de Lausanne, Date and time: 15 Dec 2022, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: room Aula Magna (Dipartimento di Matematica). You can access the full event here: https://events.dm.unipi.it/e/138 Abstract -------- The discretization of time-dependent high-dimensional PDEs suffers from an undesired effect, the so-called curse of dimensionality: The amount of data to be stored and treated grows exponentially and exceeds standard capacity of common computational devices. In this setting, time dependent model order reductions techniques are desirable. In the present seminar, we present a broad overview on dynamical low-rank approximation together with recent developments on robust numerical integrators for it. Dynamical low-rank approximation for matrices is firstly presented, and a numerical integrator with two remarkable properties is introduced: the matrix projector splitting integrator. Based upon this numerical integrator, we construct two equivalent extensions for tensors, multi-dimensional arrays, in Tucker format - a high-order generalization of the SVD decomposition for matrices. These extensions are proven to preserve the excellent qualities of the matrix integrator. Then, via a novel compact formulation of the Tucker integrator, we further extend the matrix and Tucker projector splitting integrators to the most general class of Tree Tensor Networks. Important examples belonging to this class and of interest for applications are given by (but not only restricted to) Tensor Trains.The present seminar is based upon joint works with Ch. Lubich, H. Walach, J. Kusch, and D. Sulz. -- Indico :: Email Notifier https://events.dm.unipi.it/e/138

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[Indico] Dr Gianluca Ceruti, Robust numerical integrators for dynamical low-rank approximation, 15/12/2022, 11:00 Europe/Rome
by leonardo.robol＠unipi.it 12 Dec '22

12 Dec '22

Title: Robust numerical integrators for dynamical low-rank approximation, Speaker(s): Dr Gianluca Ceruti, École Polytechnique Fédérale de Lausanne, Date and time: 15 Dec 2022, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: room Aula Riunioni (Dipartimento di Matematica). You can access the full event here: https://events.dm.unipi.it/e/138 Abstract -------- The discretization of time-dependent high-dimensional PDEs suffers from an undesired effect, the so-called curse of dimensionality: The amount of data to be stored and treated grows exponentially and exceeds standard capacity of common computational devices. In this setting, time dependent model order reductions techniques are desirable. In the present seminar, we present a broad overview on dynamical low-rank approximation together with recent developments on robust numerical integrators for it. Dynamical low-rank approximation for matrices is firstly presented, and a numerical integrator with two remarkable properties is introduced: the matrix projector splitting integrator. Based upon this numerical integrator, we construct two equivalent extensions for tensors, multi-dimensional arrays, in Tucker format - a high-order generalization of the SVD decomposition for matrices. These extensions are proven to preserve the excellent qualities of the matrix integrator. Then, via a novel compact formulation of the Tucker integrator, we further extend the matrix and Tucker projector splitting integrators to the most general class of Tree Tensor Networks. Important examples belonging to this class and of interest for applications are given by (but not only restricted to) Tensor Trains.The present seminar is based upon joint works with Ch. Lubich, H. Walach, J. Kusch, and D. Sulz. -- Indico :: Email Notifier https://events.dm.unipi.it/e/138

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Assegno di ricerca presso il Dipartimento di Matematica
by Leonardo Robol 23 Nov '22

23 Nov '22

Buongiorno, si è appena aperto un bando per un assegno di ricerca di 12 mesi presso il Dipartimento di Matematica (di Pisa), su fondi PNRR. La scadenza è il 21/12/22. Vi prego diffondere l'annuncio con chiunque possa essere interessato/a. https://bandi.unipi.it/public/Bandi/Detail/f2d456ca-5df1-4fcd-b95c-d16d0434…. A presto, -- Leonardo Robol.

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[Indico] Aaron Melman, Recent extensions of scalar and matrix polynomial properties and their interactions, 10/11/2022, 11:00 Europe/Rome
by leonardo.robol＠unipi.it 03 Nov '22

03 Nov '22

Title: Recent extensions of scalar and matrix polynomial properties and their interactions, Speaker(s): Aaron Melman, Santa Clara University, USA, Date and time: 10 Nov 2022, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Riunioni). You can access the full event here: https://events.dm.unipi.it/e/114 Abstract -------- Several results for scalar polynomials are extended and then generalized to matrix polynomials. Among them are a directional version of Pellet's theorem for both scalarand matrix polynomials, which establishes an exclusion interval for the magnitudes of polynomial zeros or eigenvalues having a given argument, as well as results involving real polynomials with sign restrictions on their coefficients. The latter lead to exclusion sectorsfor polynomial eigenvalues. In addition, it is shown how new results can be obtained by embedding scalar polynomials into a matrix polynomial framework, and examples are given of how the interactionbetween scalar and matrix polynomials benefits both. If time (and interest) permits, an improvement of theorems by Hayashi and Hurwitz from the beginning of the twentiethcentury will be presented. These theorems concern the location of polynomial zeros when the coefficients exhibit certain sign patterns. -- Indico :: Email Notifier https://events.dm.unipi.it/e/114

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Seminario di oggi (Santolo Leveque)
by Leonardo Robol 24 Oct '22

24 Oct '22

Cari tutt*, vi ricordo il seminario di oggi di Santolo Leveque, alle 16.00: https://events.dm.unipi.it/event/113/ Al contrario di come era stato scritto nei primi avvisi, il seminario sarà in Aula Riunioni, e non in Aula Magna (nel caso aveste annotato l'aula tempo fa). A dopo! -- Leonardo Robol

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Workshop on Quasi-Newton methods
by Stefano Cipolla 23 Oct '22

23 Oct '22

Dear Colleagues, we are delighted to inform you that we are organizing the event "Workshop on Quasi-Newton methods" which will be held in Edinburgh, 9th Nov 2022, please see https://www.maths.ed.ac.uk/~gondzio/qNewton2022/home.html for more information. The workshop aims at promoting the exchange of ideas and to advance the state of the art in the area of Quasi-Newton methods. The *hybrid* workshop will consist of five invited presentations by selected leading researchers. Remote and in person participation are welcome. If you are willing to take part, please register (free of charge) at your earliest convenience, but not later than 31st Oct 2022, at the link https://forms.gle/bNccQ7mTAKhnJYNW6 Very Best Regards, Jacek, Stefano -- 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.

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[Indico] Santolo Leveque, A “matching strategy” for optimal control problems with PDEs as constraints, 24/10/2022, 16:00 Europe/Rome
by leonardo.robol＠unipi.it 18 Oct '22

18 Oct '22

Title: A “matching strategy” for optimal control problems with PDEs as constraints, Speaker(s): Santolo Leveque, Scuola Normale Superiore, Pisa, Date and time: 24 Oct 2022, 16:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Riunioni). You can access the full event here: https://events.dm.unipi.it/e/113 Abstract -------- Saddle-point systems arise quite often in many areas of scientific computing. For instance, this type of system can be found in computational fluid dynamics, constrained optimization, finance, image reconstruction, and many more scientific applications. Due to their convenient structure and high dimensionality, preconditioned iterative methods are usually employed in order to solve this class of problems. By making use of saddle-point theory, one is able to derive optimal preconditioners for a general saddle-point system. However, the major drawback is that the cost of applying their inverse operator is almost as costly as inverting the original system. For this reason, one would rather find easy-to-invert approximation of the main blocks of the preconditioner considered.In this talk, we will present the “matching strategy” derived in [3] for approximating the Schur complement of a saddle-point system arsing from optimal control problems with PDE as constraints. We will mainly focus on time-dependent PDE, when employing a Crank–Nicolson discretization in time. After applying an optimize-then-discretize approach, one is faced with continuous first-order optimality conditions consisting of a coupled system of PDEs. After discretizing with Crank–Nicolson, one has to solve for a non-symmetric system. We apply a carefully tailored invertible transformation for symmetrizing the latter, and derive an ideal preconditioner by making use of saddle-point theory. The transformation is then employed within the preconditioner in order to derive optimal approximations of the (1,1)-block and of the Schur complement. We prove the latter through bounds on the eigenvalues, and test our solver against the widely-used preconditioner derived in [2] for the linear system arising from a backward Euler discretization in time. These demonstrate the effectiveness and robustness of our solver with respect to all the parameters involved in the problem considered.This talk is based on the work in [1].References[1] S. Leveque and J. W. Pearson, Fast Iterative Solver for the Optimal Control of Time-Dependent PDEs with Crank–Nicolson Discretization in Time, Numer. Linear Algebra Appl. 29, e2419, 2022.[2] J. W. Pearson, M. Stoll and A. J. Wathen, Regularization-Robust Preconditioners for Time-Dependent PDE-Constrained Optimization Problems, SIAM J. Matrix Anal. Appl. 33, 1126–1152, 2012.[3] J. W. Pearson and A. J. Wathen, A New Approximation of the Schur Complement in Preconditioners for PDE-Constrained Optimization, Numer. Linear Algebra Appl. 19, 816–829, 2012. -- Indico :: Email Notifier https://events.dm.unipi.it/e/113

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[Indico] Aaron Melman, Recent extensions of scalar and matrix polynomial properties and their interactions, 10/11/2022, 11:00 Europe/Rome
by leonardo.robol＠unipi.it 10 Oct '22

10 Oct '22

Title: Recent extensions of scalar and matrix polynomial properties and their interactions, Speaker(s): Aaron Melman, Santa Clara University, USA, Date and time: 10 Nov 2022, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Riunioni). You can access the full event here: https://events.dm.unipi.it/e/114 Abstract -------- Several results for scalar polynomials are extended and then generalized to matrix polynomials. Among them are a directional version of Pellet's theorem for both scalarand matrix polynomials, which establishes an exclusion interval for the magnitudes of polynomial zeros or eigenvalues having a given argument, as well as results involving real polynomials with sign restrictions on their coefficients. The latter lead to exclusion sectorsfor polynomial eigenvalues. In addition, it is shown how new results can be obtained by embedding scalar polynomials into a matrix polynomial framework, and examples are given of how the interactionbetween scalar and matrix polynomials benefits both. If time (and interest) permits, an improvement of theorems by Hayashi and Hurwitz from the beginning of the twentiethcentury will be presented. These theorems concern the location of polynomial zeros when the coefficients exhibit certain sign patterns. -- Indico :: Email Notifier https://events.dm.unipi.it/e/114

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[Indico] Santolo Leveque, A “matching strategy” for optimal control problems with PDEs as constraints, 24/10/2022, 16:00 Europe/Rome
by fabio.durastante＠unipi.it 05 Oct '22

05 Oct '22

Title: A “matching strategy” for optimal control problems with PDEs as constraints, Speaker(s): Santolo Leveque, Scuola Normale Superiore, Pisa, Date and time: 24 Oct 2022, 16:00 (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/113 Abstract -------- Saddle-point systems arise quite often in many areas of scientific computing. For instance, this type of system can be found in computational fluid dynamics, constrained optimization, finance, image reconstruction, and many more scientific applications. Due to their convenient structure and high dimensionality, preconditioned iterative methods are usually employed in order to solve this class of problems. By making use of saddle-point theory, one is able to derive optimal preconditioners for a general saddle-point system. However, the major drawback is that the cost of applying their inverse operator is almost as costly as inverting the original system. For this reason, one would rather find easy-to-invert approximation of the main blocks of the preconditioner considered.In this talk, we will present the “matching strategy” derived in [3] for approximating the Schur complement of a saddle-point system arsing from optimal control problems with PDE as constraints. We will mainly focus on time-dependent PDE, when employing a Crank–Nicolson discretization in time. After applying an optimize-then-discretize approach, one is faced with continuous first-order optimality conditions consisting of a coupled system of PDEs. After discretizing with Crank–Nicolson, one has to solve for a non-symmetric system. We apply a carefully tailored invertible transformation for symmetrizing the latter, and derive an ideal preconditioner by making use of saddle-point theory. The transformation is then employed within the preconditioner in order to derive optimal approximations of the (1,1)-block and of the Schur complement. We prove the latter through bounds on the eigenvalues, and test our solver against the widely-used preconditioner derived in [2] for the linear system arising from a backward Euler discretization in time. These demonstrate the effectiveness and robustness of our solver with respect to all the parameters involved in the problem considered.This talk is based on the work in [1].References[1] S. Leveque and J. W. Pearson, Fast Iterative Solver for the Optimal Control of Time-Dependent PDEs with Crank–Nicolson Discretization in Time, Numer. Linear Algebra Appl. 29, e2419, 2022.[2] J. W. Pearson, M. Stoll and A. J. Wathen, Regularization-Robust Preconditioners for Time-Dependent PDE-Constrained Optimization Problems, SIAM J. Matrix Anal. Appl. 33, 1126–1152, 2012.[3] J. W. Pearson and A. J. Wathen, A New Approximation of the Schur Complement in Preconditioners for PDE-Constrained Optimization, Numer. Linear Algebra Appl. 19, 816–829, 2012. -- Indico :: Email Notifier https://events.dm.unipi.it/e/113

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Reading course (Randomized linear algebra -- starting October 2022)
by Leonardo Robol 28 Sep '22

28 Sep '22

Cari tutti, insieme a Fabio e Stefano abbiamo pensato di organizzare per questo semestre un "Reading course", dove i partecipanti potranno alternarsi a presentare risultati significativi di analisi numerica presi da articoli e/o capitoli di libri. L'idea è di avere degli incontri informali di durata maggiore rispetto ai seminari (2h), in cui chi presenta abbia il tempo di spiegare le cose con calma (magari approfondendo anche alla lavagna, o mostrando degli esperimenti numerici). Gli incontri sono aperti a tutti, e speriamo che possano essere di particolare utilità per dottorandi / studenti magistrali. L'argomento con cui vorremmo iniziare è "Randomized Linear Algebra", per poi continuare successivamente (ammesso che l'iniziativa abbia successo) con un tema scelto in base ai desideri di chi partecipa. Anche per questo semestre abbiamo selezionato gli articoli introduttivi da cui partire, ma poi potremo scegliere cosa approfondire in base alle preferenze dell'audience. Trovate maggiori informazioni sulla pagina web: https://numpi.dm.unipi.it/reading-course Invitiamo chi volesse partecipare a segnarsi sul Doodle per la prima sessione, programmata agli inizi di Ottobre: https://doodle.com/meeting/participate/id/eXoknmgd Segnatevi entro venerdì 09/09, in modo che poi possiamo scegliere la prima data, e pubblicizzare ulteriormente l'iniziativa. A presto, -- Leonardo.

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Annuncio Seminario di Matematica, Dr. Anna Weller (26.09.2022)
by Fabio Durastante 21 Sep '22

21 Sep '22

*Avviso Seminario di Matematica* Data: Monday, September 26, 2022 Ora: 16:15 - 17:15 Luogo: Aula Volterra, Normale Speaker: Anna Weller University of Cologne Titolo: *A spectral Galerkin method for the solution of reaction-diffusion equations on metric graphs* Abstract: Weinvestigateaspectralsolutionapproachforreaction-diffusionequationsongraphs interpretedastopologicalspace(metricgraphs).Ofspecialinterestisthenumerical computationofeigenfunctionsofthenegativesecondorderderivativeactingoneach edge.Remarkably,itispossibletogiveanexplicitcharacterizationoftheseeigenfunctions andcorrespondingeigenvalues.Moreover,forequilateralgraphs,wewillshow howtoefficientlycomputeanarbitrarylowerpartofthespectrumusingaveryuseful relationshiptothegraphLaplacianmatrixoftheunderlyingcombinatorialgraph. Finally,wecanusethebasisofeigenfunctionsinaGalerkinapproachtosolvevarious PDEsonmetricgraphs,wereweherefocusonreaction-diffusionequations.This problemismotivatedbyarecentcollaborationwiththeInstituteofGeophysicsand MeteorologyoftheUniversityofCologneonthemodelingofproteindistributionin Alzheimer’sdiseasetogetherwiththeUniversityHospitalCologne1.Partofmynumerical resultsarejointworkwithProf.Dr.MarkAinsworth(BrownUniversity)and withChong-SonDroege(UniversityofCologne). References [1]M.Ainsworth,A.Weller,AspectralGalerkinmethodforthesolutionofpartialdifferential equationsonmetricgraphs,inpreparation. [2]M.Ainsworth,A.Weller,AspectralGalerkinmethodforthesolutionofreaction-diffusion equationsonmetricgraphs,OberwolfachReports,WorkshopReport36,2021. [3]A.Kunoth,A.Weller,T.Yilmaz,Acomputationalbrainspheremodelforthesimulationof Alzheimer’sDisease.SnapshotsofmodernmathematicsfromOberwolfach,inpreparation. [4]A.Weller,G.N.Bischof,P.Schl̈uter,N.Richter,J.Dronse,̈O.Onur,J.Kukolja,B.Neu- maier,A.Kunoth,Y.Shao,T.vanEimeren,A.Drzezga,Findingnewcommunities:A principleofneuronalnetworkreorganizationinAlzheimersdisease.BrainConnectivity, 11(3):225-238,2021.DOI:10.1089/brain.2020.0889 ThisworkwassupportedbytheExcellenceInitiativeoftheUniversityofCologne

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[NOMADS] Seminar today by Emre Mengi
by Francesco Tudisco 19 Sep '22

19 Sep '22

Dear all, It is my great pleasure to invite you all to today’s NOMADS seminar by Emre Mengi<http://home.ku.edu.tr/~emengi/> from Koc University (Turkey), who will present recent work on the computation of the dominant poles of a transfer function of a descriptor system. The seminar will take place **today Sept 19 at 14:30 (CET) in GSSI’s Library (NOT the main lecture hall as previously announced). Remote participation will also be possible via the zoom link: https://us02web.zoom.us/j/89668910844?pwd=TmVwQUFoNklUajAzMlEyMzB6ZVZzUT09 Below you can find title and abstract. Hope to see you all later today! All the best, —Francesco Tudisco ====== Emre Mengi, Koc University, Istanbul, Turkey http://home.ku.edu.tr/~emengi/<https://www.google.com/url?q=http://home.ku.edu.tr/~emengi/&sa=D&source=cal…> Title: Large-Scale Estimation of the Dominant Poles of a Transfer Function Abstract: The dominant poles of the transfer function of a descriptor system provide important insight into the behavior of the system. They indicate the parts of the imaginary axis where the transfer function exhibits large norm. Moreover, the dominant poles and corresponding eigenvectors can be put in use to form a reduced-order approximation to the system. In the talk, I will describe a subspace framework to compute a prescribed number of dominant poles of a large-scale descriptor system. The framework applies Petrov-Galerkin projections to the original system, then computes the dominant poles of the projected small-scale system, for instance by the QZ algorithm, and expands the subspaces so that the projected system after the subspace expansion interpolates the original system at these dominant poles. I will explain why the subspace framework converges at a quadratic rate, and report numerical results illustrating the rapid convergence, and accuracy of the approach. For more information, please see: https://num-gssi.github.io/seminar/<https://www.google.com/url?q=https://num-gssi.github.io/seminar/&sa=D&sourc…> The seminar will take place in the Library, but remote participation will also be possible via the zoom link: https://us02web.zoom.us/j/89668910844?pwd=TmVwQUFoNklUajAzMlEyMzB6ZVZzUT09<https://www.google.com/url?q=https://us02web.zoom.us/j/89668910844?pwd%3DTm…> -- 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/DB6PR05MB32237075AF…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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[NOMADS] Seminar today by Stefano Massei
by Francesco Tudisco 14 Sep '22

14 Sep '22

Dear all, It is my great pleasure to invite you all to today’s NOMADS seminar by Stefano Massei<https://sites.google.com/view/stefanomassei/home>, University of Pisa, who will present his recent work on fast parallel-in-time numerical integration of differential equations. The seminar will take place today, Sept 14, at 15:00 (CET) in GSSI’s Main Lecture Hall (the “red room”). Remote participation will also be possible via the zoom link: https://us02web.zoom.us/j/89668910844?pwd=TmVwQUFoNklUajAzMlEyMzB6ZVZzUT09 Below you can find title and abstract. Hope to see you all later today! All the best, –– Francesco Tudisco Associate Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io<https://ftudisco.gitlab.io/> Stefano Massei University of Pisa, Italy https://sites.google.com/view/stefanomassei/home<https://www.google.com/url?q=https://sites.google.com/view/stefanomassei/ho…> Title of the talk: Improved parallel-in-time integration via low-rank updates and interpolation 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. For more information, please see: https://num-gssi.github.io/seminar/<https://www.google.com/url?q=https://num-gssi.github.io/seminar/&sa=D&sourc…> The seminar will take place in the Main Lecture Hall, but remote participation will also be possible via the zoom link: https://us02web.zoom.us/j/89668910844?pwd=TmVwQUFoNklUajAzMlEyMzB6ZVZzUT09<https://www.google.com/url?q=https://us02web.zoom.us/j/89668910844?pwd%3DTm…> -- 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/DB6PR05MB32231F13C7…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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Fwd: Corso sui metodi matematici per la scienza del clima - prof. M. Ghil
by Leonardo Robol 01 Jul '22

01 Jul '22

Cari tutti, vi inoltro l'avviso di un corso di dottorato che si terrà la settimana prossima, e che potenzialmente potrebbe essere di interesse per gli iscritti alla mailing list (anche solo come fonte di applicazioni interessanti/rilevanti). La frequenza è libera, e sarà mandato in streaming anche online. A presto! -- Leonardo. -------- Forwarded Message -------- From: Simona Guidotti <simona.guidotti(a)unipi.it> To: utenti(a)fields.dm.unipi.it Subject: [Utenti] Corso sui metodi matematici per la scienza del clima - prof. M. Ghil Date: Fri, 1 Jul 2022 13:21:09 +0200 > Comunico che lunedì 4 luglio si terrà la prima lezione del corso sui > "Metodi matematici per la scienza del clima" (prof. Michael Ghil). > > Troverete tutte le informazioni alle seguenti pagine: > > https://www.dm.unipi.it/phd/phd-courses/ > > https://clima.dm.unipi.it/2022/01/26/doctorate-course-mathematical-methods-… > > Saluti, > > Simona Guidotti > > _______________________________________________ > Utenti mailing list > Utenti(a)fields.dm.unipi.it > https://fields.dm.unipi.it/listinfo/utenti

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[NOMADS] seminar - Massimiliano Fasi
by Francesco Tudisco 22 Jun '22

22 Jun '22

Dear all, You are all invited to the next NOMADS seminar on low-precision numerical computations, which will be given by Massimiliano Fasi from Durham University on Friday June 24, 2022. The seminar will take place in the GSSI’s Library, but remote participation will also be possible via the zoom link: https://us02web.zoom.us/j/89668910844?pwd=TmVwQUFoNklUajAzMlEyMzB6ZVZzUT09 Below you can find the details about his talk. Looking forward to seeing you all on Friday! – Francesco Tudisco Massimiliano Fasi (Durham University, UK) https://www.durham.ac.uk/staff/massimiliano-fasi/ Title of the talk: CPFloat: A C Library for Emulating Low-Precision Arithmetic Abstract: Low-precision floating-point arithmetic can be simulated via software by executing each arithmetic operation in hardware and rounding the result to the desired number of significant bits. For IEEE-compliant formats, rounding requires only standard mathematical library functions, but handling subnormals, underflow, and overflow demands special attention, and numerical errors can cause mathematically correct formulae to behave incorrectly in finite arithmetic. Moreover, the ensuing algorithms are not necessarily efficient, as the library functions these techniques build upon are typically designed to handle a broad range of cases and may not be optimized for the specific needs of floating-point rounding algorithms. CPFloat is a C library that offers efficient routines for rounding arrays of binary32 and binary64 numbers to lower precision. The software exploits the bit level representation of the underlying formats and performs only low-level bit manipulation and integer arithmetic, without relying on costly library calls. In numerical experiments the new techniques bring a considerable speedup (typically one order of magnitude or more) over existing alternatives in C, C++, and MATLAB. To the best of our knowledge, CPFloat is currently the most efficient and complete library for experimenting with custom low-precision floating-point arithmetic available in any language. For more information, please see: https://num-gssi.github.io/seminar/ -- 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/DB6PR05MB322380D250…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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Fwd: Fwd: PhD-positions at the University of Stuttgart
by Federico Poloni 13 Jun '22

13 Jun '22

Buongiorno, inoltro questo annuncio per alcuni posti di dottorato in "Numerical Analysis of domain decomposition methods" in caso conosciate qualche interessato. Federico -------- Messaggio Inoltrato -------- Oggetto: PhD-positions at the University of Stuttgart Data: Mon, 13 Jun 2022 09:03:26 +0000 Mittente: Stamm, Benjamin <best(a)acom.rwth-aachen.de> A: Benjamin.Stamm(a)ians.uni-stuttgart.de <Benjamin.Stamm(a)ians.uni-stuttgart.de> Dear colleagues, Please apologize for the mass mail. It is my pleasure to announce several openings for PhD-positions with my start at the University of Stuttgart this summer. I would be extremely grateful if you could forward this mail to interested students and post the attached flyers in your building. Of course, I will also diffuse it in a less analog manner, but I’d also like to do it the good old way ;-) Warm greetings, Ben Prof. Dr. Benjamin Stamm Applied and Computational Mathematics RWTH Aachen University Schinkelstraße 2, 52062 Aachen (Germany) Tel.: + 49 / 241 - 80 98672 (direct line) Tel.: + 49 / 241 - 80 98660 (secretary) e-mail: best(a)acom.rwth-aachen.de <mailto:best@acom.rwth-aachen.de> web: http://tinyurl.com/jv7h8n4

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Math colloquium today
by Francesco Tudisco 26 May '22

26 May '22

Dear all, Please note that there was a typo in the event reminder you received earlier today. The lecture by Stefano Serra-Capizzano will take place today at 15:00 in the Main Lecture Hall, not in the Auditorium! ============== GSSI, via F Crispi 7. Room: MLH. Date: 26 May at 15:00 Stefano Serra-Capizzano, University of Insubria The GLT class as a Generalized Fourier Analysis and applications Participation is also possible via the zoom link: https://us02web.zoom.us/j/89664583638?pwd=MTluRndSWUhoMG5VbU80Rlcydmg2dz09 <https://us02web.zoom.us/j/89664583638?pwd=MTluRndSWUhoMG5VbU80Rlcydmg2dz09> 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. For more information, please see: https://indico.gssi.it/event/394/ — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io <https://ftudisco.gitlab.io/> -- 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/66E0C4A0-72B8-4B7C-…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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[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 26 May '22

26 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, This is just a gentle reminder that this week's Math Colloquium will take place today at 3pm in the Main Auditorium. Looking forward to seeing you all there! 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/165354840854.1432.1…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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[NOMADS] Seminar - Paolo Cifani
by Francesco Tudisco 24 May '22

24 May '22

Dear all, You are all invited to the following NOMADS seminar by Paolo Cifani, GSSI, which will take place Today at 13:45 in MLH and online via zoom at the following address: https://us02web.zoom.us/j/83830006962?pwd=SmI1MTVKRTllU3dBR01Ybko5bzBJdz09 <https://us02web.zoom.us/j/83830006962?pwd=SmI1MTVKRTllU3dBR01Ybko5bzBJdz09> Looking forward to seeing you all later! Nicola and Francesco ============== GSSI, via F Crispi 7. Room: MLH. Date: 24 May at 13:45 Paolo Cifani (GSSI) Geometric integration of Lie-Poisson flows on the sphere In this seminar I will touch upon the recent developments in structure-preserving (geometric) integration of Euler’s equations for two-dimensional incompressible flows. It has been known for half a century that the dynamics of incompressible ideal fluids in two dimensions can be understood as an evolution equation on the contangent bundle of the infinite-dimensional Lie group of symplectic dffeomorphisms. In particular, the vorticity equation constitutes a Lie-Poisson system characterized by an infinite number of first integrals, i.e. the integrated powers of vorticity. This set of constraints, absent in three dimensions, has profound effects on the energy transfer mechanisms across scales of motion. Yet, the construction of a numerical system which preserves this rich Poisson structure has been elusive. Most attempts either fail in fully preserving the geometric structure or have a high computational complexity. Here, I will show that, thanks to our recent advances, it possible to design a geometric integrator which embeds this fundamental principle of the continuum into the discrete system at a modest computational cost. The construction of such scheme, the main numerical algorithms and their parallelisation on modern supercomputing facilities will be discussed. Finally, an application to the spectrum of homogeneous two-dimensional turbulence will be illustrated. For more information, please see: https://num-gssi.github.io/seminar/ The seminar will take place in the Main Lecture Hall, but remote participation will also be possible via the zoom link: https://us02web.zoom.us/j/89668910844?pwd=TmVwQUFoNklUajAzMlEyMzB6ZVZzUT09 — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io <https://ftudisco.gitlab.io/> -- 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/5893E020-236E-481D-…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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[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.

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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.

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