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[Indico] Prof. Andreas Frommer, Structure-aware Krylov approximations to generalized Cayley transforms, 25/10/2024, 11:00 Europe/Rome
by fabio.durastante＠unipi.it 23 Oct '24

23 Oct '24

Title: Structure-aware Krylov approximations to generalized Cayley transforms, Speaker(s): Prof. Andreas Frommer, University of Wuppertal, Date and time: 25 Oct 2024, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Scuola Normale Superiore (Aula Mancini). You can access the full event here: https://events.dm.unipi.it/e/296 Abstract -------- Generalized Cayley transforms arise in implicit numerical integration schemes for ordinary differential equations and differential-algebraic equations. We consider Arnoldi-type methods to approximate the action of such a Cayley transform on a vector and investigate how energy conservation or dissipation can be enforced at the level of each Arnoldi iterate, not just at the level of the exact solution. We also investigate generalizations to higher order collocation methods. Note ---- Reminder of tomorrow's seminar -- Indico :: Email Notifier https://events.dm.unipi.it/e/296

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Difesa dottorato - PhD defense
by Igor SIMUNEC 18 Oct '24

18 Oct '24

Cari tutti, Venerdì 25 ottobre alle 14.30 difenderò la mia tesi di dottorato, intitolata "Advances in polynomial and rational Krylov methods for matrix functions with applications", in Aula Bianchi Lettere (Scuola Normale Superiore). Dopo la difesa ci sarà un piccolo brindisi e rinfresco nel chiostro del Palazzo della Carovana. Chiunque volesse partecipare, o anche soltanto passare per un saluto, è benvenuto! A presto, Igor --- Dear all, On October 25th at 14.30 I will defend my PhD thesis, titled "Advances in polynomial and rational Krylov methods for matrix functions with applications", in Aula Bianchi Lettere (Scuola Normale Superiore). After the defense there will be some refreshments in the internal courtyard of the Palazzo della Carovana. You are all welcome to participate! Best, Igor

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[Indico] Prof. Andreas Frommer, Structure-aware Krylov approximations to generalized Cayley transforms, 10/25/24, 11:00 AM Europe/Rome
by fabio.durastante＠unipi.it 17 Oct '24

17 Oct '24

Title: Structure-aware Krylov approximations to generalized Cayley transforms, Speaker(s): Prof. Andreas Frommer, University of Wuppertal, Date and time: Oct 25, 2024, 11:00 AM (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Scuola Normale Superiore (Aula Mancini). You can access the full event here: https://events.dm.unipi.it/e/296 Abstract -------- Generalized Cayley transforms arise in implicit numerical integration schemes for ordinary differential equations and differential-algebraic equations. We consider Arnoldi-type methods to approximate the action of such a Cayley transform on a vector and investigate how energy conservation or dissipation can be enforced at the level of each Arnoldi iterate, not just at the level of the exact solution. We also investigate generalizations to higher order collocation methods. -- Indico :: Email Notifier https://events.dm.unipi.it/e/296

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Seminar announcement: A finite element approximation of a simplified model for smart fluids: an error analysis 9/10
by Fabio Durastante 08 Oct '24

08 Oct '24

Good morning, Colleagues in the Analysis section have organized this seminar by Alex Kaltenbach that may be of interest to some of us. The detailed information follows. Best, Fabio Speaker: Alex Kaltenbach, Technische Universität Berlin Seminar: A finite element approximation of a simplified model for smart fluids: an error analysis Date: October 9th at 5:00 pm, Aula Riunioni (Maths Department) Abstract: In this talk, a finite element approximation of the steady $p(\cdot)$-Navier--Stokes equations ($p(\cdot)$ is variable dependent) is examined for orders of convergence by assuming natural fractional regularity assumptions on the velocity vector field and the kinematic pressure. Numerical experiments confirm the quasi-optimality of the \textit{a priori} error estimates (for the velocity). The steady $p(\cdot)$-Navier--Stokes equations are a prototypical example of a non-linear system with variable growth conditions. They appear naturally in physical models for so-called \textit{smart fluids}, \textit{e.g.}, electro-rheological fluids, micro-polar electro-rheological fluids, magneto-rheological fluids, chemically reacting fluids, and thermo-rheological fluids, and have the potential for an application in numerous areas, \textit{e.g.}, in electronic, automobile, heavy machinery, military, and biomedical industry.

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[Indico] Mehdi Najafi Kalyani, A two-dimensional minimum residual technique for accelerating two-step iterative solvers, 04/10/2024, 11:00 Europe/Rome
by leonardo.robol＠unipi.it 02 Oct '24

02 Oct '24

Title: A two-dimensional minimum residual technique for accelerating two-step iterative solvers, Speaker(s): Mehdi Najafi Kalyani, University of Pisa, Date and time: 4 Oct 2024, 11:00 (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/289 Abstract -------- In this talk, we present a technique to speed up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each sub-iterate is minimized over a certain two-dimensional subspace. Convergence properties of the resulting method will be discussed in detail. It will be further shown that the approach can be developed to solve (regularized) normal equations arising from the discretization of ill-posed problems. Numerical experiments will be disclosed to illustrate the performance of exact and inexact variants of the method for some test problems. -- Indico :: Email Notifier https://events.dm.unipi.it/e/289

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[Indico] Mehdi Najafi Kalyani, A two-dimensional minimum residual technique for accelerating two-step iterative solvers, 04/10/2024, 11:00 Europe/Rome
by leonardo.robol＠unipi.it 18 Sep '24

18 Sep '24

Title: A two-dimensional minimum residual technique for accelerating two-step iterative solvers, Speaker(s): Mehdi Najafi Kalyani, University of Pisa, Date and time: 4 Oct 2024, 11:00 (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/289 Abstract -------- In this talk, we present a technique to speed up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each sub-iterate is minimized over a certain two-dimensional subspace. Convergence properties of the resulting method will be discussed in detail. It will be further shown that the approach can be developed to solve (regularized) normal equations arising from the discretization of ill-posed problems. Numerical experiments will be disclosed to illustrate the performance of exact and inexact variants of the method for some test problems. -- Indico :: Email Notifier https://events.dm.unipi.it/e/289

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Seminar on Quantum Computing: Andrew Daley (University of Oxford, UK) Monday 23/09/2024
by Gianna M. Del Corso 18 Sep '24

18 Sep '24

Dear All, As part of the CN1-SPOKE 10 on Quantum Computing, this year too we plan to organize a weekly seminar series. The first event this year is a talk proposed by by Marilu Chiofalo and Jorge Yago Malo. Title: Analogue and digital quantum simulation: state of the art and opportunities Speaker: Andrew Daley (University of Oxford, UK) Venue: Sala Galilei (room 131, Bldg. C, Department of Physics) Time: Monday, 23/09/2024, 15:00 Abstract: There has been impressive recent progress in developing highly controlled quantum systems, ranging from superconducting qubits to neutral atoms in tweezer arrays. These systems provide a route to medium-scale quantum computing, but also the possibility to build and study models of many-body systems. These range from electrons in solid state physics and materials across to toy models for information spreading in black holes (made possible by long-range interactions). This impressive progress had led to new opportunities for studying basic science, but has also opened pathways towards making quantum simulation useful in solving problems from chemistry, materials and wider fields. I will give an introduction to the state of the art in these systems, illustrated with our recent theoretical work on fast scrambling of quantum information in systems with long-range interactions. I will also discuss the opportunities and challenges associated with important questions, including (1) To which degree can analogue devices be quantitatively reliable? And (2) when can we use these systems to give us access to useful information that we cannot compute with conventional supercomputers? Everyone is welcome! @@@@@@@@@@@@@@@@@ Gianna M. Del Corso, PhD Dipartimento di Informatica, Università di Pisa Largo Pontecorvo, 3 56127 Pisa, Italy ph. +39-050-2213118 @@@@@@@@@@@@@@@@@

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Upcoming workshop: NumPI day
by Stefano Massei 18 Sep '24

18 Sep '24

Dear all, I am glad to announce to you that Monday 23rd September we will have a one-day workshop of numerical analysis titled NumPI day. Anyone interested is welcome! The event will take place from 9 a.m. to 16 p.m. in the Aula Magna of the department of Mathematics, see the attached schedule. Best regards, Stefano

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[Indico] Dr Maria Strazzullo, Nonlinear Feedback Control via Dynamical Low-Rank Approximation, 09/09/2024, 15:30 Europe/Rome
by noreply＠cs.dm.unipi.it 09 Sep '24

09 Sep '24

Title: Nonlinear Feedback Control via Dynamical Low-Rank Approximation, Speaker(s): Dr Maria Strazzullo, Politecnico di Torino, Date and time: 9 Sept 2024, 15:30 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento Di Matematica (Sala Riunioni). You can access the full event here: https://events.dm.unipi.it/e/288 Abstract -------- Feedback control plays a crucial role in optimizing the performance of dynamical systems by minimizing a predefined cost functional, to stabilize the system towards a desired state. Despite its undeniable effectiveness, the applicability of feedback control is often limited by the high dimensionality of state spaces, a challenge that is even more pronounced in parametric settings. To overcome these limitations, we employ the Dynamical Low-Rank Approximation (DLRA) methodology, which offers an efficient and accurate solution to high-dimensional feedback control problems. Our approach significantly accelerates the solution of State-Dependent Riccati Equations (SDREs) for infinite horizon optimal control by providing a compact, low-dimensional representation of the system that evolves dynamically with respect to the problem. This not only enhances accuracy but also provides effective real-time control, solving several parametric instances simultaneously. To further accelerate the solution of the SDREs, we propose cascade-control (cc-) algorithms that leverage the Riccati solution from a previous parameter to improve the convergence of Newton-based methods applied to SDREs. The robustness and efficiency of our algorithms are validated through nonlinear test cases. Comparative analysis demonstrates that the proposed ccDLRA outperforms global Proper Orthogonal Decomposition model order reduction (ccPOD), offering superior speed and accuracy when compared to the full-order model (ccFOM) solution. Note ---- Reminder for this afternoon's seminar. -- Indico :: Email Notifier https://events.dm.unipi.it/e/288

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[Indico] Dr Maria Strazzullo, Nonlinear Feedback Control via Dynamical Low-Rank Approximation, 09/09/2024, 15:30 Europe/Rome
by fabio.durastante＠unipi.it 05 Sep '24

05 Sep '24

Title: Nonlinear Feedback Control via Dynamical Low-Rank Approximation, Speaker(s): Dr Maria Strazzullo, Politecnico di Torino, Date and time: 9 Sept 2024, 15:30 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento Di Matematica (Sala Riunioni). You can access the full event here: https://events.dm.unipi.it/e/288 Abstract -------- Feedback control plays a crucial role in optimizing the performance of dynamical systems by minimizing a predefined cost functional, to stabilize the system towards a desired state. Despite its undeniable effectiveness, the applicability of feedback control is often limited by the high dimensionality of state spaces, a challenge that is even more pronounced in parametric settings. To overcome these limitations, we employ the Dynamical Low-Rank Approximation (DLRA) methodology, which offers an efficient and accurate solution to high-dimensional feedback control problems. Our approach significantly accelerates the solution of State-Dependent Riccati Equations (SDREs) for infinite horizon optimal control by providing a compact, low-dimensional representation of the system that evolves dynamically with respect to the problem. This not only enhances accuracy but also provides effective real-time control, solving several parametric instances simultaneously. To further accelerate the solution of the SDREs, we propose cascade-control (cc-) algorithms that leverage the Riccati solution from a previous parameter to improve the convergence of Newton-based methods applied to SDREs. The robustness and efficiency of our algorithms are validated through nonlinear test cases. Comparative analysis demonstrates that the proposed ccDLRA outperforms global Proper Orthogonal Decomposition model order reduction (ccPOD), offering superior speed and accuracy when compared to the full-order model (ccFOM) solution. -- Indico :: Email Notifier https://events.dm.unipi.it/e/288

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