NumPI October 2022

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3 participants
5 discussions

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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NumPI October 2022