PhD program on Mathematical Models and Methods in Engineering - Dipartimento di Matematica

General information

The Department of Mathematics of the Politecnico di Milano is hosting a PhD program in Mathematical Models and Methods in Engineering, aiming at training high level researchers in advanced areas of Pure and Applied Mathematics. The teaching activities include a broad range of possibilities designed for the PhD program. As a successful approach to practical applications depends on a deep understanding of real-world phenomena and knowledge of mathematical tools for their description and design, both modelling, methodological and theoretical aspects are included. Courses are offered in various areas of mathematics, and may vary every year.

Geometrindi e Matematindi (Luigi Serafini 2002)

Numerical simulation of blood flow in the heart
(courtesy of Prof. Alfio Quarteroni)

Objectives

The development of advanced technologies in Science and Engineering brings an increasing demand of advanced mathematical theories and methods, which in turn fosters the demand for education and training of skilled mathematicians in pure and applied research. The main scope of the Ph.D. course “Mathematical Models and Methods in Engineering” is to train high-level researchers in various fields of pure and applied mathematics.

Professional Opportunities

Expected professional placements for Ph.D. doctorates are: academic research in Italian or International Universities and Research Institutions, R & D divisions of private companies, study and research centers of public Agencies, financial and insurance Institutions.

Today's events

apr 03 thu 2025

jul 10 thu 2025

WorkShop
Mathematics colloquium of milano: inaugural cycle
04/03/2025 - 07/10/2025
- WORKSHOP
- MCM
  Mathematics colloquium of milano: inaugural cycle
- organizers
  Fabrizio Andreatta, Giovanni Catino, Fabio E. G. Cipriani, Gregorio Falqui, Vincenzo Marra, Kevin Payne, Giuseppe Savaré, Thomas Weigel
- The departments of mathematics of the major Milano universities (Università di Milano, Politecnico di Milano, Università di Milano-Bicocca and Università Bocconi) are pleased to announce the inaugural cycle of a new distinguished lecture series, entitled: The Mathematics Colloquium of Milano Breakthroughs and Perspectives Over the years to come, mathematicians of international prominence will present and discuss the most important new ideas and breakthroughs in contemporary mathematics and its applications. Each lecture should be suitable for a general mathematical audience, especially Ph.D. students and Post-docs. The inaugural cycle of lectures is scheduled to take place from early April until mid-July of 2025.
- Thursday, 3 April 2025 - Thursday, 10 July 2025
  Milano
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
may 26 mon 2025

may 30 fri 2025

WorkShop
Quantum mathematics @ polimi 2025 : mathematics of condensed matter systems
05/26/2025 - 05/30/2025
- WORKSHOP
- QMP25 - MCMS
  Quantum mathematics @ polimi 2025 : mathematics of condensed matter systems
- organizers
  D. Fermi, M. Moscolari, A. Olgiati (PoliMi)
- Quantum Mathematics @ Polimi is a three-months intensive research period focusing on several aspects of the mathematics of quantum systems.
- Monday, 26 May 2025 - Friday, 30 May 2025
  Hotel Lombardia, Viale Lombardia 74
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
may 29 thu 2025

Seminar
Vittorino Pata, Weak Solutions of Linear Differential Equations in Hilbert Spaces, 05-29-2025, 15:15
- Seminar
- Vittorino Pata
- Politecnico di Milano
- Weak Solutions of Linear Differential Equations in Hilbert Spaces
- Thursday, 29 May 2025 at 15:15
- Aula Seminari - III Piano
- Abstract
  
  We address the well-posedness of weak solutions for a general linear evolution problem on a separable Hilbert space. For this classical problem there is a well-known challenge of obtaining a priori estimates, as a constructed weak solution may not be regular enough to be utilized as a test function. This issue presents an obstacle for obtaining uniqueness and continuous dependence of solutions.
  When formal energy estimates ara available, we provide a general notion of weak solution and, through a straightforward observation, obtain that arbitrary weak solutions have additional time regularity and obey an a priori estimate. This yields weak well-posedness. Our result rests upon a central hypothesis asserting the existence of a "good" Galerkin basis for the construction of a weak solution. A posteriori, a strongly continuous semigroup may be obtained for weak solutions, and by uniqueness, weak and semigroup solutions are equivalent.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

Upcoming events

may 30 fri 2025

Seminar
Hakima Bessaih, Synchronization in Stochastic Systems: Models and Applications, 05-30-2025, 11:00
- Seminar
- Hakima Bessaih
- Florida International University
- Synchronization in Stochastic Systems: Models and Applications
- Friday, 30 May 2025 at 11:00
- Aula Seminari - III piano. Zoom link: polimi-it.zoom.us/j/97744268266?pwd=JinYaL7ZNixmf5IcNgWHkNFVwFhfXI.1
- Abstract
  
  Synchronization phenomena describe the long-time behavior of systems composed of interacting particles or agents that eventually reach a common state. In this talk, we will present several stochastic models and investigate their synchronization properties under both additive and multiplicative noise. We will also explore an application to networked systems, modeled by stochastic reaction-diffusion equations on a graph.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
jun 03 tue 2025

jun 06 fri 2025

WorkShop
Quantum mathematics @ polimi 2025 : recent advances in operator theory and applications
06/03/2025 - 06/06/2025
- WORKSHOP
- QMP25 - RAOTA
  Quantum mathematics @ polimi 2025 : recent advances in operator theory and applications
- organizers
  A. De Martino, D. Fermi, M. Moscolari, A. Olgiati, P. Schlosser (PoliMi)
- Quantum Mathematics @ Polimi is a three-months intensive research period focusing on several aspects of the mathematics of quantum systems.
- Tuesday, 3 June 2025 - Friday, 6 June 2025
  Politecnico di Milano
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
jun 05 thu 2025

Seminar
Jonas Stange, A convective Cahn–Hilliard model with dynamic boundary conditions, 06-05-2025, 14:15
- Seminar
- Jonas Stange
- University of Regensburg
- A convective Cahn–Hilliard model with dynamic boundary conditions
- Thursday, 5 June 2025 at 14:15
- Aula Seminari - III Piano
- Abstract
  
  We consider a general class of convective bulk-surface Cahn–Hilliard systems
  with singular potentials. In contrast to classical Neumann boundary conditions,
  the dynamic boundary conditions of Cahn–Hilliard type allow for dynamic
  changes of the contact angle between the diffuse interface and the boundary, a
  convection-induced motion of the contact line as well as absorption of material
  by the boundary. The coupling conditions for bulk and surface quantities involve
  parameters $K,L\in [0,\infty]$, whose choice declares whether these conditions
  are of Dirichlet, Robin or Neumann type.
  In this talk, I present some recent results on the well-posedness of this system.
  After briefly recalling the results for regular potentials, we focus on singular
  potentials. Here, we make use of the Yosida approximation to regularise these
  potentials, which allows us to apply the results for regular potentials and eventually
  pass to the limit in this approximation scheme to obtain a global-in-time
  weak solution. Afterwards, under additional assumptions on the mobility functions,
  we prove higher regularity estimates for two different classes of velocity
  fields, and in particular, for those having Leray-type regularity. Finally, exploiting
  these higher regularity estimates, we can establish separation properties of
  the phase-fields.
  This is based on joint work with Andrea Giorgini and Patrik Knopf.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
jun 09 mon 2025

MOX Seminar
Lucas Bouck, Thin Sheets of Liquid Crystal Elastomers: Modeling, Approximation, and Computation, 06-09-2025, 11:30
- MOX Seminar
- Lucas Bouck
- Carnegie Mellon University
- Thin Sheets of Liquid Crystal Elastomers: Modeling, Approximation, and Computation
- Monday, 9 June 2025 at 11:30
- Aula seminari MOX, VI piano
- Abstract
  
  Liquid crystal elastomers (LCEs) are materials where a nematic liquid crystal is coupled with a rubbery material. When actuated with heat or light, the interaction of the liquid crystal with the rubber creates complex shapes. Thin bodies of LCEs are natural candidates for soft robotics applications. Starting from the classical 3D trace energy formula of Bladon, Warner and Terentjev (1994), we derive a 2D plate theory as the asymptotic limit of the 3D energy using the tools of Gamma-convergence. The resulting bending problem consists of minimizing an energy that is a function of the curvatures of the parameterized surface, subject to a metric constraint. This metric constraint is the leading order behavior that drives large deformations of LCEs. Numerically, we solve this metric constraint by numerical minimization of a formally derived stretching energy with the bending energy serving as a regularization for the discrete problem. We prove that minimizers of the discrete energy converge to zero energy states of the stretching energy in the spirit of Gamma convergence. We solve the discrete minimization problem via an energy stable gradient flow scheme. We present computations showing the geometric effects that arise from liquid crystal defects as well as computations of nonisometric origami, both within and beyond theory. The plate theory derivation is joint work with P. Plucinsky and D. Padilla-Garza and the computational work is joint with R.H. Nochetto and S. Yang.
  
  Contatto:
  marco.verani@polimi.it
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
jun 12 thu 2025

jun 13 fri 2025

WorkShop
Financial education – why, what works, what doesn't and for whom
06/12/2025 - 06/13/2025
- WORKSHOP
- EDUFIN25
  Financial education – why, what works, what doesn't and for whom
- organizers
  Emilio Barucci
- The objective of the conference is twofold: the first is to analyse the importance of financial literacy in supporting financial well-being, financial inclusion, financial market development and enabling a wider economic prosperity; the second is to review concrete experiences, comparing what worked and what didn't and for whom. The aim is to have an international conference on best practices in financial education with a multidisciplinary scientific approach involving academia and policy-makers.
- Thursday, 12 June 2025 - Friday, 13 June 2025
  Politecnico di Milano
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
jun 12 thu 2025

Seminar
Alberto Bressan, Modeling Traffic Flow, 06-12-2025, 15:30
- Seminar
- Alberto Bressan
- Penn State University
- Modeling Traffic Flow
- Thursday, 12 June 2025 at 15:30
- aula U5-3014 del Dip. di Matematica e Applicazioni, Università Bicocca
- Abstract
  
  The talk will survey various models of traffic flow, with particular focus on new mathematical problems arising from some of these models. A large literature is currently available on particle models, describing the position of every car in terms of a large number of ODEs, and macroscopic models, where the traffic density is determined by a PDE.
  Vehicular traffic can also be analyzed from the point of view of decision theory. Indeed, daily traffic patterns arise as the outcome of the decisions of a large number of drivers, who choose their departure time and route to destination in an ``optimal" way. Some recent work and open problems will be discussed.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
jun 23 mon 2025

jun 27 fri 2025

WorkShop
29th international conference on domain decomposition methods
06/23/2025 - 06/27/2025
- WORKSHOP
- DD29
  29th international conference on domain decomposition methods
- organizers
  Paola F. Antonietti, Lourenco Beirao da Veiga, Silvia Bertoluzza, Michele Botti, Claudio Canuto, Gabriele Ciaramella, Paola Gervasio, Luca Pavarino, Alfio Quarteroni, Simone Scacchi, Christian Vergara
- The purpose of the meeting is to discuss recent developments in various aspects of domain decomposition methods, bringing together mathematicians, computational scientists, and engineers working on numerical analysis, scientific computing, high-performance computing, machine learning, and computational science with industrial and societal applications. This event is part of the activities of the Department of Exellence 2023-27.
- Monday, 23 June 2025 - Friday, 27 June 2025
  Politecnico di Milano
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
jun 30 mon 2025

jul 04 fri 2025

WorkShop
Differential geometry @ l'aquila 2025
06/30/2025 - 07/04/2025
- WORKSHOP
- Differential geometry @ l'aquila 2025
- organizers
  Lucio Bedulli, Luciano Mari, Giuseppe Pipoli, Mario Santilli, Alberto Roncoroni, Luigi Vezzoni
- The aim of the workshop is to focus on different recent advances in differential geometry and its applications, with particular emphasis on riemannian, metric and global differential geometry, theory of submanifolds and geometric flows.
- Monday, 30 June 2025 - Friday, 4 July 2025
  Università degli Studi dell'Aquila
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
jul 01 tue 2025

Seminar
Florian Fischer, Optimal Poincaré-Hardy inequalities on graphs, 07-01-2025, 14:15
- Seminar
- Florian Fischer
- University of Bonn
- Optimal Poincaré-Hardy inequalities on graphs
- Tuesday, 1 July 2025 at 14:15
- Aula Seminari III Piano
- Abstract
  
  We review a method to obtain optimal Poincaré-Hardy inequalities on the hyperbolic spaces by Berchio, Ganguly and Grillo. Then we show how to transfer the basic idea to the discrete setting. This yields optimal Poincaré-Hardy-type inequalities on model graphs which include fast enough growing trees and anti-trees. Moreover, this method yields optimal weights which are larger outside of a ball than the optimal weights constructed via the Fitzsimmons ratio of the square root of the minimal positive Green's function. Joint work with Christian Rose.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
jul 07 mon 2025

jul 11 fri 2025

WorkShop
New perspectives in nonlocal and nonlinear pde
07/07/2025 - 07/11/2025
- WORKSHOP
- New perspectives in nonlocal and nonlinear pde
- organizers
  José Antonio Carrillo (Univ. of Oxford), Antonio Esposito (Univ. dell'Aquila), Filomena Feo (Univ. "Parthenope"), Giuseppe Savarè (Univ. Bocconi), Bruno Volzone (Politecnico di Milano)
- The goal of this workshop is to gather researchers working in the field of Partial Differential Equations with expertise in nonlocal and nonlinear equations. Among others, one of the simplest mathematical ways to describe many real-world problems is to start from a set of interacting particles, resulting in nonlocal and nonlinear PDEs in the many-particle limit. Despite the past progress in this field, recent discoveries in biology, plasma physics, and data science, among others, shed the lights on new challenges involving nonlocal structures, such as networks or graphs, and highly nonlinear and singular aggregation-diffusion equations. During the workshop we will focus on various mathematical issues in this direction, for instance: micro-macro description of diffusion process, evolutions on graphs, fluxes with nonlinear mobility, fourth-order aggregation-diffusion equations, etc. This workshop is partially funded by the Advanced Grant Nonlocal-CPD: "Nonlocal PDEs for Complex Particle Dynamics: Phase Transitions, Patterns and Synchronization" of the European Research Council Executive Agency (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 883363).
- Monday, 7 July 2025 - Friday, 11 July 2025
  Anacapri
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

jul 15 tue 2025

jul 16 wed 2025

WorkShop
Workshop 2025 - digimath il ruolo delle tecnologie digitali a supporto della didattica della matematica: esperienze di buone pratiche a livello universitario
07/15/2025 - 07/16/2025

WORKSHOP
DIGiMATH
Workshop 2025 - digimath il ruolo delle tecnologie digitali a supporto della didattica della matematica: esperienze di buone pratiche a livello universitario
organizers
COMITATO SCIENTIFICO Domenico Brunetto Monica Conti Michele G. Fiorentino Annamaria Miranda COMITATO ORGANIZZATORE Caterina Bassi Domenico Brunetto Monica Conti Helena Dell'Anna
Il gruppo UMI DIGiMATH lavora per favorire lo sviluppo della cultura digitale per l'innovazione dei processi di insegnamento e apprendimento della matematica a livello universitario. Lo scopo del workshop è quello di confrontare e discutere le esperienze già in atto nelle università italiane di pratiche e ricerche sull’uso delle tecnologie digitali nella didattica della matematica e promuovere lo sviluppo di collaborazioni tra ricercatori in didattica della matematica e in altre aree della matematica per la definizione di pratiche e ricerche congiunte. I temi di discussione includono quelli già individuati da DIGiMATH e quelli emersi dal precedente Workshop - difficoltà, progettazione, valutazione, individualizzazione/personalizzazione - declinati lungo i tre contesti di transizione scuola/università, corsi di base di matematica, formazione insegnanti (iniziale e in continuo). Lo stile della giornata sarà improntato a favorire la discussione e la collaborazione tra i partecipanti, pertanto sarà dato ampio spazio al confronto e all’elaborazione delle idee. Inoltre, a chiusura del workshop ci sarà una sessione di brainstorming di programmazione di future attività di DIGiMATH.
Tuesday, 15 July 2025 - Wednesday, 16 July 2025
Aula Laboratorio FDS

Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568

sep 08 mon 2025

sep 11 thu 2025

WorkShop
Perspectives in geometric analysis
09/08/2025 - 09/11/2025
- WORKSHOP
- PGA25
  Perspectives in geometric analysis
- organizers
  Giovanni Catino, Dario D. Monticelli, Alberto Roncoroni
- The aim of the workshop is to focus on different recent advances in geometric analysis and its applications.
- Monday, 8 September 2025 - Thursday, 11 September 2025
  Aula Consiglio - 7th floor
Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
sep 18 thu 2025

MOX Colloquia
Malgorzata Peszynska, Multi-* mathematics and simulations of coupled processes the Arctic, 09-18-2025, 14:00
- MOX Colloquia
- Malgorzata Peszynska
- Department of Mathematics, Oregon State University
- Multi-* mathematics and simulations of coupled processes the Arctic
- Thursday, 18 September 2025 at 14:00
- Sala Consiglio, Edificio 14, Politecnico di Milano
- Abstract
  
  We present our joint work with many collaborators on multi-physics and multiple scales, with focus on processes in the Arctic, a vast and complex environment of great current interest, with physical models sharing some (but not all) features with high alpine environments and other cold regions. Our interest is in robust, accurate and conservative computational schemes for the multi-physics: thermal, flow and mechanical deformation (TpHM) in the snow, ice and soils responding to the forcings from the environment for which the data is sparse. The models account for multiple phases and components and present challenges due to the presence of free boundary e.g. of freezing/thawing/sublimation, strong dependence of constitutive parameters on the micro-physics of TpHM, disparate time scales, and micro- and macro heterogeneity. We show how to build constitutive relationships for Darcy scale models from the first principles at the interface- and pore-scale by a combination of mathematically rigorous theory, practical computational upscaling, and surrogate data science tools. We illustrate with simulations of practical scenarios.
  
  Contatto:
  alessio.fumagalli@polimi.it
- Malgorzata Peszynska
  Malgorzata Peszynska received her Ph.D. in Mathematics from University of Augsburg, and M.S. and Habilitation from Warsaw University of Technology. She held academic positions at Polish Academy Of Sciences, Warsaw University of Technology, Purdue University, and The University of Texas at Austin. She has been at Oregon State since 2003 as a full professor since 2012. In 2019-21 she served as a Program Director at the NSF DMS (National Science Foundation, Division of Mathematical Sciences). She is a 2024 University Distinguished Professor, 2022-24 Joel Davis Faculty Scholar, AAAS Honorary Fellow; 2021 SIAM Geosciences Career Prize recipient; 2017 Kosciuszko Foundation College of Eminent Scientists, and holder of OSU Mathematics Graduate mentoring award (2016), Joel Davis Excellence award (2016). She is a 2009-10 Fulbright Research Fellow, as well as Mortar Board professor (2004). She believes in "paying it forward" : M. Peszynska also held leadership and service positions at SIAM (Society for Industrial and Applied Mathematics) including President of SIAM Pacific Northwest Section (2018-20) and SIAM Geosciences (2009-10) and AWM (Association for Women in Mathematics), is serving on editorial boards for 4+ journals, and on the Executive Board of Pacific Math Alliance. She directed several postdocs, doctoral, masters and undergraduate students; see MP people. Her research is in broadly defined applied and computational mathematics modeling of real life phenomena, with foundations in analysis and other core mathematics, and with interdisciplinary applications and collaborations in geosciences (hydrology and oceanography), engineering, and material science.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
oct 09 thu 2025

MOX Colloquia
Mark Girolami, Statistical Finite Element Methods, 10-09-2025, 14:00
- MOX Colloquia
- Mark Girolami
- University of Cambridge
- Statistical Finite Element Methods
- Thursday, 9 October 2025 at 14:00
- Aula Consiglio - VII piano
- Abstract
  
  The finite element method (FEM) is one of the great triumphs of applied mathematics, numerical analysis and software development. Recent developments in sensor and signalling technologies enable the phenomenological study of complex natural and physical systems. The connection between sensor data and FEM has been restricted to solving inverse problems placing unwarranted faith in the fidelity of the mathematical description of the system under study. If one concedes mis-specification between generative reality and the FEM then a framework to systematically characterise this uncertainty is required. This talk will present a statistical construction of the FEM which systematically blends mathematical description with data observations by endowing the Hilbert space of FEM solutions with the additional structure of a Probability Measure.
- Mark Girolami
  Mark Girolami is the Sir Kirby Laing Professor of Civil Engineering within the Department of Engineering at the University of Cambridge where he also holds the Royal Academy of Engineering Research Chair in Data Centric Engineering. Prior to joining the University of Cambridge Professor Girolami held the Chair of Statistics in the Department of Mathematics at Imperial College London. He is the Chief Scientist of the Alan Turing Institute, which is the UK national institute for Data Science and AI. Professor Girolami is an elected fellow of the Royal Academy of Engineering and the Royal Society of Edinburgh, he was an EPSRC Advanced Research Fellow (2007-2012), an EPSRC Established Career Research Fellow (2012-2018), a recipient of a Royal Society Wolfson Research Merit Award, and in 2023 was awarded the Guy Medal in Silver by the Royal Statistical Society. He delivered the IMS Medallion Lecture at the Joint Statistical Meeting 2017, and the Bernoulli Society Forum Lecture at the European Meeting of Statisticians 2017.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568
oct 16 thu 2025

MOX Colloquia
Colin Cotter, Compatible finite elements for numerical weather prediction, 10-16-2025, 14:00
- MOX Colloquia
- Colin Cotter
- Imperial College
- Compatible finite elements for numerical weather prediction
- Thursday, 16 October 2025 at 14:00
- Sala Consiglio, Dipartimento di Matematica, Politecnico di Milano
- Abstract
  
  I will discuss the application of compatible finite element methods to large scale atmosphere and ocean simulation. Compatible finite element methods extend Arakawa's “C-grid” finite difference scheme to the finite element world. They are constructed from a discrete de Rham complex, which is a sequence of finite element spaces which are linked by the operators of differential calculus. The use of discrete de Rham complexes to solve partial differential equations is well established, but in this talk I focus on the specifics of dynamical cores for simulating weather, oceans and climate. The most important consequence of the discrete de Rham complex is the Hodge-Helmholtz decomposition, which has been used to exclude the possibility of several types of spurious oscillations from linear equations of geophysical flow. This means that compatible finite element spaces provide a useful framework for building dynamical cores. In this talk I will introduce the main concepts of compatible finite element spaces, and discuss their wave propagation properties. I will then cover a selection of the following topics (depending on recent advances, and interests of the audience): practical application to numerical weather prediction and ocean models, structure preserving methods, and scalable iterative solver techniques.
- Colin Cotter
  Colin Cotter is Professor of Computational Mathematics at Imperial College, researching numerical analysis and scientific computing focusses on the design, analysis and implementation of numerical methods and data assimilation algorithms for weather forecasting, ocean modelling and climate simulation. His work on compatible finite element methods underpins the next generation Met Office forecast modelling system. He has co-authored over 100 journal publications, and co-authored a book with Sebastian Reich on data assimilation published by Cambridge University Press. He has served on the editorial board of three journals. He was awarded a PhD in Mathematics at Imperial in 2004 under the supervision of Sebastian Reich, and subsequently held positions in the departments of Earth Science and Engineering and Aeronautics before rejoining the department of Mathematics in 2014, where he is is currently the head of Applied Mathematics in the Department of Mathematics at Imperia, and is co-Director of the UCL/Imperial EPSRC Centre for Doctoral Training in Collaborative Computational Modelling at the Interface.
- Politecnico di Milano, Dipartimento di Matematica ed. 14 "Nave", Piazza Leonardo da Vinci, 32, 20133 Milano, Telefono: +39 0223994505 - Fax: +39 0223994568