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About Me

Curriculum Vitæ

Currently i work for ABB, where i am responsible for a group in the Research and Devlopment function, carrying out mathematical modeling and numerical simulations, Intellectual Property (IP, i.e., mainly patents) and knowledge management (KM). >> top

Scientific Interests

My main working areas are: >> top

Collected Papers

Publications on Refereed Journals

  1. L. Ghezzi, L.F. Pavarino, E. Zampieri, Overlapping Schwarz preconditioned eigensolvers for spectral element discretizations, Applied Mathematics and Computation, 218 (15): 7700-7710, 2012. [download]

  2. L. Ghezzi, F. Rapetti, Current identification in vacuum circuit breakers as a least square problem, ESAIM: Proceedings, 38: 361-375, 2012. [download]

  3. L. Ghezzi, D. Piva, L. Di Rienzo, Current density reconstruction in vacuum arcs by inverting magnetic field data, IEEE Transactions on Magnetics, 48 (8): 2324-2333, 2012. [download]

  4. M.A. Pucheta, A. Butti, V. Tamellini, A. Cardona, L. Ghezzi, Topological synthesis of planar metamorphic mechanisms for low-voltage circuit breakers, Mechanics Based Design of Structures and Machines: An International Journal, 40 (4): 453-468, 2012. [download]

  5. L. Ghezzi, L.F. Pavarino, E. Zampieri, Overlapping Schwarz preconditioners for spectral element methods in nonstandard domains and heterogeneous media, Journal of Computational and Applied Mathematics, 234:1492-1504, 2010. [download]

  6. F. Bizzarri, A.M. Brambilla, L. Ghezzi, F. Rigamonti, Circuit level model for miniature circuit breakers, IEEE Transactions on Power Delivery, 33 (6): 2700-2709, 2018. [download]

  7. F. Bizzarri, L. Ghezzi, M. Maglio, F. Rigamonti, A.M. Brambilla, Simulations of three-phase current interruptions through a black-box model of miniature circuit breakers IEEE Transactions on Power Delivery, to appear, 2019. [download]

  8. A. Balestrero, L. Ghezzi, M. Popov, G. Tribulato, L. van der Sluis, Black box modeling of low voltage circuit breakers, IEEE Transactions on Power Delivery, 25 (4):2481-2488, 2010. [download]

  9. A. Balestrero, L. Ghezzi, M. Popov, L. van der Sluis, Current Interruption in Low Voltage Circuit Breakers, IEEE Transactions on Power Delivery, 25 (1):206-211, 2010. [download]

  10. J.W. McBride, A. Balestrero, L. Ghezzi, G. Tribulato, K.J. Cross, Optical fiber imaging for high speed plasma motion diagnostics: Applied to low voltage circuit breakers, AIP Review of Scientific Instruments, 81 (5), 2010. [download]

  11. A. Frangi, L. Ghezzi, P. Faure-Ragani, Accurate Force Evaluation for Industrial Magnetostatics Applications with Fast Bem-Fem Approaches, Computer Modeling in Engineering & Sciences (CMES), 15 (1):41-48, 2006. [download]

  12. A. Frangi, P. Faure-Ragani, L. Ghezzi, Magneto-mechanical simulations by a coupled fast multipole method-finite element method and multigrid solvers, Computer & Structures, 83 (10-11):718-726, 2005. [download]

  13. C. Bottasso, A. Croce, L. Ghezzi, P. Faure, On the Solution of Inverse Dynamics and Trajectory Optimization Problems for Multibody Systems, Multibody System Dynamics, 11:1-22, 2004. [download]

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Congress Papers

  1. A. Frangi, L. Ghezzi, P. Faure-Ragani, Analysis Of Large Scale Industrial Coupled Magneto-Mechanical Problems, Proceedings of the AIMETA XVI Congress, Ferrara, Italy, September 9-12, 2003 (on CD-ROM). [download]

  2. A. Frangi, P. Faure-Ragani, L. Ghezzi, Magneto-mechanical simulations by a coupled Fast-Multipole Method-Finite Element Method, Proceedings of the Second M.I.T. Conference, Boston, June 2003, K.J.Bathe ed., vol.2, pp.1347-1350, Elsevier, 2003. [download]

  3. A. Frangi, P. Faure-Ragani, L. Ghezzi, Coupled Fast Multipole Method - Finite Element Method for the analysis of magneto-mechanical problems, Proceedings of the Sixth French National Congress "Calcul des structures", Giens, France, May 20-23, M. Bonnet, M. Potier Ferry, A. Bignonnet eds., vol 3, pp. 273-280, 2003. [download]

  4. M. Pucheta, A. Butti, V. Tamellini, L. Ghezzi, A. Cardona, A methodology for the topological synthesis of metamorphic mechanisms for circuit breakers, Multibody Dynamics 2011, ECCOMAS Thematic Conference, Bruxelles, Belgium, July 4-7, J.C. Samin, P. Fisette eds., 2011.

  5. M. Pucheta, A. Butti, V. Tamellini, A. Cardona, L. Ghezzi, Number synthesis of metamorphic mechanisms using subgraph constraints, Proceedings of MuSMe 2011, the 4th International Symposium on Multibody Systems and Mechatronics, Valencia, Spain, October 25-28, 2011. [download]

  6. L. Ghezzi, L. Di Rienzo, D. Piva, Dongwei Li, Current Identification in Vacuum Circuit Breakers by Inverting Magnetic Field Data, Proceedings of ICEPE 2011, the 1st International Conference on Electric Power Equipment - Switching Technologies, Xi'an, China, October 23-27, 2011.

  7. F. Bizzarri, A. Brambilla, L. Ghezzi, F. Rigamonti, The Urbanek black box arc model in passive resonance circuit breakers for HVDC applications, 2018 IEEE International Symposium on Circuits and Systems (ISCAS), Florence, 2018. [download]

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My Background


In the year 2010 i received a Ph.D. from the Technische Universiteit Delft (Delft University of Technology), in the Netherlands. The title earned is officially termed "Doctor" according to Dutch law, and is frequently called Ph.D., as the post-graduate education received in the anglosaxon world to which is de facto equivalent. The 4-year doctoral research was carried out together with my friend and colleague Andrea Balestrero. We studied the electric arc plasma found in low voltage circuit breakers, an issue which is of strategic interest for the company we work for. Our work was promoted by Prof.ir. Lou van der Sluis, to whom my gatefulness goes for this opportunity, which has been truly wonderful both from the professional and also from the personal side. I had also the possibility to admire the outstanding facilities and resources available at TU Delft, and to sadly compare with the Italian situation. It is really disappointing to assist to the technological and scientific suicide of Italy, a country whose shortsighted and insane governments which succeeded along the years have chosen not to invest any longer in research, thus condemning an entire nation to a future of decandence and misery.


Technische Universiteit Delft (Delft University of Technology)
Faculteit Elektrotechniek, Wiskunde en Informatica
(Faculty of Electrical Engineering, Mathematics and Computer Sciences)
Delft, the Netherlands, October 12th, 2010

Doctoral dissertation defended by Luca Ghezzi
Promotor Prof. ir. Lou van der Sluis, Co-promotor Prof. Marjan Popov

Synopsis. Modeling and Simulation of Low Voltage Arcs is an attempt to improve the physical understanding, mathematical modeling and numerical simulation of the electric arcs that are found during current interruptions in low voltage circuit breakers. An empirical description is gained by refined electrical measures and fiber optics based imaging. Ways to assess with a graded scale the interruption performance of a circuit breaker are developed. A theoretical review of the arc plasma physics allows to gain an insight in the governing phenomenon, namely the balance between particle energy gain from the electric field and particle energy redistribution through collisions. The elaboration of this idea to a more abstract level of modeling detail allows to develop a new black box model, based on non equilibrium theory and with increased realism, as well as to address the problem with predictive purposes by means of a computational, multi-physics approach.

Sommario. Modeling and Simulation of Low Voltage Arcs é un contributo volto a migliorare la comprensione fisica, la modellazione matematica e la simulazione numerica degli archi elettrici che si sviluppano negli interruttori di bassa tensione durante l'interruzione di corrente. Si é condotta un'analisi sperimentale mediante misure elettriche di precisione allo zero di corrente e mediante una tecnica di monitoraggio dell'arco e delle sue radici con fibre ottiche. Si sono definiti degli indicatori di merito con cui giudicare l'esito di un'interruzione di corrente con una scala continua, anziché semplicemente con un voto di tipo "successo" / "fallimento", e con il vantaggio di poter valutare la distanza dalla capacitá ultima dell'interruttore. L'interpretazione dell'evidenza sperimentale alla luce della teoria della fisica dei plasmi ha permesso di individuare un fenomeno cruciale che governa la dinamica dell'arco, ossia l'equilibrio tra il meccanismo di cessione energetica dal campo elettrico alle particelle cariche, specialmente quelle piú leggere, cioé gli elettroni, ed il meccanismo di redistribuzione energetica per collisioni tra particelle di specie diverse, che é piú efficace tra particelle di massa simile. La modellazione dell'entitá della violazione di questo equilibrio rispetto all'energia cinetica media delle particelle si é rivelata essere di grande importanza, sia nella condizione di plasma freddo e prossimo all'estinzione, allo zero di corrente, sia in presenza di forti campi elettrici che nell'arco in bassa tensione si sviluppano comunque nelle radici dell'arco. L'elaborazione di questo concetto a livelli diversi di astrazione modellistica ha permesso di proporre un nuovo modello balck-box per l'arco elettrico in bassa tensione, con un grado di realismo piú elevato rispetto ai modelli classici basati sulla fisica dell'equilibrio, e anche di affrontare il problema simulativo con fini predittivi per mezzo di un approccio computazionale basato sulla magnetoidrodinamica.

[download] proefschrift (Ph.D. thesis), full pdf document
[download] stellingen (propositions to be defended along with the thesis)

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M.Sc., Mathematics

I studied Mathematics for its beauty and elegance. If i describe it fancily, Mathematics is the art of looking at things from the point of view such that they appear simple. This is the link to my second alma mater, the University of Milan, and to the Department of Mathematics F. Enriques. My thesis was about the most important problem for engineers: the initial-boundary value problem for systems of PDE, dealt with the spectral element method (a pseudo-Galerkin approach ensuring more than algebraic convergence rate in case of infinitely differentiable solutions) and preconditioned by means of Schwarz method (a classical domain decomposition technique). Here it is:


Università degli Studi di Milano, Facoltà di Scienze Matematiche, Fisiche e Naturali
Corso di Laurea Quadriennale in Matematica, Anno Accademico 2006/2007

Tesi di laurea di Luca Ghezzi
Relatore Prof.ssa Elena Zampieri, Correlatore Prof. Luca Pavarino

Sommario. In questa tesi si studia l'approssimazione numerica di equazioni alle derivate parziali con elementi spettrali di tipo quadrangolare e nodi di Gauss-Lobatto-Legendre. In particolare si intende generalizzare queste metodologie a problemi classici della Fisica Matematica o a problemi applicativi di diversa natura, definiti in geometrie complesse e nel caso di materiali non omogenei.

Synopsis. Spectral elements in complex geometries and heterogeneous media: theory, algorithms and applications - The thesis is about the numerical approximation of hyperbolic PDE's with the Spectral Element Method (SEM) for spatial discretization. Tensor product elements with Gauss-Lobatto-Legendre (GLL) nodes are used, with transfinite interpolation enabling the application to complex geometries. Space discretization is carried out either with Newmark schemes (implicit or explicit) or with BDF schemes. Since spectral matrices are very ill-conditioned, preconditioning is mandatory and the Overlapping Schwarz (OS) technique is adopted. This approach, based on the domain decomposition method, is intrinsically suitable for parallel computing and allows a very natural and effective treatment of strong discontinuities in material properties. After the formal introduction of the numerical methods used, an intensive phase of numerical experimentation is carried out, leading (among the others) to the verification of convergence properties of the SEM and scalability of the OS preconditioner (in the literature, these properties are rigorously proven on simple geometries such as the square). Numerous problems from physical and engineering applications are solved, in order to prove the versatility of the method. These include acoustic wave propagation with Absorbing Boundary Conditions (ABC), enabling unbounded domains to be artifically cut into bounded ones. Also, electromagnetism is a very interesting applicative field, with differential forms and de Rham cohomology used to easily set the differential problem in a suitable form. Modal approach may also be managed, leading to a generalized eigenvalue problem. This is used to solve both membrane vibrations and the Schroedinger equation in quantum mechanics. Particularly, the possible degeneracy of eigenvalues leads to very interesting considerations related to symmetry. In order to recover symmetries possibly not caught by the numerical eigenvalue solver, an algebraic method is formulated, formally proven and practically tested.

[download] thesis, full pdf document
[download] presentation, pdf document
[download] presentation, zip archive inclusive of movies

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M.Sc., Structural Engineering

Besides being a mathematician, i am also a civil, structural engineer. This is the link to the Politecnico di Milano (Technical University of Milan) and to the Department of Structural Engineering, where i studied. Here is my thesis, in computational poro-elasto-plasticity.


Politecnico di Milano, Facoltà di Ingegneria - Dipartimento di Ingegneria Strutturale
Anno Accademico 1997/1998

Tesi di laurea di Luca Ghezzi
Relatore Prof. Giulio Maier, Correlatore Dott. Giuseppe Cocchetti

Synopsis. Shakedown analysis: theory and computational methods by mathematical programming - The thesis develops methods for computational elastoplasticity and poroplasticity (a solid continuum impregnated with a fluid continuum, like a sponge or a humid soil). Plastic constitutive laws are not holonomic, that is, they are history dependent, which turns into very cumbersome evolutionary analysis. None the less, very often what is needed in engineering practice is simply the maximum allowable amplitude of loads. This may be deduced also by turning the plasticity problem into a constrained optimization problem, that may be addressed by mathematical programming techniques. Shakedown (also known as adaptation) is the engineering term identifying the eventual return into purely elastic regime of a structure or a continuum subjected to cyclically varying loads, after unrecoverable plastic strains have been developed. Optimization methods are used to compute the maximum allowable homothetic amplification of the convex hull of the load cycle, as well as for estimating the magnitude of mechanical quantities, tipically strains, in post-adaptation phase (this ensures the admissibility of adaptation with reference to safety margins and service functionality). Particularly, the problem falls into the realm of convex analysis and linear and non linear programming approaches are followed (Simplex, Sequential Quadratic Programming and specifically written algorithms). Associated plasticity is considered with von Mises as well as Drucker-Prager yielding criteria. The finite element mehod is used for spatial discretization and generalized Prager's variable approach is followed, leading to multi-field discretization. The theoretical setting of the shakedown problem is deeply discussed, showing how the classical theorems of limit analysis (maximum allowable, statically imposed load) are special cases of shakedown analysis theorems and proving an extension theorem for a special class of poroplastic materials.

[download] thesis, zip archive

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Back in the Days

Back in the days when i was young! Here is the link to my high school, Liceo Scientifico "Leonardo da Vinci" di Gallarate (when i was a student it was nameless).

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