Math SOMMa Junior Meeting

The automotive design process is complex and time-consuming, requiring collaboration between engineers from different areas of expertise to predict and optimize every aspect of the product. Meeting numerous targets and regulations while keeping up with the fast-paced global market adds further challenges. To remain competitive, automotive companies must improve development efficiency by reducing time-to-market and production costs without compromising quality. Simulation-based studies are crucial in the early design phase, but the extensive computational requirements of detailed vehicle models make them impractical for exploring the entire design space. Therefore, the industry persists in employing trial-and-error approaches, limiting design exploration to a few thousand variants out of billions of possibilities, thus potentially missing better solutions. A possible solution is represented by ROM technique that can be employed to allow multidimensional design exploration.

This work introduces an innovative methodology to assess the noise and vibration (NVH) performance of car-body structures. NVH simulation engineering plays a critical role in ensuring that the product meets noise and vibration criteria, thereby improving comfort, quality, and customer satisfaction. This target is highly influenced by the global static and dynamic stiffness of the vehicle body structure, making it extremely sensitive to changes in design parameters. To address this challenge, the proposed approach extends the well-known Proper Generalized Decomposition (PGD) technique to solve parametrically the dynamic and static analysis of a structure characterized by material and/or geometric design variables. The main idea is to construct a parametric FE model of the structure and then employ a PGD-based parametric solver. By utilizing the proposed method, engineers can develop predictive models capable of rapidly evaluating multiple design configurations, facilitating the identification of optimal choices that meet NVH requirements. The proposed method was developed in the context of the doctoral thesis “Static and dynamic global stiffness analysis for automotive pre-design” (more info at: https://www.lacan.upc.edu/ProTechTion/ ). The thesis was supervised by the Universitat Politècnica de Catalunya (UPC) and Swansea University (SU), in collaboration with the automotive company SEAT S.A. as industrial partner. The project is currently in a “Proof of Concept” stage at SEAT, such that it can be included in the current SEAT workflow.

 

Dr. Fabiola Cavaliere is currently responsible of the “AI structural simulation” activities at the SEAT R&D Center in Barcelona. In April 2022 she successfully obtained her doctorate in Mathematical and Computational Modeling from Polytechnic University of Catalonia (UPC) in Spain and Swansea University (SU) in UK. During her research activity in close collaboration with SEAT, she developed a novel methodology based on a machine learning approach to optimize the development process of a car structure. The method allows to maximize the driving comfort and vibroacoustic performance of the vehicle already from the preliminary phase of a project.

I will explain how homotopical methods are useful in order to distinguish and classify spaces with different geometric structures. In particular, I will review interesting homotopical properties of complex and almost complex manifolds, symplectic and Kähler manifolds among others.

 

Joana Cirici is Professora Agregada at Universitat de Barcelona. She works on Algebraic Topology and its interactions with Algebraic Geometry and Complex Geometry. She defended her PhD in 2012 at Universitat de Barcelona. Then, she spent 6 years as a postdoctoral researcher in Germany (Berlin and Münster) before coming back to Barcelona in 2018. She is currently Vice-Dean of Research of the Faculty of Mathematics and Computer Science at UB.

Web: https://www.ub.edu/topologia/jcirici/

A Schur multiplier is a linear operator that associated to a matrix M that acts on other matrices by entry wise multiplication. The boundedness of Schur multipliers in the Schatten-von Neumann classes is an interesting question in operator algebra that was already considered by Grothendieck. In this talk, we will explain how smoothness of the matrix M (seen as a function of two variables) is key to finding sufficient conditions for the boundedness of the corresponding Schur multiplier and other operators of the same flavor. This will come from a surprising connection with Fourier multipliers and noncommutative Calderón-Zygmund theory. Based on joint work with Adrián M. González Pérez, Javier Parcet and Eduardo Tablate.

 

José M. Conde Alonso is a Ramón y Cajal fellow at Universidad Autónoma de Madrid. He previously worked at Brown University, Universitat Autònoma de Barcelona and ICMAT. He works in the interface of harmonic analysis and operator algebra, especially in problems involving operator valued functions and noncommutative Lp spaces.

Web: https://sites.google.com/view/josecondealonso 

A compact flat Lorentzian manifold is the quotient of the Minkowski space by a discrete subgroup $\Gamma$ of the isometry group, acting properly, freely and cocompactly on it. A classical result by Goldman, Fried and Kamishima states that, up to finite index, $\Gamma$ is a uniform lattice in some connected Lie subgroup of the isometry group, acting properly and cocompactly, generalizing Bieberbach theorem to the Lorentzian signature. Such compact quotients are called “standard”. More generally, a compact quotient of a homogeneous space $G/H$ of a Lie group $G$ is standard if the fundamental group action  extends to a proper cocompact action of a connected Lie subgroup of $G$. It turns out that looking for standard quotients is an easier problem when studying the existence of compact quotients of homogeneous spaces. This talk is about compact locally homogeneous plane waves. Plane waves can be thought of as a deformation of Minkowski spacetime, they are of great mathematical and physical interests. In this talk, we describe the isometry group of a 1-connected homogeneous non-flat plane wave, and show that compact quotients are “essentially” standard. As an application, we obtain that the parallel flow of a compact plane wave is equicontinuous. This is a joint work with M. Hanounah, I. Kath and A. Zeghib.

 

Lilia Mehidi is a Postdoc at University of Granada and member of the IMAG. She works in  Lorentzian Geometry. More precisely, she is interested in questions around Lorentzian dynamics: geodesic dynamics in Lorentzian signature, isometric group actions, theory of quotients (or Clifford–Klein forms) of homogeneous spaces.  She defended her PhD in 2019 at the University of Bordeaux (France) under the supervision of prof. Christophe Bavard and then she spent three years as a Postdoc at the ENS de Lyon (France).

Web:  https://mehidi.pages.math.cnrs.fr/siteweb/ 

TBP

 

Teijeiro received his PhD in Artificial Intelligence and Computer Science from the Centro Singular de Investigación en Tecnoloxías Intelixentes (CITIUS), University of Santiago de Compostela, in 2017. In the 2018-2022 period he worked as a postdoctoral researcher with the Embedded Systems Laboratory (ESL) at the EPFL, Switzerland, where he focused on energy efficient machine learning methods for wearable devices. Since January 2023 he is with BCAM – Basque Center for Applied Mathematics as a Ramón y Cajal Research Fellow. His research interests include knowledge representation, non-monotonic temporal reasoning, efficient machine learning, event-based sensing, and their application to biomedical signal processing. He is also a co-founder of the Sensemodi start-up, aimed at developing intelligent wearable devices for monitoring musculoskeletal disorders.

 

Web: https://orcid.org/0000-0002-2175-7382