Mini symposia

MS 01 - Mathematical Models for Socio-Epidemiological Dynamics

Caterina MILLEVOI, Università degli Studi di Padova, caterina.millevoi@unipd.it

Martina RAMA*, Università degli Studi di Trento and Fondazione Bruno Kessler, martina.rama@unitn.it

In the context of complex socio-epidemiological systems, mathematical models offer a structured framework to comprehend and predict social phenomena such as epidemic spreading, social contagion, opinion and information transmission.

The mini-symposium aims at showcasing cutting-edge research in mathematical modeling techniques tailored to unravel socio-epidemiological complexities. Topics of discussion will encompass various approaches - including compartmental models and network-based approaches, among others - based on different methodologies - e.g., numerical solvers, machine learning, hybrid methods, and so on. Emphasis will be placed on the integration of empirical data, theoretical insights, and computational techniques to construct models that capture the nuanced social dynamics within social networks, communities, and populations.

By fostering interdisciplinary dialogue and collaboration, the goal of the mini-symposium is to pave the way for innovative approaches to address current and emerging challenges of socio-epidemiological dynamics.

MS 02 - Efficient numerical methods for evolutionary Partial Differential Equations, with applications

Fabio CASSINI*, Università degli Studi di Verona, fabio.cassini@univr.it

Federica FERRARESE, Università degli Studi di Ferrara, federica.ferrarese@unife.it

Evolutionary Partial Differential Equations (PDEs) are of great interest for many fields of science and engineering. These kinds of equations are at the basis of many models for physical, chemical, economic, and social phenomena (see, for instance, References [1,2,3]).

In this context, devising numerical techniques to determine an approximated solution is of paramount importance since the analytical solution of the involved equations are rarely available. Moreover, we typically have to take special care in the development of 

efficient solvers because of intrinsic properties when dealing with evolutionary PDEs (curse of dimensionality, stiffness, nonlinearities, discontinuities, and boundary conditions that may vary with time, for instance).

The main goal of the minisymposium is to bring together young researchers of different communities and to present recent advances in the field of the efficient numerical solution of evolutionary PDEs, in all its aspects. A particular emphasis will be put on the diverse applications where these methods find their utility, as for instance simulations of crowd movement, pedestrian flow, modeling of traffic congestion, vehicular dynamics, kinetic equations with nonlocal interactions, and advection-diffusion-reaction equations for biological and corrosion models.

References

[1] W. Hundsdorfer and J. G. Verwer. Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations, volume 33 of Springer Series in Computational Mathematics, Springer, 2003.

[2] A. Quarteroni and A. Valli. Numerical Approximation of Partial Differential Equations,

volume 23 of Computational Mathematics, Springer, 2008.

[3] G. Naldi, L. Pareschi, and G. Toscani. Mathematical modeling of collective behavior in socio-economic and life sciences. Springer Science & Business Media, 2010.

MS 03 - Multi-scale approaches and machine learning techniques in material modelling

Salvatore DI STEFANO*, Politecnico di Bari, salvatore.distefano@poliba.it 

Vincenzo FAZIO, Università degli Studi di Trento, vincenzo.fazio@unitn.it 

Claudia BINETTI, Politecnico di Bari, University of Lille, claudia.binetti@iemn.fr 

Alessandro GIAMMARINI, Politecnico di Torino, alessandro.giammarini@polito.it

The mechanical characterization of materials, both of an industrial origin (e.g. hierarchical composites, adhesives, rubber-like media, metamaterials, functionally graded materials) and of a biological nature (biological tissues, cell aggregates, silks), involves several challenging scientific questions that require dedicated tools to be answered.  In this context, attention is directed towards a specific category of materials, namely those wherein the microscopic behaviour strongly impacts the overall macroscopic response. Consequently, to accurately characterize such materials, multi-scale approaches are chosen to correctly identify the type of microstructural processes and deduce macroscopic properties from the information available at smaller scales. 

In the last decades, in parallel with the development of increasingly refined models, this intricate issue has been tackled by a large portion of the experimental literature, which, thanks to increasingly sophisticated techniques, is furnished with large libraries of data on hierarchical systems from the nano- and microscale to the macroscale.

There is an ongoing debate regarding the necessity of effective methodologies that can facilitate the interaction between theoretical insights and large amounts of empirical data. In this perspective, machine learning approaches, in a broad sense, appear to be a promising tool. However, a major limitation of using machine learning techniques for theoretical modelling is their tendency to produce 'black box' approaches, which lack interpretability and hinder the extension of knowledge.

The main scope of our mini-symposium is to bring together scientific works in the field of multi-scale study of materials, also encompassing data-driven techniques, and to permit young researchers to build new collaborations in light of a fruitful and continuous sharing of ideas to address the open questions introduced above.

The mini-symposium is expected to involve different but synergic points of view, with the common scope of giving new insights and perspectives to the study of materials. In this sense, we foresee the mini-symposium to call for researchers in the fields of theoretical modelling, experimental studies and approaches based on the new path outlined by physical-driven machine learning.

MS 04 - Nonlinear material behavior: computational methods and numerical modeling

Gregorio BERTANI, Università di Bologna, gregorio.bertani2@unibo.it

Francesco Salvatore LIGUORI, Università della Calabria, francesco.liguori@unical.it

Elisabetta MONALDO*, Università degli Studi Roma Tre, elisabetta.monaldo@uniroma3.it 

Materials characterized by a nonlinear behavior are widely present in engineering applications, encompassing more traditional reinforced concrete and masonry structures as well as advanced components in mechanical, aerospace and biomedical engineering. However, the accurate modeling of such materials is still a complex and challenging topic. Numerical simulations of such structures require dealing with strongly non-linear constitutive models, for which robust and efficient computational techniques have to be developed. Moving from these premises, this symposium aims to bring together scientific contributions related to computational methods for nonlinear materials. Key topics of discussion include, but are not limited to:

- Computational damage and fracture mechanics

- Computational plasticity 

- Material instability

- Advanced discretization techniques (FEM, IGA, VEM,…)

- Multiscale and multiphysics simulations

MS 05 - Computational Methods for Shells and Spatial Structures

Claudia CHIANESE*, Università degli Studi di Napoli Federico II, claudia.chianese@unina.it

Claudio INTRIGILA, Università degli Studi di Roma Tor Vergata, intrigila@ing.uniroma2.it

Jonathan MELCHIORRE, Politecnico di Torino, jonathan.melchiorre@polito.it

Arianna VENETTONI, Università degli Studi Roma Tre, ARIANNA.VENETTONI@uniroma3.it

Shell and spatial structures constitute inherently architecturally expressive solutions, enabling a rich synthesis of structural efficiency and optimized use of material. Given the escalating need for innovative and sustainable designs in architecture and engineering, the availability of computational methods has become increasingly crucial.

The mini-symposium provides a platform to young researchers to showcase cutting-edge contributions and recent advancements in the field of computational methodologies for the conceptual design, modelling, analysis, form finding, structural optimization, manufacturing, testing and maintenance techniques with application to shell and spatial structures.

Topics of interest may concern, but are not limited to, tension and membrane structures, framed and lattice structures, gridshells and active-bending structures, shell roofs, tensegrity structures, pneumatic and inflatable structures, active and deployable structures, concrete, metal, timber, masonry and bio-based, spatial structures.

MS 06 - Advances in Computational Mechanics and Applied Mathematics for the Assessment, Monitoring, and Design of Masonry Structures

Sam COCKING, University of Cambridge, sc740@cam.ac.uk

Antonino IANNUZZO, Università degli Studi del Sannio, aniannuzzo@unisannio.it

Carlo OLIVIERI, Telematic University Pegaso, carlo.olivieri@unipegaso.it

Vittorio PARIS, Università degli Studi di Bergamo, vittorio.paris@unibg.it

Davide PELLECCHIA*, University of Naples Federico II, davide.pellecchia@unina.it

This minisymposium aims to showcase the latest technological developments and innovative numerical methodologies with applications in civil engineering, focusing in particular on challenges and solutions related to masonry structures. It will bring together a diverse group of researchers, practitioners, and academics who will present their work on computational mechanics and applied mathematics, emphasizing their application in the design, analysis, and monitoring of masonry constructions.

The symposium will cover a broad range of topics, including but not limited to, the development of new computational models for the analysis of masonry structures, the integration of advanced mathematical techniques in the assessment of their structural integrity, and the application of state-of-the-art monitoring technologies for the maintenance and preservation of heritage structures. Through a combination of keynote speeches, technical presentations, and interactive discussions, participants will explore these and other innovative approaches to structural analysis, such as novel finite element methods, machine learning algorithms, and digital twins, which offer enhanced accuracy and efficiency in the diagnosis and management of masonry structures.

Key sessions will address the challenges in simulating the complex behavior of masonry under various loads and conditions, the advancement of non-destructive testing methods to aid in the preservation of historic structures, and the implementation of sustainable and resilient design practices. Ultimately, the minisymposium aims to foster a multidisciplinary dialogue, encouraging the exchange of ideas and fostering collaborations that will push the boundaries of current knowledge and practice in the field.

UPDATE: Contributors in our MS will also have the opportunity to submit an extended and original version of their contribution for publication in a Special Issue of the International Journal of Space Structures (Editors-in-Chief Prof. Sigrid Adriaenssens and Prof. Alireza Behnejad). The special issue will run from September to January 2025. Further details regarding this will be provided in due course.

MS 07 - Nonlinear phenomena in physics and engineering

Mario ARGENZIANO*, University of Palermo, mario.argenziano@unipa.it

Enrico BABILIO, University of Naples Federico II, enrico.babilio@unina.it

Natural phenomena are often nonlinear and the same is true for the behavior of structures and mechanisms of engineering interest. There are already countless applications in which nonlinearities are exploited or they could be. This is a clear motivation for a deep paradigm shift about nonlinear dynamics and, therefore, the subject of one of the most active and exciting scientific frontiers is also fast becoming of paramount importance for understanding of phenomena and designing real applications. In this regard, the MS aims to collect contributions that consider any analytical, computational, or experimental aspect of nonlinear dynamics. Topics include but are not limited to continuous and discrete systems; non-smooth contact; composite, smart, lattice, or tensegrity structures; synchronization phenomena; parametric excitation; periodic, quasi-periodic, and chaotic motion; dynamical integrity; analytical and numerical methods for nonlinear analysis; and geometrically exact beam models.

MS 08 - Particles in Numerical Simulations: trends and applications

Elisa IACOMINI*, University of Ferrara, elisa.iacomini@unife.it

Marta MENCI, Università Campus Bio-Medico di Roma,  m.menci@unicampus.it

Nowadays numerical simulations involving particle-based methodologies are becoming prominent in various applications.

In fluid dynamics, smoothed particle hydrodynamics (SPH) methods have been used over the years to simulate complex fluid flows, and particle-in-cell (PIC) methods have shown good results in simulating phenomena involving particle-fluid interactions.

In the biological field, particle-based models and simulations contribute to understanding drug delivery mechanisms, cellular interactions and many physiological processes.

Due to the increasing availability of data in social contexts, including traffic and pedestrian dynamics, particle-based techniques have been considered to calibrate mathematical models against collected data, that usually refer to microscopic quantities (for instance state, position, velocity of each agent). 

Concerning opinion dynamics, the increasing accessibility of data on social networks enables agent-based methods to become progressively more accurate.

Furthermore, Particle Swarm Optimization (PSO) and Consensus Based Optimization (CBO) methods as well as particle-based filtering procedures offer several advantages in the field of numerical optimization and decision-making processes.

Due to the great variety of applications, the aim of this minisymposium is hence to gather young researchers who are interested in discussing contemporary particle-centric approaches.

The focus will be on the computational aspects encountered in the study of the models and to open challenges. Advantages and drawbacks of the different techniques will be discussed, together with possible development of algorithms aimed at reducing computational costs and new fields of application.

MS 09 - Non-Newtonian complex fluids: recent advancements in mathematical modeling and applications

Lorenzo FUSI*, Università degli Studi di Firenze, lorenzo.fusi@unifi.it

Luigi VERGONI, Università degli Studi di Perugia, luigi.vergori@unipg.it

Roberta DE LUCA, Università degli Studi di Napoli Federico II, roberta.deluca@unina.it

A vast number of materials exhibit complex and non-Newtonian rheological behavior. Many geophysical, industrial, biological fluids display mix of elastic, viscoelastic, plastic, viscoplastic and non-linear response to stresses and forces. These responses can be extremely complex due to heterogeneities and to the underlying small-scale structure of the materials. Quite often, the constitutive relations of these materials are of implicit and/or differential type. This mini symposium aims at gathering recent studies on non-Newtonian fluid mechanics in terms of mathematical modelling and possible applications. Although Non-Newtonian complex fluids have a long history, advancements in this field are still going on, proving the state of good health of this kind of research.  

Our intention is to collect several studies that span from ‘classical’ non-Newtonian research to more complex systems such as granular suspension, muti-phase, and multi-component fluids.

MS 10 - Computational approaches for integral and differential models: real-world applications

Federica PES*, University of Pisa, federica.pes@dcci.unipi.it, federicapes26@gmail.com

Patricia DIAZ DE ALBA, University of Salerno, pdiazdealba@unisa.it

Mathematical models composed of integral and/or differential equations play an important role in many real-world applications. The resolution of these problems requires suitable computational methods for the discretized problem. To obtain desirable results, numerical approximation and various techniques from numerical linear algebra are needed, so an interaction between experts in these two fields is crucial. Although different approaches have been developed during the last years to solve this kind of problems, it is still an important challenge to build accurate, stable, and efficient methods. The goals of this mini-symposium are mainly two: the first one is to show new mathematical developments from the theoretical and numerical points of view; the second one is to display how to apply the proposed computational techniques to real-world applications. To this end, this mini-symposium brings together several young researchers from numerical analysis who work on this topic to present their main results and exchange ideas.

MS 11 - Advanced Analytical and Computational Approaches for Complex Dynamical Systems

Nicolò VAIANA*, University of Naples Federico II, nicolo.vaiana@unina.it

Ida MASCOLO, University of Naples Federico II, ida.mascolo@unina.it

Marialuigia SANGIARDI, University of Oxford, marialuigia.sangirardi@eng.ox.ac.uk

The study of complex dynamical systems plays a crucial role in different fields of science. For such a reason, many researchers are currently focusing on the advancement of analytical and computational approaches for the investigation and simulation of the complex behavior exhibited by such dynamical systems.

The main purpose of the Mini-Symposium is to highlight and discuss the most recent advancements achieved in this field by young researchers, both in the framework of Mathematical Physics and of Solid and Structural Mechanics. 

Submissions proposing novel analytical and computational techniques suitable for the study of dynamical systems and/or the simulation of their experimental behavior are highly welcome. Of particular interest are contributions on one of the following topics: stability and bifurcation, identification of parameters and uncertainties, and shock and vibration control.

MS 12 - Mathematical modeling in mechanobiology

Giulia POZZI*, Politecnico di Torino, giulia.pozzi@polito.it

Giulio LUCCI, Sapienza University of Rome, giulio.lucci@uniroma1.it

Living organisms constantly respond to their environments, not just through chemical signals, but also through physical forces. Mechanobiology, a rapidly evolving field, investigates the intricate relationship between mechanical cues and biological processes, revealing how cells interpret physical stresses and translate them into cellular responses that govern growth, differentiation, and behavior.

Within this context the mini-symposium aims to showcase recent advancements in mathematical modeling applied to mechanobiology, emphasizing the active response of living cells and tissues to chemo-mechanical stimuli. Topics will span from microstructural changes at the subcellular level to phenomena at larger spatial scales such as cell reorientation and tissue reorganization in response to multi-physical cues.

Key themes of the mini-symposium will thus include, but are not limited to: cell mechanosensing and mechanotransduction, exploring how cells translate forces like pressure and tension into biochemical signals, ultimately triggering downstream cellular responses; cell migration, which is fundamental in processes like development, wound healing, and immune response; cell adhesion and reorientation, which are heavily influenced by mechanical forces; multi-scale modeling and tissue mechanics, bridging the gap between the microscopic and macroscopic scales. Both theoretical and computational mathematical approaches to such topics will be welcomed.

Finally, the Symposium will provide a platform for young researchers to convene, share perspectives, and foster collaborations, driving forward the understanding of mechanobiology and its implications across disciplines.

MS 13 - Advanced numerical methods for coupled problems on complex domains

Andrea BORIO, Politecnico di Torino, andrea.borio@polito.it, 

Francesca MARCON, Politecnico di Torino, francesca.marcon@polito.it,

Michele VISINONI*, Politecnico di Milano, michele.visinoni@polimi.it

Recently, there has been significant interest within scientific communities in the study and design of numerical methods for solving partial differential equations (PDEs) capable of handling complex geometries, which may arise in many applications, such as geological fractures and porous media, crack or wave propagation, roots-soil interactions or vascularized biological tissues.

Partially, this interest is driven by the geometric flexibility inherent in such meshes, providing a highly convenient framework to handle hanging nodes, cuts, agglomeration, and non-matching interfaces. Moreover, an additional challenge frequently arises due to the multiphysics nature of these problems. The models involve coupled terms and transmission conditions that, when the geometric complexity of the problem increases, it is essential to represent and treat these interactions without compromising their efficiency.

The aim of this mini-symposium is to bring together young researchers working on these advanced schemes and their applications.

MS 14 - Mathematical models in oncology: cancer development and treatment optimisation

Francesca BALLATORE, Politecnico di Torino, francesca.ballatore@polito.it

David MORSELLI*, Politecnico di Torino, Swinburne University of Technology, david.morselli@polito.it

In recent years, the field of mathematical oncology has flourished, shedding light on the intricate relationship between tumours and treatments, potentially leading to unprecedented advances in cancer care. The resulting models cover different morphological and functional aspects of tumour growth, often integrating clinical data to enhance their accuracy. It has become evident that experimental results alone often cannot discern between reasonable hypotheses about tumour development dynamics; mechanistic models provide a pathway to deeper insights, as seen in the study of epigenetic characterization of tumour masses. Additionally, the increase of pressure and stress often caused by tumour growth on the surrounding tissues has significant effects on the patient’s health and mathematical models incorporating mechanics provide a valid tool to evaluate them. Moreover, mathematical models can propose optimal cancer therapies, taking into account factors like toxic side effects and drug resistance even before clinical trials. The aim of this mini-symposium is to give an overview of the current research topics in mathematical oncology, including both analytical theoretical results and numerical simulations, with a special focus on the modelisation of therapies. We plan to include contributions from a gender-balanced group of promising young speakers working in various institutions across different countries.

MS 15 - Advances in mechanics of biological systems and bioinspired materials

Angelo Rosario CAROTENUTO*, University of Napoli Federico II, angelorosario.carotenuto@unina.it

Stefania PALUMBO, University of Napoli Federico II, stefania.palumbo@unina.it 

Through the combined use of analytical results, enhanced computational methods and ad hoc experiments, Continuum Mechanics is assuming a pivotal position in simulating and characterizing the intrinsic complexity of many biological systems at different scale levels. By melding information from system biology and biomedical sciences, innovative theories and increasingly advanced applications indeed allow to skip the fences among disciplines and shed light on the multiphysic phenomena behind cell and tissue mechanobiology, potentially suggesting new engineered strategies for diagnosis and therapy in medicine.

Furthermore, the observation of these living architectures -refined over millennia through adaptation and evolution- often inspires effective ways to conceive optimized constructs that overcome the limits of standard materials by obtaining unconventional responses for applications in many engineering fields, from soft robotics to aerospace.

With this in mind, this mini-symposium aims to fertilize the multidisciplinary ground of mechanics of biological and bioinspired materials to promote collaborations strengthening the progress in the different fields of biomechanics.

To this end, contributions considering the following topics will be warmly welcome:

- Coupled problems in biomechanics;

- Growth, remodelling and morphogenesis of biological tissues;

- Single-cell mechanics;

- Constitutive behaviour of living materials;

- Mechanotransduction and chemo-mechanical processes;

- Bioinspired structures and metamaterials;

- Computational problems for biomedical applications;

- Experimental approaches in biomechanics.

MS 16 - Young advances in numerical approximation of differential problems with applications

Stefano DI GIOVACCHINO, University of L'Aquila, stefano.digiovacchino@univaq.it

Massimo FRITTELLI, University of Salento, massimo.frittelli@unisalento.it 

Giovanni PAGANO*, University of Salerno, gpagano@unisa.it

Carmela SCALONE, University of L'Aquila, carmela.scalone@univaq.it

The interest of the numerical community in differential problems of various kinds has always been relevant, due to the ability of such problems to capture the dynamics of real phenomena in the most diverse fields of application, such as biology, chemistry, electronics, physics, but also social and epidemiological sciences. This motivates the constant development of advanced numerical techniques for the efficient and accurate solution of differential equations arising  from applications. The numerical analysis of differential problems also has as one of its main targets the conservation of geometric structures and qualitative features of the continuous problems, e.g., preservation of invariants and positivity, and the identification of specific techniques to handle challenges and unexplored issues, such as stiffness and strong oscillations of the exact solutions.

The aim of this minisymposium is to bring together the above-mentioned topics recently brought forward by young researchers, considering different perspectives; from a more classical standpoint of research in numerical analysis, i.e. from the definition of methods appropriate to the problems under investigation, with the related study of their fundamental properties, to the fundamental tools for an efficient design of the schemes, and on to the new techniques related to neural networks and machine learning.

MS 17 - Advances in optimization methods with applications to real-world challenges

Dario CARBONARO, Politecnico di Torino, dario.carbonaro@polito.it

Nicola FERRO*, Politecnico di Milano, nicola.ferro@polimi.it

Francesco MEZZADRI, Università degli studi di Modena e Reggio Emilia, francesco.mezzadri@unimore.it

Optimization problems are ubiquitous across a multitude of real-world applications including, for instance, healthcare, product design, and computer vision. Solving such problems is therefore of fundamental importance, but it can also be complex and challenging. Thus, the formulation and analysis of numerical methods -  ranging from traditional techniques to cutting-edge approaches - is an active research topic.

This mini-symposium aims to serve as a platform to discuss and share recent advancements in numerical methods for optimization problems, with a specific focus on complex applied scenarios where the balance between theoretical robustness and practical applicability is crucial. The session welcomes i) contributions that are application-oriented, but primarily focus on the theoretical formulation and analysis of the numerical method; ii) research studies where the role of the applications is more pronounced, emphasizing the practical impact of the optimization methods.

Topics of interest for this mini-symposium include, but are not limited to:

- Complementarity problems;

- Optimization methods for neural networks;

- Image processing techniques;

- Shape and topology optimization;

- Process optimization.

MS 18 - New trends in approximation

Francesco MARCHETTI*, Università di Padova, francesco.marchetti@unipd.it

Emma PERRACCHIONE, Politecnico di Torino, emma.perracchione@polito.it

This minisymposium aims at bringing together young researchers studying and/or applying approximation methods that are enhanced by modern tools from different fields. On the one hand, there is a growing interest towards the usage of machine learning techniques combined with classical approximation methods, such as polynomial- and kernel-based approaches. On the other hand, new theoretical findings can lead to even more sophisticated data analysis tools for applications.

MS 19 - Optimization methods for classical and data-driven approaches

Matteo CALDANA, Politecnico di Milano, matteo.caldana@polimi.it

Marco GAMBARINI, Politecnico di Milano, marco.gambarini@polimi.it

Stefano PAGANI, Politecnico di Milano, stefano.pagani@polimi.it

Giovanni ZIARELLI*, Politecnico di Milano, giovanni.ziarelli@polimi.it

Engineering applications often use optimization techniques to manage the interaction between data and models, enabling model discovery, parameter estimation, control, and decision-making under uncertainty. Finding an optimal balance between efficiency, accuracy, and robustness remains an open challenge, particularly for problems with high dimensionality, uncertainties, and many local minima. The aim of this minisymposium is to bring together researchers to share their latest advances in this field. The topics of discussion will include (but are not limited to) novel physics-based and data-driven modeling and control, machine learning acceleration of simulations, training strategies for neural networks and digital twinning.

MS 20 - Challenges and recent advancements in polytopal methods for PDEs

Stefano BONETTI, Politecnico di Milano, stefano.bonetti@polimi.it

Michele BOTTI, Politecnico di Milano, michele.botti@polimi.it

Ivan FUMAGALLI*, Politecnico di Milano, ivan.fumagalli@polimi.it

The recent years have seen a progressive establishment of Galerkin methods based on polytopal meshes for the discretization of Partial Differential Equations (PDEs), both in numerical analysis and in several applications. This success stems from several advantages of these methods with respect to more classical simplicial/tensorial finite element methods, such as the following: enhanced geometric accuracy in dealing with complex boundaries and internal interfaces; robustness to mesh distortion;  easier and more efficient mesh refinement/coarsening strategies, including the natural handling of hanging nodes; more natural encoding of physical properties in structure-preserving schemes.

This minisymposium aims to discuss significant challenges, novel theoretical advancements, and the design of efficient solvers for differential problems by polytopal methods. To this aim, we want to gather young researchers working on different methods of the polytopal family (such as, e.g., Discontinuous Galerkin, Virtual Element, Hybrid High-Order, Hybridizable Discontinuous Galerkin), to foster cross-contamination and combine the advantages of each strategy. 

MS 21 - Recent High-Order Numerical Methods for Partial Differential Equations and Their Applications

Emanuele MACCA*, University of Catania, emanuele.macca@unict.it

Partial differential equations (PDEs) are foundational in modeling various phenomena, necessitating sophisticated numerical methods to handle complexities like high-order accuracy, implicit-explicit strategies, well-balanced reconstructions, order-adaptive schemes, and asymptotic-preserving techniques. High-order schemes enable enhanced accuracy and efficiency, capturing fine details with precision. Implicit-explicit strategies tackle stiff terms and nonlinearities effectively, broadening the scope of computationally tractable problems. Well-balanced reconstruction preserves physical properties in complex systems, aided by order-adaptive schemes optimizing resolution and computational costs. Asymptotic-preserving methods ensure accurate solutions across disparate scales or regimes. 

The primary objective of the mini-symposium is to unite young researchers from diverse communities and present recent advancements in efficiently solving evolutionary partial differential equations (PDEs) across all facets of the field.

* corresponding organizer