Plenary talk: Mixed dimensional problems on non-matching grids at the exascale: solutions, challenges, and perspectives

• Luca Heltai (Università di Pisa)

Room: Aula A, Aula B (in streaming) This presentation addresses the challenges and solutions associated with mixed-dimensional problems on non-matching grids, with a perspective towards exascale computing. Many physical phenomena involve coupled partial differential equations (PDEs) defined on domains of heterogeneous dimensions, leading to non-matching coupling at the interfaces. To tackle these problems, the reduced Lagrange multiplier method [2] provides a general mathematical framework for analysis and approximation. This approach sheds light on the stability, well-posedness, and error associated with dimensionality reduction, but requires the efficient solution of saddle point problems involving non-matching discretizations. For the efficient numerical solution of the resulting large-scale systems, particularly on complex geometries like vascular networks embedded in biological tissues [1], we borrow a technique that was developed for non-nested multigrid methods, which offer the required flexibility by allowing the exchange of information between arbitrarily overlapping and distributed grid hierarchies with a matrix-free implementation [3], and we developed augmented Lagrangian-based preconditioners that offer optimal and scalable solutions [4]. The continued development of such robust and scalable algorithms within high-performance finite element libraries like deal.II is crucial for tackling these challenging problems at the exascale. [1] Luca Heltai, Alfonso Caiazzo, and Lucas O. Müller, Multiscale coupling of one-dimensional vascular models and elastic tissues, Annals of Biomedical Engineering 49 (2021), 3243–3254. [2] Luca Heltai and Paolo Zunino, Reduced lagrange multiplier approach for non-matching coupling of mixed-dimensional domains, Mathematical Models and Methods in Applied Sciences 33 (2023), no. 12, 2425–2462. [3] Marco Feder, Luca Heltai, Martin Kronbichler, and Peter Munch, Matrix-free implementation of the non-nested multigrid method, Arxiv, 2024. [4] Michele Benzi, Marco Feder, Luca Heltai, and Federica Mugnaioni, Optimal and scalable augmented Lagrangian preconditioners for fictitious domain problems, Arxiv, 2025.

Junior plenary talk: Enhancing Spatial Filters for Convection-Dominated Flows: VMS Models and Parameter Optimization

• Maria Strazzullo (Politecnico di Torino, DISMA)

Room: Aula A, Aula B (in streaming) The evolve-filter (EF) strategy is a spatial filter-based numerical stabilization technique for convection-dominated flows. In under-resolved regimes, classical numerical approaches may lack accuracy due to the presence of spurious numerical oscillations. EF offers a simple, modular, and effective approach to smooth out these instabilities. However, it is well known that when the filter action is too strong, the method may lead to inaccurate and over-diffusive results. In this talk, we present novel strategies to mitigate the over-diffusivity of EF when large filter radii are employed, while preserving the main flow features. We explore two complementary directions: modifying the model and optimizing its parameters. From an algorithmic perspective, we propose a new approach based on the variational multiscale (VMS) framework, which allows us to separate the resolved large scales from the resolved small scales in the evolved velocity field. The filtered small scales are then used to correct the large scales, enhancing accuracy without losing important flow information. From an optimization perspective, we demonstrate the crucial role of the filter parameter and introduce a reinforcement learning strategy for its selection. Notably, the training of the network does not rely on direct numerical simulations, significantly reducing the computational cost of the learning procedure.

Plenary talk: Modelling the multiphysics of the human eye

• Anna Pandolfi (Politecnico di milano)

Room: Aula A, Aula B (in streaming) The research presented in this talk investigates the multiphysics modelling of the human eye through a set of dedicated, tissue-specific studies regarding cornea, iris, vitreous body, and retina. Each ocular component is analysed independently isolating its dominant physical mechanisms. The cornea is modelled as a layered, anisotropic soft tissue, with particular emphasis on stromal collagen architecture and its influence on nonlinear, hyperelastic mechanical behaviour under intraocular pressure and external loading. Microstructure-informed constitutive formulations are employed to connect collagen organisation to macroscopic stress and deformation. The iris is examined as an active elastic fiber reinforced structure, where geometry and material response govern pupil dynamics and anterior segment mechanics. The vitreous body is described as a poro-elastic medium, capturing its role in load transmission, damping, and mechanical interaction with surrounding tissues. The retina is modelled as a thin, layered structure, composed by structural element with distinct mechanical properties, focusing on deformation, stress localisation, and interaction with the vitreous under physiological and pathological conditions. All together, these separated yet conceptually aligned studies define a coherent multiphysics perspective on ocular mechanics. The proposed modelling framework provides tissue-specific insight and lays the groundwork for future integrated simulations, disease modelling, and clinically oriented applications.

Junior plenary talk: Isogeometric methods for the study of fracture mechanics via phase-field modelling

• Luigi Greco (University of Pavia)

Room: Aula A, Aula B (in streaming) Fracture mechanics remains one of the most challenging and impactful research areas in engineering. The ability to accurately predict fracture phenomena is essential for the safe and efficient design of structural systems, with profound economic, environmental, and societal implications. Preventing structural failure reduces maintenance costs, material losses, environmental hazards associated with catastrophic spills, and the loss of human life. The foundations of modern fracture mechanics can be traced back to the seminal work of Griffith [1], who introduced the energetic interpretation of fracture and the concept of fracture energy associated with crack evolution. Since then, the continuous growth of computational capabilities has driven the development of increasingly sophisticated numerical approaches for fracture analysis. Among these, phase-field methods have emerged as one of the most powerful and versatile frameworks for the simulation of complex fracture processes. Their main strength lies in the ability to represent crack evolution through a continuous description of discontinuous interfaces, naturally handling complex crack topologies without ad-hoc tracking strategies. Within this framework, the accurate modeling of fracture energy dissipation plays a central role. In recent years, high-order phase-field formulations have attracted growing attention due to their enhanced regularity properties and their potential to significantly improve computational efficiency and solution accuracy [2]. The resulting high-order partial differential equations find a particularly suitable discretization environment in Isogeometric Analysis [3], whose high-continuity basis functions provide a natural framework for their numerical treatment. This talk will discuss recent advances in high-order phase-field models for fracture, with particular emphasis on both static and dynamic regimes [4]. Special attention will be devoted to the interplay between variational modeling, numerical efficiency, and predictive capabilities, highlighting how high-order formulations can substantially reduce computational costs while preserving remarkable accuracy in the simulation of complex fracture phenomena. References [1] Griffith, A. A., Taylor, G. I. VI. e phenomena of rupture and flow in solids, Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, 221, 163-198, 1921. [2] Greco, L., Maggiorelli, E., Patton, A., Negri, & Reali, A. AT1 fourth-order isogeometric phase-field modeling of brittle fracture. Mathematical Models and Methods in Applied Sciences, 13, 2741-2795, 2025. [3] Hughes, T. J., Cottrell, J. A., & Bazilevs, Y. Isogeometric analysis: CAD, finite elements, NUReBS, exact geometry and mesh refinement. Computer methods in applied mechanics and engineering, 194(39-41), 4135-4195, 2005. [4] Greco, L., Kiendl, J., Patton, A., Negri, & Reali, A. Fourth-order isogeometric phase-field modeling of dynamic brittle fracture: Numerical study and comparison with second-order models. Computer methods in applied mechanics and engineering, 449, 118513, 2026.

Junior plenary talk: Computational modeling and simulation of advanced bioprinting techniques

• Francesco Chirianni (Università di Roma Tor Vergata)

Room: Aula A, Aula B (in streaming) This work presents a computational framework for the optimization of extrusion-based bioprinting processes, with particular emphasis on standard and coaxial bioprinting technologies. Extrusion-based bioprinting is widely used for the fabrication of biomimetic structures containing living cells, thanks to its ability to process a broad range of biomaterials and bio-inks. However, the quality of the printed constructs strongly depends on the complex rheological behavior of the bio-inks, which directly affects printability, cell viability, and shape fidelity. In particular, coaxial bioprinting introduces additional challenges related to fluid–fluid interactions and interface stability, making process optimization particularly difficult. The study addresses the problem from a dual perspective, considering both the flow inside the extruder and the dynamics of the material after extrusion. Inside the nozzle, a reduced-order predictive model is developed to correlate key process parameters — including nozzle diameter, extrusion pressure, and flow rate — with the stresses acting on embedded cells and the resulting cell viability. The framework is further translated into practical graphical tools to support rapid process design and parameter selection. Outside the nozzle, the extrusion process is formulated as a viscoelastic free-surface flow problem, extended to coaxial bioprinting through a multiphase approach. An Arbitrary Lagrangian–Eulerian (ALE) finite element framework is implemented to capture phenomena such as die swell, filament evolution, and interfacial stresses between core and shell fluids. Numerical simulations are used to investigate the influence of rheological and viscoelastic parameters on printing resolution and stress distribution in both standard and coaxial configurations, providing predictive tools for the design and optimization of advanced bioprinting processes. References 1. Chirianni, F., Vairo, G., Marino, M. (2024). Development of process design tools for extrusion-based bioprinting: From numerical simulations to nomograms through reduced-order modeling. Computer Methods in Applied Mechanics and Engineering, 419, 116685. 2. Chirianni, F., Vairo, G., Marino, M. (2024). Influence of extruder geometry and bio-ink type in extrusion-based bioprinting via an in silico design tool. Meccanica, 59(8), 1285-1299.