A capillary network and a fractured rock block walk into a bar…” - Numerical challenges in PDEs on complex geometries

Numerical modeling of physical systems often requires the solution of PDEs defined on complex geometries. Such complexity may arise from lower-dimensional structures embedded in higher-dimensional domains, small-scale geometric features, or time-evolving geometries undergoing large deformations.

My research activity addresses these challenges across different application fields. Part of my previous work focused on mixed-dimensional modeling, including 3D-1D coupling strategies for the simulation of flow in capillary networks and tissue perfusion. I also worked on geometry simplification through defeaturing approaches, where an a posteriori error estimator guides the removal of small geometric features while controlling the impact on solution accuracy.

My current research focuses instead on numerical challenges related to fracture propagation in rock masses, where progressive material degradation may lead to failure and detachment. In this context, complexity arises from evolving discontinuities (the fractures) and possible large deformations, both tackled by using a Material Point Method coupled with a phase-field approach.

In this talk I will provide an overview of my research interests, presenting current work and future perspectives, and exploring what the capillary network and the fractured rock block might eventually have to discuss at the bar.

Contatto:
andrea1.manzoni@polimi.it