Immersed methods for multiscale and multiphysics problems (IMMEDIATE)

This project addresses the challenges of solving multiscale and multiphysics problems, particularly those involving biphasic systems with embedded interfaces, such as vascularized tissues or fiber-reinforced materials. Traditional numerical methods struggle with these problems due to the vastly different scales involved, making it impractical to resolve the full geometrical complexity. A mesoscale approach, which bridges phenomena at different scales, is proposed to overcome these difficulties. The research focuses on developing numerical methods, including Mixed-Dimensional Partial Differential Equations (MD-PDEs), and advanced techniques like the immersed finite element method and Lagrange multipliers. These methods aim to model complex systems like blood flow in vascular networks, potentially impacting medical research in areas such as cancer and neurological disorders. The project is supported by research units with expertise in advanced discretization schemes and medical applications.