WS, Chiara Sorgentone: Fast Integral Solvers for Self-Similar Geometries

Speaker
Chiara Sorgentone,Sapienza University of Rome

Abstract
Partial differential equations posed in domains with irregular interfaces arise in a wide range of scientific and engineering applications, such as composite materials, fluid-structure interaction, and multiphase flows. These problems exhibit geometrically complex domains that challenge both analytical approaches and numerical approximations. It could be important for industrial technologies to enhance the surface effects with respect to the surrounded volume, by increasing the surface (or the length); hence fractal boundaries and interfaces turn out to be a good tool in different applications, e.g. in heat transfer through fibrous composites, or in modeling diffusion of sprays in the lungs.
To address the challenges posed by such domains, we adopt a boundary integral equation approach, which naturally reduces the problem dimension and provides accurate treatment of interface conditions. Nonetheless, the intricate, non-smooth structure of self-similar geometries introduces singularities at edges and corners that classical discretizations and numerical solvers cannot effectively handle.
In this work, we discuss a fast integral solver designed for self-similar and prefractal domains. The method incorporates the Recursively Compressed Inverse Preconditioning (RCIP) method for accurate and efficient integration over non-smooth boundaries.