Sara Zahedi

Professor of Numerical Analysis at the Department of Mathematics, KTH. I am currently one of the teacher representatives at the SCI Faculty Board.

Research

My research focuses on the development, analysis, and implementation of computational methods for solving Partial Differential Equations (PDEs) in evolving domains. Such PDEs occur for example in multiphase flow simulations, where the evolving domains are defined by interfaces that separate immiscible fluids. Finite Element Methods (FEM) are well-known for efficiently solving PDEs in complex geometries. However, when the geometry undergoes large deformations, standard FEM requires re-meshing and interpolation, as conforming meshes are necessary to ensure accuracy and robustness, but this can be both expensive and cumbersome.  To address this challenge, we propose an alternative: Cut Finite Element Methods (CutFEM). These methods allow evolving geometries to cut through the computational mesh in an arbitrary manner, without loosing accuracy and without problems with ill-conditioned linear systems.