A numerical solution method for the dbar-equation in the plane

In this project a fast method for solving dbar-equations in the plane is developed. The method is based on the formulation of the problem as a weakly singular integral equation, and a general multigrid method for such problems is adapted. A rigorous analysis of the convergence and complexity of the method is given. Moreover, one-grid and two-grid versions of the method are implemented and their effectiveness is demonstrated on an application arising in electrical impedance tomography (EIT). The project is joint with Jennifer Mueller, Colorado State University, Fort Collins, USA, and Samuli Siltanen, GE Healthcare, Finland.