Numerical solution method for the dbar-equation in the plane

A fast method for solving ∂̄-equations of the form ∂̄v=Tv is presented, where v and T are complex-valued functions of two real variables. The multigrid method of Vainikko [Int. Soc. Anal. Appl. Comput. 5 (2000)] is adapted to the problem with a FFT implementation. Convergence with rate O(h) is proved for the method applied to equations of the form above. 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).