Numerical solution method for the dbar-equation in the plane

Authors:
K. Knudsen;J. Mueller;S. Siltanen
Affiliations:
Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, DK-9220 Aalborg Ø, Denmark;Department of Mathematics, Colorado State University, Fort Collins, CO;Instrumentarium Corporation, Finland and Department of Mathematics, Gunma University, Tenjin-cho 1-5-1, 376-8515 Kiryu, Japan
Venue:
Journal of Computational Physics
Year:
2004

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Abstract

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).