Michael Lukaschewitsch et al 2003 Inverse Problems 19 585 doi:10.1088/0266-5611/19/3/308
Michael Lukaschewitsch1, Peter Maass2 and Michael Pidcock3
Show affiliationsThe mathematical analysis of geoelectric applications leads to the inverse problem of electric impedance tomography on unbounded domains. We introduce appropriate function spaces for this setting and discuss the analytic properties of the related forward operator on unbounded domains with Lipschitz boundaries. For the numerical approximation we consider Tikhonov regularization for a finite number of measurements. The main theorem states that this yields an approximation process which converges with an optimal rate to a minimum norm solution. Finally, numerical results in two and three dimensions, which are obtained from simulated, noisy data, confirm the theoretical findings.
91.25.-r Geomagnetism and paleomagnetism; geoelectricity
02.60.Cb Numerical simulation; solution of equations
02.30.Mv Approximations and expansions
02.60.Lj Ordinary and partial differential equations; boundary value problems
65N12 Stability and convergence of numerical methods
41A25 Rate of convergence, degree of approximation
86A25 Geo-electricity and geomagnetism (See also 76W05, 78A25)
Issue 3 (June 2003)
Received 18 October 2002, in final form 18 February 2003
Published 4 April 2003
Michael Lukaschewitsch et al 2003 Inverse Problems 19 585
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