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Classically transmission conditions between subdomains are optimized for asimplified two subdomain decomposition to obtain optimized Schwarz methods formany subdomains. We investigate here if such a simplified optimization sufficesfor the magnetotelluric approximation of Maxwell's equation which leads to acomplex diffusion problem. We start with a direct analysis for 2 and 3subdomains, and present asymptotically optimized transmission conditions ineach case. We then optimize transmission conditions numerically for 4, 5 and 6subdomains and observe the same asymptotic behavior of optimized transmissionconditions. We finally use the technique of limiting spectra to optimize for avery large number of subdomains in a strip decomposition. Our analysis showsthat the asymptotically best choice of transmission conditions is the same inall these situations, only the constants differ slightly. It is thereforeenough for such diffusive type approximations of Maxwell's equations, whichinclude the special case of the Laplace and screened Laplace equation, tooptimize transmission parameters in the simplified two subdomain decompositionsetting to obtain good transmission conditions for optimized Schwarz methodsfor more general decompositions.

Optimizing transmission conditions for multiple subdomains in the Magnetotelluric Approximation of Maxwell's equations