A Schwarz Method for the Magnetotelluric Approximation of Maxwell's equations
This work provides a convergent domain decomposition method for a specific geophysical simulation problem, but is incremental as it adapts existing Schwarz methods to a new equation.
The authors propose a classical Schwarz method for solving the magnetotelluric approximation of Maxwell's equations, prove its convergence using maximum principle techniques, and validate with numerical experiments.
The magnetotelluric approximation of the Maxwell's equations is used to model the propagation of low frequency electro-magnetic waves in the Earth's subsurface, with the purpose of reconstructing the presence of mineral or oil deposits. We propose a classical Schwarz method for solving this magnetotelluric approximation of the Maxwell equations, and prove its convergence using maximum principle techniques. This is not trivial, since solutions are complex valued, and we need a new result that the magnetotelluric approximations satisfy a maximum modulus principle for our proof. We illustrate our analysis with numerical experiments.