A Schwarz method for the magnetotelluric approximation of Maxwell's equations

DOI10.1007/978-3-030-56750-7_48zbMath1502.65243arXiv1903.03813OpenAlexW3173225447MaRDI QIDQ2100380

Martin J. Gander, Fabrizio Donzelli, Ronald D. Haynes

Publication date: 21 November 2022

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/1903.03813

zbMATH Keywords

Maxwell's equations geomagnetism Schwarz method geoelectricity magnetotelluric approximation

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) PDEs in connection with optics and electromagnetic theory (35Q60) Maximum principles in context of PDEs (35B50) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Parallel numerical computation (65Y05) Technical applications of optics and electromagnetic theory (78A55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Electromagnetic theory (general) (78A25) Geo-electricity and geomagnetism (86A25) PDEs in connection with geophysics (35Q86) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)