# A Schwarz Method for the Magnetotelluric Approximation of Maxwell's equations

## TL;DR

This paper introduces a Schwarz iterative method for solving the magnetotelluric approximation of Maxwell's equations, with proven convergence and numerical validation, aiding subsurface resource detection.

## Contribution

It develops a classical Schwarz method tailored for complex-valued magnetotelluric equations and proves its convergence using a novel maximum modulus principle.

## Key findings

- Convergence of the Schwarz method is established.
- Numerical experiments confirm the theoretical results.
- The approach effectively models electromagnetic wave propagation in Earth's subsurface.

## 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.