Stochastic domain decomposition for the solution of the two-dimensional magnetotelluric problem

TL;DR

This paper introduces a stochastic domain decomposition method using Monte-Carlo techniques and meshless solvers to efficiently solve 2D magnetotelluric Maxwell's equations across subdivided sub-domains.

Contribution

It presents a novel stochastic domain decomposition approach combining Monte-Carlo evaluation with meshless methods for magnetotelluric problems.

Findings

Successfully applied to classical magnetotelluric problems

Demonstrated effectiveness in quarter-space, block-in-half-space, and triangle-in-half-space cases

Offers a new computational framework for 2D electromagnetic modeling

Abstract

Stochastic domain decomposition is proposed as a novel method for solving the two-dimensional Maxwell's equations as used in the magnetotelluric method. The stochastic form of the exact solution of Maxwell's equations is evaluated using Monte-Carlo methods taking into consideration that the domain may be divided into neighboring sub-domains. These sub-domains can be naturally chosen by splitting the sub-surface domain into regions of constant (or at least continuous) conductivity. The solution over each sub-domain is obtained by solving Maxwell's equations in the strong form. The sub-domain solver used for this purpose is a meshless method resting on radial basis function based finite differences. The method is demonstrated by solving a number of classical magnetotelluric problems, including the quarter-space problem, the block-in-half-space problem and the triangle-in-half-space problem.