An oversampling technique for the multiscale finite volume method to simulate electromagnetic responses in the frequency domain

TL;DR

This paper introduces an oversampling multiscale finite volume method for simulating electromagnetic responses in heterogeneous media, significantly reducing computational costs while maintaining accuracy in frequency domain Maxwell's equations.

Contribution

The paper develops a novel oversampling technique within the multiscale finite volume framework for efficient electromagnetic simulations in complex geophysical media.

Findings

Reduces computational time compared to traditional methods.

Maintains high accuracy in approximating fine-scale electromagnetic responses.

Demonstrated effectiveness on a synthetic 3D mineral deposit example.

Abstract

In order to reduce the computational cost of the simulation of electromagnetic responses in geophysical settings that involve highly heterogeneous media, we develop a multiscale finite volume method with oversampling for the quasi-static Maxwell's equations in the frequency domain. We assume a coarse mesh nested within a fine mesh that accurately discretizes the problem. For each coarse cell, we independently solve a local version of the original Maxwell's system subject to linear boundary conditions on an extended domain, which includes the coarse cell and a neighborhood of fine cells around it. The local Maxwell's system is solved using the fine mesh contained in the extended domain and the mimetic finite volume method. Next, these local solutions (basis functions) together with a weak-continuity condition are used to construct a coarse-mesh version of the global problem. The basis functions can be used to obtain the fine-mesh details from the solution of the coarse-mesh problem. Our approach leads to a significant reduction in the size of the final system of equations and the computational time, while accurately approximating the behavior of the fine-mesh solutions. We demonstrate the performance of our method using a synthetic 3D example of a mineral deposit.