# Multilevel Monte Carlo Simulation of the Eddy Current Problem With Random Parameters

## TL;DR

This paper applies the multilevel Monte Carlo method to an electromagnetism problem with random parameters, demonstrating variance reduction and cost distribution across different resolution levels.

## Contribution

It introduces the application of multilevel Monte Carlo to an electromagnetic problem with random parameters, highlighting cost efficiency and variance reduction.

## Key findings

- Main costs are concentrated on the coarsest level
- Variance is significantly reduced by the multilevel approach
- Method is effective for electromagnetism problems with uncertainties

## Abstract

The multilevel Monte Carlo method is applied to an academic example in the field of electromagnetism. The method exhibits a reduced variance by assigning the samples to multiple models with a varying spatial resolution. For the given example it is found that the main costs of the method are spent on the coarsest level.