# Algorithms of the Potential Field Calculation in a Three Dimensional Box

## TL;DR

This paper compares three methods for calculating the magnetic potential field inside a 3D box, assessing their accuracy and efficiency using artificial models with known solutions.

## Contribution

It provides a detailed analysis and comparison of three potential field calculation methods in a 3D box, highlighting their performance and accuracy.

## Key findings

- All three methods successfully compute the potential field.
- Performance varies depending on the method used.
- Accuracy is validated against known solutions.

## Abstract

Calculation of the potential field inside a three-dimensional box with the normal magnetic field component given on all boundaries is needed for estimation of important quantities related to the magnetic field such as free energy and relative helicity. In this work we present an analysis of three methods for calculating potential field inside a three-dimensional box. The accuracy and performance of the methods are tested on artificial models with a priori known solutions.