# Magneto Static - Integral Method : principles

## Introduction

Since its version 2020, Flux provides an alternative application for simulating devices under Magnetostatic conditions. This approach is based on the Volume Integral Method (VIM) [1], which is known to be advantageous in the case of specific problems, such as devices immersed in unbounded, inactive (i.e., source-free) volume regions such as air or vacuum.

A key aspect of the Volume Integral Method is that it does not require representing or meshing the air around the modeled device nor imposing a boundary condition at infinity. Consequently, the Infinite Box typically used in the classical Finite Element Method (FEM) applications of Flux is not required in projects based upon this integral method. It also follows from this feature of the method that Flux does not have to re-mesh the air regions in VIM projects containing moving parts (Mechanical Sets) at each computation step. Thus, significant improvements in computation time may be observed under such conditions.

When compared to the FEM, the VIM generally provides accurate Magnetostatic solutions using relatively coarser meshes. On the other hand, the VIM approach leads to the assembly and resolution of a non-sparse system of equations, which require efficient management of the numerical memory and specialized solvers. These techniques are conveniently implemented in Flux: a user familiar with the classical Magnetostatic FEM application will not notice any significant change in the workflow.

Typical devices that can be efficiently modeled with the VIM-based approach in Flux include electromagnetic sensors and other similar devices. Rotating electric machinery and other electromagnetic devices characterized by narrow air-gaps and closed magnetic circuits are not among the recommended applications.

## How to use it

This application is available in Beta mode for Flux3D. This user mode must be activated in Flux Supervisor, before creating a new project, as follows:

- In Flux Supervisor, click “Options”;
- In the “Options” window, choose “User Mode” among the “System” configurations;
- Change the mode from “Standard” to “Beta” and click OK to complete the modification.

The user must create a new Flux3D project from scratch in order to safely use this feature. Destroying a classical application in an existing Flux3D project and replacing it with the Magnetostatic VIM application is highly inadvisable.

## Recommendations

As already mentioned, this feature is available in Beta mode only. Therefore, the following recommendations and remarks should also be considered while creating a project based on the Magnetostatic VIM application:

- The application must be assigned to the project before meshing the geometry;
- The project must contain only volume regions;
- Differently from the classical FEM applications in Flux, no action such as creating an Infinite Box or assigning boundary conditions is required to model an unbounded domain. The user must not describe air regions surrounding the active parts of the device nor include symmetries or periodicities in his project.
- After the solution and while in post-processing, the local quantities evaluated by Flux (e.g., magnetic flux density) are constant per element.
- The numerical solver used in the Magnetostatic VIM application is external to other Flux processes. Thus, the solver will use the memory available at solving time, as in the case of the MuMPS solver. Therefore, the user needs to reduce the memory assigned to Flux3D in Flux Supervisor to maximize the amount of memory available for numerical solution.

## References

[1] : V. Le-Van, G. Meunier, O. Chadebec and J.-M. Guichon, «A Volume Integral
Formulation Based on Facet Elements for Nonlinear Magnetostatic Problems,» *IEEE
Transactions on Magnetics, *vol. 51, n° 17, July 2015.